Stochastic optimization methods, such as genetic algorithms, search for the global minimum of the misfit function within a given parameter range and do not require any calculation of the gradients of the misfit surfaces. More importantly, these methods collect a series of models and associated likelihoods that can be used to estimate the posterior probability distribution. However, because genetic algorithms are not a Markov chain Monte Carlo method, the direct use of the genetic-algorithm-sampled models and their associated likelihoods produce a biased estimation of the posterior probability distribution. In contrast, Markov chain Monte Carlo methods, such as the Metropolis–Hastings and Gibbs sampler, provide accurate posterior probability distributions but at considerable computational cost. In this paper, we use a hybrid method that combines the speed of a genetic algorithm to find an optimal solution and the accuracy of a Gibbs sampler to obtain a reliable estimation of the posterior probability distributions. First, we test this method on an analytical function and show that the genetic algorithm method cannot recover the true probability distributions and that it tends to underestimate the true uncertainties. Conversely, combining the genetic algorithm optimization with a Gibbs sampler step enables us to recover the true posterior probability distributions. Then, we demonstrate the applicability of this hybrid method by performing one-dimensional elastic full-waveform inversions on synthetic and field data. We also discuss how an appropriate genetic algorithm implementation is essential to attenuate the “genetic drift” effect and to maximize the exploration of the model space. In fact, a wide and efficient exploration of the model space is important not only to avoid entrapment in local minima during the genetic algorithm optimization but also to ensure a reliable estimation of the posterior probability distributions in the subsequent Gibbs sampler step.

In this paper, we introduce a new method of geophysical data interpretation based on simultaneous analysis of images and sounds. The final objective is to expand the interpretation workflow through multimodal (visual–audio) perception of the same information. We show how seismic data can be effectively converted into standard formats commonly used in digital music. This conversion of geophysical data into the musical domain can be done by applying appropriate time–frequency transforms. Using real data, we demonstrate that the Stockwell transform provides a very accurate and reliable conversion. Once converted into musical files, geophysical datasets can be played and interpreted by using modern computer music tools, such as sequencers. This approach is complementary and not substitutive of interpretation methods based on imaging. It can be applied not only to seismic data but also to well logs and any type of geophysical time/depth series. To show the practical implications of our integrated visual–audio method of interpretation, we discuss an application to a real seismic dataset in correspondence of an important hydrocarbon discovery.

The output from the hydraulic vibrators typically used for land seismic surveys is controlled by monitoring the acceleration measured by accelerometers mounted on the reaction mass and baseplate. The considerable energy output by such vibrators, which are coupled with the sensitivity of the accelerometers used, results in crosstalk if more than one vibrator is being used. In this paper, we present the results of a field experiment in which we measured the crosstalk between two adjacent vibrators. We found that the level of crosstalk was approximately -20 dB when the vibrators were adjacent but decreased with increasing frequency and separation. This result has implications for measurements of vibrator performance, source-signature deconvolution, and in particular, estimates of the total energy output by a fleet of vibrators.

Time-lapse refraction can provide complementary seismic solutions for monitoring subtle subsurface changes that are challenging for conventional P-wave reflection methods. The utilization of refraction time lapse has lagged behind in the past partly due to the lack of robust techniques that allow extracting easy-to-interpret reservoir information. However, with the recent emergence of the full-waveform inversion technique as a more standard tool, we find it to be a promising platform for incorporating head waves and diving waves into the time-lapse framework. Here we investigate the sensitivity of 2D acoustic, time-domain, full-waveform inversion for monitoring a shallow, weak velocity change (−30 m/s, or −1.6%). The sensitivity tests are designed to address questions related to the feasibility and accuracy of full-waveform inversion results for monitoring the field case of an underground gas blowout that occurred in the North Sea. The blowout caused the gas to migrate both vertically and horizontally into several shallow sand layers. Some of the shallow gas anomalies were not clearly detected by conventional 4D reflection methods (i.e., time shifts and amplitude difference) due to low 4D signal-to-noise ratio and weak velocity change. On the other hand, full-waveform inversion sensitivity analysis showed that it is possible to detect the weak velocity change with the non-optimal seismic input. Detectability was qualitative with variable degrees of accuracy depending on different inversion parameters. We inverted, the real 2D seismic data from the North Sea with a greater emphasis on refracted and diving waves’ energy (i.e., most of the reflected energy was removed for the shallow zone of interest after removing traces with offset less than 300 m). The full-waveform inversion results provided more superior detectability compared with the conventional 4D stacked reflection difference method for a weak shallow gas anomaly (320 m deep).

Surface removal and internal multiple removal are explained by recursively separating the primary and multiple responses at each depth level with the aid of wavefield prediction error filtering. This causal removal process is referred to as “data linearization.” The linearized output (primaries only) is suitable for linear migration algorithms. Next, a summary is given on the migration of full wavefields (primaries + multiples) by using the concept of secondary sources in each subsurface gridpoint. These secondary sources are two-way and contain the gridpoint reflection and the gridpoint transmission properties. In full wavefield migration, a local inversion process replaces the traditional linear imaging conditions. Finally, Marchenko redatuming is explained by iteratively separating the full wavefield response from above a new datum and the full wavefield response from below a new datum. The redatuming output is available for linear migration (Marchenko imaging) or, even better, for full wavefield migration. Linear migration, full wavefield migration, and Marchenko imaging are compared with each other. The principal conclusion of this essay is that multiples should not be removed, but they should be utilized, yielding two major advantages: (i) illumination is enhanced, particularly in the situation of low signal-to-noise primaries; and (ii) both the upper side and the lower side of reflectors are imaged. It is also concluded that multiple scattering algorithms are more transparent if they are formulated in a recursive depth manner. In addition to transparency, a recursive depth algorithm has the flexibility to enrich the imaging process by inserting prior geological knowledge or by removing numerical artefacts at each depth level. Finally, it is concluded that nonlinear migration algorithms must have a closed-loop architecture to allow successful imaging of incomplete seismic data volumes (reality of field data).

Modern regional airborne magnetic datasets, when acquired in populated areas, are inevitably degraded by cultural interference. In the United Kingdom context, the spatial densities of interfering structures and their complex spatial form severely limit our ability to successfully process and interpret the data. Deculturing procedures previously adopted have used semi-automatic methods that incorporate additional geographical databases that guide manual assessment and refinement of the acquired database. Here we present an improved component of that procedure that guides the detection of localized responses associated with non-geological perturbations. The procedure derives from a well-established technique for the detection of kimberlite pipes and is a form of moving-window correlation using grid-based data. The procedure lends itself to automatic removal of perturbed data, although manual intervention to accept/reject outputs of the procedure is wise. The technique is evaluated using recently acquired regional United Kingdom survey data, which benefits from having an offshore component and areas of largely non-magnetic granitic response. The methodology is effective at identifying (and hence removing) the isolated perturbations that form a persistent spatial noise background to the entire dataset. Probably in common with all such methods, the technique fails to isolate and remove amalgamated responses due to complex superimposed effects. The procedure forms an improved component of partial automation in the context of a wider deculturing procedure applied to United Kingdom aeromagnetic data.

The time-invariant gain-limit-constrained inverse *Q*-filter can control the numerical instability of the inverse *Q*-filter, but it often suppresses the high frequencies at later times and reduces the seismic resolution. To improve the seismic resolution and obtain high-quality seismic data, we propose a self-adaptive approach to optimize the *Q* value for the inverse *Q*-filter amplitude compensation. The optimized *Q* value is self-adaptive to the cutoff frequency of the effective frequency band for the seismic data, the gain limit of the inverse *Q*-filter amplitude compensation, the inverse *Q*-filter amplitude compensation function, and the medium quality factor. In the processing of the inverse *Q*-filter amplitude compensation, the optimized *Q* value, corresponding gain limit, and amplitude compensation function are used simultaneously; then, the energy in the effective frequency band for the seismic data can be recovered, and the seismic resolution can be enhanced at all times. Furthermore, the small gain limit or time-variant bandpass filter after the inverse *Q*-filter amplitude compensation is considered to control the signal-to-noise ratio, and the time-variant bandpass filter is based on the cutoff frequency of the effective frequency band for the seismic data. Synthetic and real data examples demonstrate that the self-adaptive approach for *Q* value optimization is efficient, and the inverse *Q*-filter amplitude compensation with the optimized *Q* value produces high-resolution and low-noise seismic data.

Microplasticity manifestations caused by acoustical wave in the frequency range of about 4.5 kHz–7.0 kHz are detected in consolidated artificial sandstone. Equipment was tested by means of comparison of data obtained for a standard material (aluminium) and sandstone. Microplasticity manifestations in acoustic records are present in the form of the ladder-like changes in the amplitude course. The stress plateaus in the acoustic trace interrupt the amplitude course, transform the wavefront, and shift the arrival time along the time axis. Microplasticity contribution to the acoustic record changes with the increase in the strain amplitude value. The combined elastic–microplastic process conditions the wavefront steepness and its duration. Stress plateaus exert influence on the waveform and, accordingly, on pulse frequency response. These results confirm the earlier data obtained for weakly consolidated rock. This contribution to wave propagation physics can be useful in solving applied problems, as, for instance, the reservoir properties prediction by means of wave attenuation in acoustic logging and seismic prospecting.

We present a novel approach to automated volume extraction in seismic data and apply it to the detection of allochthonous salt bodies. Using a genetic algorithm, we determine the optimal size of volume elements that statistically, according to the *U*-test, best characterize the contrast between the textures inside and outside of the salt bodies through a principal component analysis approach. This information was used to implement a seeded region growing algorithm to directly extract the bodies from the cube of seismic amplitudes. We present the resulting three-dimensional bodies and compare our final results to those of an interpreter, showing encouraging results.

A new azimuthal acoustic receiver sonde with a body and corresponding circuits was designed for a downhole tool. The 64-sensor receiver sonde holds eight receiver stations that can be combined into at least 64 three-sensor receiver subarrays. As a result, the receiver sonde can use different sensor combinations instead of different transducer types to produce multiple modes, including a phased azimuthal reception mode and conventional monopole, dipole, and quadruple modes. Laboratory measurements were conducted to study the performance of the azimuthal acoustic receiver sonde for a downhole tool, and the experimental results indicate that the receiver sonde provides a consistent reception performance. Individual sensors receive similar time-domain waveforms, and their corresponding frequency bands and sensitivities are consistent within the measurement errors of around 5%. The direction of the reception main lobe is approximately parallel to its exterior normal direction. In addition, a receiver subarray with three sensors receives waveforms that have higher energy and narrower beamwidths. For individual sensors, the angular width of the dominant reception lobe is 191.3^{°} on average, whereas that of the individual receiver subarrays is approximately 52.1^{°} on average. The amplitude of the first arrival received by the receiver subarray centred at the primary sensor directly pointing to the source is approximately 2.2 times the average amplitude of the first arrivals received by the other receiver subarrays in the same receiver station. Thus, the maximum amplitude of the waveforms received by the receiver subarrays can be used to determine the direction of the incident waves. This approach represents a promising method for determining the reflector azimuth for acoustic reflection logging and three-dimensional acoustic logging.

A novel, fast, and approximate forward modelling routine for time-domain electromagnetic responses is presented. It is based on the separation of the forward problem into a configuration-independent part, mapping conductivity as a function of depth onto apparent conductivity as a function of time, and a configuration-dependent part, i.e., the half-space step response. The response of a layered model is then found as the half-space response for a half-space conductivity equal to the apparent conductivity. The mapping is ten times faster than traditional accurate forward modelling routines, and through stochastic modelling, it is found that the standard deviation of the modelling error is 0.7 %. The forward mapping lends itself to integration in a modern state-of-the-art inversion formulation in exactly the same way as traditionally computed responses, and a field example is included where inversion results using the approximate forward response are compared with those of an accurate forward response for helicopterborne transient electromagnetic data. In addition to being used in its own right in inversion of transient data, the speed and accuracy of the approximate inversion mean that it is well suited for quality control and fast turnaround data delivery of survey results to a client. It can also be used in hybrid inversion formulations by supplying initial iterations and high-quality derivatives in an inversion based on accurate forward modelling.

In many cases, seismic measurements are coarsely sampled in at least one dimension. This leads to aliasing artefacts and therefore to problems in the subsequent processing steps. To avoid this, seismic data reconstruction can be applied in advance. The success and reliability of reconstruction methods are dependent on the assumptions they make on the data. In many cases, wavefields are assumed to (locally) have a linear space–time behaviour. However, field data are usually complex, with strongly curved events. Therefore, in this paper, we propose the double focal transformation as an efficient way for complex data reconstruction. Hereby, wavefield propagation is formulated as a transformation, where one-way propagation operators are used as its basis functions. These wavefield operators can be based on a macro velocity model, which allows our method to use prior information in order to make the data decomposition more effective. The basic principle of the double focal transformation is to focus seismic energy along source and receiver coordinates simultaneously. The seismic data are represented by a number of localized events in the focal domain, whereas aliasing noise spreads out. By imposing a sparse solution in the focal domain, aliasing noise is suppressed, and data reconstruction beyond aliasing is achieved. To facilitate the process, only a few effective depth levels need to be included, preferably along the major boundaries in the data, from which the propagation operators can be calculated. Results on 2D and 3D synthetic data illustrate the method's virtues. Furthermore, seismic data reconstruction on a 2D field dataset with gaps and aliased source spacing demonstrates the strength of the double focal transformation, particularly for near-offset reflections with strong curvature and for diffractions.

We propose a fast method for imaging potential field sources. The new method is a variant of the “Depth from Extreme Points,” which yields an image of a quantity proportional to the source distribution (magnetization or density). Such transformed field is here transformed into source-density units by determining a constant with adequate physical dimension by a linear regression of the observed field versus the field computed from the “Depth from Extreme Points” image. Such source images are often smooth and too extended, reflecting the loss of spatial resolution for increasing altitudes. Consequently, they also present too low values of the source density. We here show that this initial image can be improved and made more compact to achieve a more realistic model, which reproduces a field consistent with the observed one. The new algorithm, which is called “Compact Depth from Extreme Points” iteratively produces different source distributions models, with an increasing degree of compactness and, correspondingly, increasing source-density values. This is done through weighting the model with a compacting function. The compacting function may be conveniently expressed as a matrix that is modified at any iteration, based on the model obtained in the previous step. At any iteration step the process may be stopped when the density reaches values higher than prefixed bounds based on known or assumed geological information. As no matrix inversion is needed, the method is fast and allows analysing massive datasets. Due to the high stability of the “Depth from Extreme Points” transformation, the algorithm may be also applied to any derivatives of the measured field, thus yielding an improved resolution. The method is investigated by application to 2D and 3D synthetic gravity source distributions, and the imaged sources are a good reconstruction of the geometry and density distributions of the causative bodies. Finally, the method is applied to microgravity data to model underground crypts in St. Venceslas Church, Tovacov, Czech Republic.

Hydrocarbon prediction from seismic amplitude and amplitude-versus-offset is a daunting task. Amplitude interpretation is ambiguous due to the effects of lithology and pore fluid. In this paper, we propose a new attribute “*J*” based on a Gassmann–Biot fluid substitution to reduce ambiguity. Constrained by seismic and rock physics, the *J* attribute has good ability to detect hydrocarbons from seismic data. There are currently many attributes for hydrocarbon prediction. Among the existing attributes, far-minus-near times far and fluid factor are commonly used. In this paper, the effectiveness of these two existing attributes was compared with the new attribute. Numerical modelling was used to test the new attribute “*J*” and to compare “*J*” with the two existing attributes. The results showed that the *J* attribute can predict the existence of hydrocarbon in different porosity scenarios with less ambiguity than the other two attributes. Tests conducted with real seismic data demonstrated the effectiveness of the *J* attribute. The *J* attribute has performed well in scenarios in which the other two attributes gave inaccurate predictions. The proposed attribute “*J*” is fast and simple, and it could be used as a first step in hydrocarbon analysis for exploration.

An alternative laboratory technique to measure the elastic constants of solid samples, based on the analysis of the cross-correlation spectra of the vibratory response of randomly excited short solid cylinders, has been recently proposed. The aim of this paper is to check the ability of the technique called passive ultrasonic interferometry to monitor fluid substitution in different rock samples. Velocity variations due to fluid substitution are easily measured if the wave attenuation in the fluid-saturated rock is not too large (typically in rocks with few cracks or microfractures).

The experimental results are in agreement with the predictions of Biot–Gassmann poroelastic theory. The effect of substituting water with a stiffer saturating fluid, such as ethylene glycol, is to increase the overall bulk modulus of the rock, without any substantial effect on shear modulus. Furthermore, the experimental results compare well with those obtained independently with conventional pulse-transmission technique using ultrasonic transducers. However, the measured pulse-transmission bulk moduli are slightly larger than the corresponding measured ultrasonic interferometry moduli, with the deviation increasing with increasing fluid viscosity. This can be explained by dispersion due to wave-induced flow of the viscous fluid since pulse-transmission experiments involve higher frequencies than ultrasonic interferometry experiments.

Reflection tomography is the industry standard tool for velocity model building, but it is also an ill-posed inverse problem as its solution is not unique. The usual way to obtain an acceptable result is to regularize tomography by feeding the inversion with some *a priori* information. The simplest regularization forces the solution to be smooth, implicitly assuming that seismic velocity exhibits some degree of spatial correlation. However, velocity is a rock property; thus, the geometry and structure of rock formations should drive correlation in velocity depth models. This observation calls for constraints driven by geological models.

In this work, we present a set of structural constraints that feed reflection tomography with geometrical information. These constraints impose the desired characteristics (flatness, shape, position, etc.) on imaged reflectors but act on the velocity update. Failure to respect the constraints indicates either velocity inaccuracies or wrong assumptions concerning the constraints.

Reflection tomography with structural constraints is a flexible framework that can be specialized in order to achieve different goals: among others, to flatten the base of salt bodies or detachment surfaces, to recover the horizontalness of oil–water contacts, or to impose the co-location of the same imaged horizon between PP and PS images.

The straightforward application of structural constraints is that of regularizing tomography through geological information, particularly at the latest stages of the depth imaging workflow, when the depth migration structural setting reached a consistent geological interpretation. Structural constraints are also useful in minimizing the well-to-seismic mis-ties. Moreover, they can be used as a tool to check the consistency of interpreters' hypothesis with seismic data. Indeed, inversion with structural constraints will preserve image focusing only if the interpreters' insights are consistent with the data.

Results from synthetic and real data demonstrate the effectiveness of reflection tomography with structural constraints.

CO_{2} geosequestration is an efficient way to reduce greenhouse gas emissions into the atmosphere. Carbonate rock formations are one of the possible targets for CO_{2} sequestration due to their relative abundance and ability to serve as a natural trapping reservoir. The injected supercritical CO_{2} can change properties of the reservoir rocks such as porosity, permeability, tortuosity, and specific surface area due to dissolution and precipitation processes. This, in turn, affects the reservoir characteristics, i.e., their elastic properties, storage capacity, stability, etc.

The tremendous progresses made recently in both microcomputed X-ray tomography and high-performance computing make numerical simulation of physical processes on actual rock microstructures feasible. However, carbonate rocks with their extremely complex microstructure and the presence of microporosity that is below the resolution of microcomputed X-ray tomography scanners require novel, quite specific image processing and numerical simulation approaches.

In the current work, we studied the effects of supercritical CO_{2} injection on microstructure and elastic properties of a Savonnières limestone. We used microtomographic images of two Savonnières samples, i.e., one in its natural state and one after injection and residence of supercritical CO_{2}. A statistical analysis of the microtomographic images showed that the injection of supercritical CO_{2} led to an increase in porosity and changes of the microstructure, i.e., increase of the average volume of individual pores and decrease in the total number of pores. The CO_{2} injection/residence also led to an increase in the mean radii of pore throats, an increase in the length of pore network segments, and made the orientation distribution of mesopores more isotropic. Numerical simulations showed that elastic moduli for the sample subjected to supercritical CO_{2} injection/residence are lower than those for the intact sample.

Least-squares reverse time migration provides better imaging result than conventional reverse time migration by reducing the migration artefacts, improving the resolution of the image and balancing the amplitudes of the reflectors. However, it is computationally intensive. To reduce its computational cost, we propose an efficient amplitude encoding least-squares reverse time migration scheme in the time domain. Although the encoding scheme is effective in increasing the computational efficiency, it also introduces the well-known crosstalk noise in the gradient that degrades the quality of the imaging result. We analyse the cause of the crosstalk noise using an encoding correlation matrix and then develop two numerical schemes to suppress the crosstalk noise during the inversion process. We test the proposed method with synthetic and field data. Numerical examples show that the proposed scheme can provide better imaging result than reverse time migration, and it also generates images comparable with those from common shot least-squares reverse time migration but with less computational cost.

Igneous intrusions, notably carbonatitic–alkalic intrusions, peralkaline intrusions, and pegmatites, represent significant sources of rare-earth metals. Geophysical exploration for and of such intrusions has met with considerable success. Examples of the application of the gravity, magnetic, and radiometric methods in the search for rare metals are presented and described. Ground gravity surveys defining small positive gravity anomalies helped outline the shape and depth of the Nechalacho (formerly Lake) deposit within the Blatchford Lake alkaline complex, Northwest Territories, and of spodumene-rich mineralization associated with the Tanco deposit, Manitoba, within the hosting Tanco pegmatite. Based on density considerations, the bastnaesite-bearing main ore body within the Mountain Pass carbonatite, California, should produce a gravity high similar in amplitude to those associated with the Nechalacho and Tanco deposits. Gravity also has utility in modelling hosting carbonatite intrusions, such as the Mount Weld intrusion, Western Australia, and Elk Creek intrusion, Nebraska.

The magnetic method is probably the most successful geophysical technique for locating carbonatitic–alkalic host intrusions, which are typically characterized by intense positive, circular to sub-circular, crescentic, or annular anomalies. Intrusions found by this technique include the Mount Weld carbonatite and the Misery Lake alkali complex, Quebec. Two potential carbonatitic–alkalic intrusions are proposed in the Grenville Province of Eastern Quebec, where application of an automatic technique to locate circular magnetic anomalies identified several examples. Two in particular displayed strong similarities in magnetic pattern to anomalies accompanying known carbonatitic or alkalic intrusions hosting rare-metal mineralization and are proposed to have a similar origin.

Discovery of carbonatitic–alkalic hosts of rare metals has also been achieved by the radiometric method. The Thor Lake group of rare-earth metal deposits, which includes the Nechalacho deposit, were found by follow-up investigations of strong equivalent thorium and uranium peaks defined by an airborne survey. Prominent linear radiometric anomalies associated with glacial till in the Canadian Shield have provided vectors based on ice flow directions to source intrusions. The Allan Lake carbonatite in the Grenville Province of Ontario is one such intrusion found by this method. Although not discovered by its radiometric characteristics, the Strange Lake alkali intrusion on the Quebec–Labrador border is associated with prominent linear thorium and uranium anomalies extending at least 50 km down ice from the intrusion. Radiometric exploration of rare metals hosted by pegmatites is evaluated through examination of radiometric signatures of peraluminous pegmatitic granites in the area of the Tanco pegmatite.

Geoelectrical and induced polarization data from measurements along three profiles and from one 3D survey are acquired and processed in the central Skellefte District, northern Sweden. The data were collected during two field campaigns in 2009 and 2010 in order to delineate the structures related to volcanogenic massive sulphide deposits and to model lithological contacts down to a maximum depth of 1.5 km. The 2009 data were inverted previously, and their joint interpretation with potential field data indicated several anomalous zones. The 2010 data not only provide additional information from greater depths compared with the 2009 data but also cover a larger surface area. Several high-chargeability low-resistivity zones, interpreted as possible massive sulphide mineralization and associated hydrothermal alteration, are revealed. The 3D survey data provide a detailed high-resolution image of the top ∼450 m of the upper crust around the Maurliden East, North, and Central deposits. Several anomalies are interpreted as new potential prospects in the Maurliden area, which are mainly concentrated in the central conductive zone. In addition, the contact relationship between the major geological units, e.g., the contact between the Skellefte Group and the Jörn Intrusive Complex, is better understood with the help of 2010 deep-resistivity/chargeability data. The bottommost part of the Vargfors basin is imaged using the 2010 geoelectrical and induced polarization data down to ∼1-km depth.

Three-dimensional seismic survey design should provide an acquisition geometry that enables imaging and amplitude-versus-offset applications of target reflectors with sufficient data quality under given economical and operational constraints. However, in land or shallow-water environments, surface waves are often dominant in the seismic data. The effectiveness of surface-wave separation or attenuation significantly affects the quality of the final result. Therefore, the need for surface-wave attenuation imposes additional constraints on the acquisition geometry. Recently, we have proposed a method for surface-wave attenuation that can better deal with aliased seismic data than classic methods such as slowness/velocity-based filtering. Here, we investigate how surface-wave attenuation affects the selection of survey parameters and the resulting data quality. To quantify the latter, we introduce a measure that represents the estimated signal-to-noise ratio between the desired subsurface signal and the surface waves that are deemed to be noise. In a case study, we applied surface-wave attenuation and signal-to-noise ratio estimation to several data sets with different survey parameters. The spatial sampling intervals of the basic subset are the survey parameters that affect the performance of surface-wave attenuation methods the most. Finer spatial sampling will reduce aliasing and make surface-wave attenuation easier, resulting in better data quality until no further improvement is obtained. We observed this behaviour as a main trend that levels off at increasingly denser sampling. With our method, this trend curve lies at a considerably higher signal-to-noise ratio than with a classic filtering method. This means that we can obtain a much better data quality for given survey effort or the same data quality as with a conventional method at a lower cost.

Microplasticity manifestations caused by acoustic wave in the frequency range of about 4.5 kHz–7.0 kHz are detected in consolidated artificial sandstone. Equipment was tested by means of comparison of data obtained for a standard material (aluminium) and sandstone. Microplasticity manifestations in acoustic records are present in the form of ladder-like changes in the amplitude course. The stress plateaus in the acoustic trace interrupt the amplitude course, transform the wavefront, and shift the arrival time along the time axis. Microplasticity contribution to the acoustic record changes with the increase in the strain amplitude value. The combined elastic–microplastic process conditions the wavefront steepness and its duration. Stress plateaus exert influence on the waveform and, accordingly, on pulse frequency response. These results confirm the earlier data obtained for weakly consolidated rock. This contribution to wave propagation physics can be useful in solving applied problems in material science, seismic prospecting, diagnostics, etc.

Microseismic monitoring in the oil and gas industry commonly uses migration-based methods to locate very weak microseismic events. The objective of this study is to compare the most popular migration-based methods on a synthetic dataset that simulates a strike-slip source mechanism event with a low signal-to-noise ratio recorded by surface receivers (vertical components). The results show the significance of accounting for the known source mechanism in the event detection and location procedures. For detection and location without such a correction, the ability to detect weak events is reduced. We show both numerically and theoretically that neglecting the source mechanism by using only absolute values of the amplitudes reduces noise suppression during stacking and, consequently, limits the possibility to retrieve weak microseismic events. On the other hand, even a simple correction to the data polarization used with otherwise ineffective methods can significantly improve detections and locations. A simple stacking of the data with a polarization correction provided clear event detection and location, but even better results were obtained for those data combined with methods that are based on semblance and cross-correlation.

In anisotropic media, several parameters govern the propagation of the compressional waves. To correctly invert surface recorded seismic data in anisotropic media, a multi-parameter inversion is required. However, a tradeoff between parameters exists because several models can explain the same dataset. To understand these tradeoffs, diffraction/reflection and transmission-type sensitivity-kernels analyses are carried out. Such analyses can help us to choose the appropriate parameterization for inversion. In tomography, the sensitivity kernels represent the effect of a parameter along the wave path between a source and a receiver. At a given illumination angle, similarities between sensitivity kernels highlight the tradeoff between the parameters. To discuss the parameterization choice in the context of finite-frequency tomography, we compute the sensitivity kernels of the instantaneous traveltimes derived from the seismic data traces. We consider the transmission case with no encounter of an interface between a source and a receiver; with surface seismic data, this corresponds to a diving wave path. We also consider the diffraction/reflection case when the wave path is formed by two parts: one from the source to a sub-surface point and the other from the sub-surface point to the receiver. We illustrate the different parameter sensitivities for an acoustic transversely isotropic medium with a vertical axis of symmetry. The sensitivity kernels depend on the parameterization choice. By comparing different parameterizations, we explain why the parameterization with the normal moveout velocity, the anellipitic parameter η, and the δ parameter is attractive when we invert diving and reflected events recorded in an active surface seismic experiment.

Multiple scattering is usually ignored in migration algorithms, although it is a genuine part of the physical reflection response. When properly included, multiples can add to the illumination of the subsurface, although their crosstalk effects are removed. Therefore, we introduce full-wavefield migration. It includes all multiples and transmission effects in deriving an image via an inversion approach. Since it tries to minimize the misfit between modeled and observed data, it may be considered a full waveform inversion process. However, full-wavefield migration involves a forward modelling process that uses the estimated seismic image (i.e., the reflectivities) to generate the modelled full wavefield response, whereas a smooth migration velocity model can be used to describe the propagation effects. This separation of modelling in terms of scattering and propagation is not easily achievable when finite-difference or finite-element modelling is used. By this separation, a more linear inversion problem is obtained. Moreover, during the forward modelling, the wavefields are computed separately in the incident and scattered directions, which allows the implementation of various imaging conditions, such as imaging reflectors from below, and avoids low-frequency image artefacts, such as typically observed during reverse-time migration. The full wavefield modelling process also has the flexibility to image directly the total data (i.e., primaries and multiples together) or the primaries and the multiples separately. Based on various numerical data examples for the 2D and 3D cases, the advantages of this methodology are demonstrated.

We derived the velocity and attenuation of a generalized Stoneley wave being a symmetric trapped mode of a layer filled with a Newtonian fluid and embedded into either a poroelastic or a purely elastic rock. The dispersion relation corresponding to a linearized Navier–Stokes equation in a fracture coupling to either Biot or elasticity equations in the rock via proper boundary conditions was rigorously derived. A cubic equation for wavenumber was found that provides a rather precise analytical approximation of the full dispersion relation, in the frequency range of 10^{−3} Hz to 10^{3} Hz and for layer width of less than 10 cm and fluid viscosity below 0.1 Pa· s [100 cP]. We compared our results to earlier results addressing viscous fluid in either porous rocks with a rigid matrix or in a purely elastic rock, and our formulae are found to better match the numerical solution, especially regarding attenuation. The computed attenuation was used to demonstrate detectability of fracture tip reflections at wellbore, for a range of fracture lengths and apertures, pulse frequencies, and fluid viscosity.

Distributed acoustic sensing is an emerging technology using fibre-optic cables to detect acoustic disturbances such as flow noise and seismic signals. The technology has been applied successfully in hydraulic fracture monitoring and vertical seismic profiling. One of the limitations of distributed acoustic sensing for seismic recording is that the conventional straight fibres do not have broadside sensitivity and therefore cannot be used in configurations where the raypaths are essentially orthogonal to the fibre-optic cable, such as seismic reflection methods from the surface. The helically wound cable was designed to have broadside sensitivity. In this paper, a field trial is described to validate in a qualitative sense the theoretically predicted angle-dependent response of a helically wound cable. P-waves were measured with a helically wound cable as a function of the angle of incidence in a shallow horizontal borehole and compared with measurements with a co-located streamer. The results show a similar behaviour as a function of the angle of incidence as the theory. This demonstrates the possibility of using distributed acoustic sensing with a helically wound cable as a seismic detection system with a horizontal cable near the surface. The helically wound cable does not have any active parts and can be made as a slim cable with a diameter of a few centimetres. For that reason, distributed acoustic sensing with a helically wound cable is a potential low-cost option for permanent seismic monitoring on land.

Until now, a simple formula to estimate the depth of investigation of the electrical resistivity method that takes into account the positions of all of the electrodes for a general four-electrode array has not been available. While the depth sensitivity function of the method for a homogeneous infinite half-space is well known, previous attempts to use it to characterize the depth of investigation have involved calculating its peak and median, both of which must be determined numerically for a general four-electrode array. I will show that the mean of the sensitivity function, which has not been considered previously, does admit a very simple mathematical formula. I compare the mean depth with the median and peak sensitivity depths for some common arrays. The mean is always greater than or equal to the median that is always greater than the peak. All three measures give reasonable estimates to the depths of actual structures for most circumstances. I will further show that, for 1D soundings, the use of the mean sensitivity depth as the pseudo-depth assigns an apparent resistivity to a given pseudo-depth that is consistent between different arrays. One consequence of this is that smoother depth soundings are obtained as “clutches,” caused by a change in the depth sensitivity due to moving the potential electrodes, are effectively removed. I expect that the mean depth formula will be a useful “rule of thumb” for estimating the depth of investigation before the resistivity structure of the ground is known.

Marine magnetotelluric measurements using “free-fall’’ instruments without effective compasses suffer from the problem of unknown orientation of the receivers at the seafloor. While past works indicate that marine magnetotelluric orientation of the instruments can be estimated by reference to land deployments of known orientation using the transfer tensor method, there is limited published information on how this is implemented in practice. We document this method and propose a set of new time- and frequency-domain approaches to solve this orientation problem of the seafloor receivers. We test these methodologies in onshore and offshore magnetotelluric data whose orientations are well known and apply these techniques to marine magnetotelluric data with unknown orientation. For the controlled tests, both time- and frequency-domain approaches produce overall comparable results. To investigate the effects of the subsurface structure distribution on the orientation process, a dimensionality analysis of a controlled dataset is carried out. In subsequent analysis using the available disoriented marine magnetotelluric data from offshore Brazil and from the Vassouras magnetic observatory on the mainland for remote referencing, frequency-domain methods yield approximate orientation angles among themselves with low standard deviation each. Time-domain results are consistent for most cases but differ from frequency-domain results for some situations.

We present an automatic method of processing microseismic data acquired at the surface by a star-like array. The back-projection approach allows successive determination of the hypocenter position of each event and of its focal mechanisms. One-component vertical geophone groups and three-component accelerometers are employed to monitor both P- and S-waves. Hypocenter coordinates are determined in a grid by back-projection stacking of the short-time-average-to-long-time-average ratio of absolute amplitudes at vertical components and polarization norm derived from horizontal components of the P- and S-waves, respectively. To make the location process more efficient, calculation is started with a coarse grid and zoomed to the optimum hypocenter using an oct-tree algorithm. The focal mechanism is then determined by stacking the vertical component seismograms corrected for the theoretical P-wave polarity of the focal mechanism. The mechanism is resolved in the coordinate space of strike, dip, and rake angles. The method is tested on 34 selected events of a dataset of hydraulic fracture monitoring of a shale gas play in North America. It was found that, by including S-waves, the vertical accuracy of locations improved by a factor of two and is equal to approximately the horizontal location error. A twofold enhancement of horizontal location accuracy is achieved if a denser array of geophone groups is used instead of the sparse array of three-component seismometers. The determined focal mechanisms are similar to those obtained by other methods applied to the same dataset.

Although there is no assumption of pore geometry in derivation of Gassmann's equation, the pore geometry is in close relation with hygroscopic water content and pore fluid communication between the micropores and the macropores. The hygroscopic water content in common reservoir rocks is small, and its effect on elastic properties is ignored in the Gassmann theory. However, the volume of hygroscopic water can be significant in shaly rocks or rocks made of fine particles; therefore, its effect on the elastic properties may be important. If the pore fluids in microspores cannot reach pressure equilibrium with the macropore system, assumption of the Gassmann theory is violated. Therefore, due to pore structure complexity, there may be a significant part of the pore fluids that do not satisfy the assumption of the Gassmann theory. We recommend that this part of pore fluids be accounted for within the solid rock frame and effective porosity be used in Gassmann's equation for fluid substitution. Integrated study of ultrasonic laboratory measurement data, petrographic data, mercury injection capillary pressure data, and nuclear magnetic resonance *T _{2}* data confirms rationality of using effective porosity for Gassmann fluid substitution. The effective porosity for Gassmann's equation should be frequency dependent. Knowing the pore geometry, if an empirical correlation between frequency and the threshold pore-throat radius or nuclear magnetic resonance

This article introduces an alternative experimental procedure for measuring the elastic properties of a solid material at laboratory scale, using both the principles of passive seismic interferometry and resonance ultrasound spectroscopy. We generate noise into the studied sample with a pneumatic air blow gun, and we cross-correlate the signals recorded with two passive piezoelectric sensors put in soft contact with the sample surface. Resonance phenomena are induced in the sample, but in contrast with conventional resonance ultrasound spectroscopy experiments, we have no control over the injected frequencies that are sent all together within the noise spectrum. The spectrum of the correlogram is a good approximation of the resonance spectrum of the vibrating sample and can be inverted in terms of the elastic moduli of the constituent material of the sample.

The experimental procedure is validated on samples made of standard materials (here, aluminium and Plexiglas) by consistently comparing the inverted elastic velocities with the velocities independently measured with the conventional technique of ultrasonic pulse transmission. Moreover, we got similar positive results on dry rock samples, such as Vilhonneur limestone. These encouraging preliminary results open up promising prospects for monitoring fluid substitution in rock samples using the technique described in this paper.

We explore the link between basin modelling and seismic inversion by applying different rock physics models. This study uses the E-Dragon II data in the Gulf of Mexico. To investigate the impact of different rock physics models on the link between basin modelling and seismic inversion, we first model relationships between seismic velocities and both (1) porosity and (2) effective stress for well-log data using published rock physics models. Then, we build 1D basin models to predict seismic velocities derived from basin modelling with different rock physics models, in a comparison with average sonic velocities measured in the wells. Finally, we examine how basin modelling outputs can be used to aid seismic inversion by providing constraints for the background low-frequency model. For this, we run different scenarios of inverting near angle partial stack seismic data into elastic impedances to test the impact of the background model on the quality of the inversion results. The results of the study suggest that the link between basin modelling and seismic technology is a two-way interaction in terms of potential applications, and the key to refine it is establishing a rock physics models that properly describes changes in seismic signatures reflecting changes in rock properties.

How to use cepstrum analysis for reservoir characterization and hydrocarbon detection is an initial question of great interest to exploration seismologists. In this paper, wavelet-based cepstrum decomposition is proposed as a valid technology for enhancing geophysical responses in specific frequency bands, in the same way as traditional spectrum decomposition methods do. The calculation of wavelet-based cepstrum decomposition, which decomposes the original seismic volume into a series of common quefrency volumes, employs a sliding window to move over each seismic trace sample by sample. The key factor in wavelet-based cepstrum decomposition is the selection of the sliding-window length as it limits the frequency ranges of the common quefrency section. Comparison of the wavelet-based cepstrum decomposition with traditional spectrum decomposition methods, such as short-time Fourier transform and wavelet transform, is conducted to demonstrate the effectiveness of the wavelet-based cepstrum decomposition and the relation between these two technologies. In hydrocarbon detection, seismic amplitude anomalies are detected using wavelet-based cepstrum decomposition by utilizing the first and second common quefrency sections. This reduces the burden of needing dozens of seismic volumes to represent the response to different mono-frequency sections in the interpretation of spectrum decomposition in conventional spectrum decomposition methods. The model test and the application of real data acquired from the Sulige gas field in the Ordos Basin, China, confirm the effectiveness of the seismic amplitude anomaly section using wavelet-based cepstrum decomposition for discerning the strong amplitude anomalies at a particular quefrency buried in the broadband seismic response. Wavelet-based cepstrum decomposition provides a new method for measuring the instantaneous cepstrum properties of a reservoir and offers a new field of processing and interpretation of seismic reflection data.

The existence of rugged free-surface three-dimensional tunnel conditions in the coal seams, caused either by geological or mining processes, will inevitably influence wave propagation characteristics when the seismic waves go through the coal mines. Thus, a modified image algorithm has been developed to account for seismic channel waves propagating through this complicated topography with irregular free surfaces. Moreover, the seismic channel waves commonly exhibit damped and dispersive signatures, which is not only because of their own unique sandwich geometry of rock–coal–rock but also because of the viscoelastic behavior of coal. Considering the complexity of programming in three-dimensional tunnel models with rugged free surfaces, an optimized vacuum grid search algorithm, enabling to model highly irregular topography and to compute efficiently, is also proposed when using high-order staggered finite-difference scheme to simulate seismic channel wave propagations in viscoelastic media. The numerical simulations are implemented to investigate the accuracy and stability of the method and the impact of coal's viscoelastic behavior on seismic channel wave propagation characteristics. The results indicate that the automatic vacuum grid search algorithm can be easily merged into high-order staggered finite-difference scheme, which can efficiently be applied to calculate three-dimensional tunnel models with rugged free surfaces in the viscoelastic media. The simulation also suggests that the occurrence of a three-dimensional tunnel with free surfaces has a remarkable influence on the seismic channel wave propagation characteristics and elastic energy distribution.

Most positive/negative curvature and flexure are among the most useful seismic attributes for detecting faults and fractures in the subsurface based on the geometry of seismic reflections. When applied to fracture characterization and modelling of a fractured reservoir, their magnitude and azimuth help quantify both the intensity and orientation of fracturing, respectively. However, previous efforts focus on estimating only the magnitude of both attributes, whereas their associated azimuth is ignored in three-dimensional (3D) seismic interpretation. This study presents an efficient algorithm for simultaneously evaluating both the magnitude and azimuth of most positive/negative curvature and flexure from 3D seismic data. The approach implemented in this study is analytically more accurate and computationally more efficient compared with the existing approach. The added value of extracting most positive/negative curvature and flexure is demonstrated through the application to a fractured reservoir at Teapot Dome (Wyoming). First, the newly extracted attributes make computer-aided fault/fracture decomposition possible. This allows interpreters to focus on one particular component for fracture characterization at a time, so that a composite fractured reservoir could be partitioned into different components for detailed analysis. Second, curvature/flexure azimuth allows interpreters to plot fracture histogram and/or rose diagram in an automatic and quantitative manner. Compared with the conventional plotting rose diagram based on manual measurements, automatic plotting is more efficient and offers unbiased insights into fracture systems by illuminating the most likely orientations of natural fractures in fractured reservoirs.

We present an overall description of moveout formulas of P–SV converted waves in vertically inhomogeneous transversely isotropic media with a vertical symmetry axis by using the generalized moveout approximation. The term “generalized” means that this approximation can be reduced to some existing approximations by specific selections of parameters, which provides flexibility in application depending on objectives. The generalized moveout approximation is separately expressed in the phase and group domains. All five parameters of the group domain (or phase domain) generalized moveout approximation are determined using the zero offset (or horizontal slowness) ray and an additional nonzero offset (or horizontal slowness) ray. We discuss the selection of parameters to link the generalized moveout approximation to some existing approximations. The approximations presented are tested on homogeneous, factorized, and layered transversely isotropic models. The results illustrate that utilizing an additional reference ray significantly improves the accuracy of phase-domain and group-domain moveout approximations for a large range of horizontal slownesses and source–receiver offsets.

Four-dimensional imaging using geophysical data is of increasing interest in the oil and gas industries. While travel-time and amplitude variations are commonly used to monitor reservoir properties at depth, their interpretation can suffer from a lack of information to decipher the parts played by different parameters. In this context, this study focuses on the slowness and azimuth angle measured at the surface using source and receiver arrays as complementary observables. In the first step, array processing techniques are used to extract both azimuth and incidence angles at the source side (departure angles) and at the receiver side (arrival angles). In the second step, the slowness and angle variations are monitored in a laboratory environment. These new observables are compared with traditional arrival-time variations when the propagation medium is subject to temperature fluctuations. Finally, field data from a heavy-oil permanent reservoir monitoring system installed onshore and facing steam injection and temperature variations are investigated. The slowness variations are computed over a period of 152 days. In agreement with Fermat's principle, strong correlations between the slowness and arrival-time variations are highlighted, as well as good consistency with other techniques and field pressure measurements. Although the temporal variations of slowness and arrival time show the same features, there are still differences that can be considered for further characterization of the physical changes at depth.

Surface waves in seismic data are often dominant in a land or shallow-water environment. Separating them from primaries is of great importance either for removing them as noise for reservoir imaging and characterization or for extracting them as signal for near-surface characterization. However, their complex properties make the surface-wave separation significantly challenging in seismic processing. To address the challenges, we propose a method of three-dimensional surface-wave estimation and separation using an iterative closed-loop approach. The closed loop contains a relatively simple forward model of surface waves and adaptive subtraction of the forward-modelled surface waves from the observed surface waves, making it possible to evaluate the residual between them. In this approach, the surface-wave model is parameterized by the frequency-dependent slowness and source properties for each surface-wave mode. The optimal parameters are estimated in such a way that the residual is minimized and, consequently, this approach solves the inverse problem. Through real data examples, we demonstrate that the proposed method successfully estimates the surface waves and separates them out from the seismic data. In addition, it is demonstrated that our method can also be applied to undersampled, irregularly sampled, and blended seismic data.

We study the azimuthally dependent hyperbolic moveout approximation for small angles (or offsets) for quasi-compressional, quasi-shear, and converted waves in one-dimensional multi-layer orthorhombic media. The vertical orthorhombic axis is the same for all layers, but the azimuthal orientation of the horizontal orthorhombic axes at each layer may be different. By starting with the known equation for normal moveout velocity with respect to the surface-offset azimuth and applying our derived relationship between the surface-offset azimuth and phase-velocity azimuth, we obtain the normal moveout velocity versus the phase-velocity azimuth. As the surface offset/azimuth moveout dependence is required for analysing azimuthally dependent moveout parameters directly from time-domain rich azimuth gathers, our phase angle/azimuth formulas are required for analysing azimuthally dependent residual moveout along the migrated local-angle-domain common image gathers. The angle and azimuth parameters of the local-angle-domain gathers represent the opening angle between the incidence and reflection slowness vectors and the azimuth of the phase velocity ψ_{phs} at the image points in the specular direction. Our derivation of the effective velocity parameters for a multi-layer structure is based on the fact that, for a one-dimensional model assumption, the horizontal slowness and the azimuth of the phase velocity ψ_{phs} remain constant along the entire ray (wave) path. We introduce a special set of auxiliary parameters that allow us to establish equivalent effective model parameters in a simple summation manner. We then transform this set of parameters into three widely used effective parameters: fast and slow normal moveout velocities and azimuth of the slow one. For completeness, we show that these three effective normal moveout velocity parameters can be equivalently obtained in both surface-offset azimuth and phase-velocity azimuth domains.

A modular borehole monitoring concept has been implemented to provide a suite of well-based monitoring tools that can be deployed cost effectively in a flexible and robust package. The initial modular borehole monitoring system was deployed as part of a CO_{2} injection test operated by the Southeast Regional Carbon Sequestration Partnership near Citronelle, Alabama. The Citronelle modular monitoring system transmits electrical power and signals, fibre-optic light pulses, and fluids between the surface and a reservoir. Additionally, a separate multi-conductor tubing-encapsulated line was used for borehole geophones, including a specialized clamp for casing clamping with tubing deployment. The deployment of geophones and fibre-optic cables allowed comparison testing of distributed acoustic sensing. We designed a large source effort (>64 sweeps per source point) to test fibre-optic vertical seismic profile and acquired data in 2013. The native measurement in the specific distributed acoustic sensing unit used (an iDAS from Silixa Ltd) is described as a localized strain rate. Following a processing flow of adaptive noise reduction and rebalancing the signal to dimensionless strain, improvement from repeated stacking of the source was observed. Conversion of the rebalanced strain signal to equivalent velocity units, via a scaling by local apparent velocity, allows quantitative comparison of distributed acoustic sensing and geophone data in units of velocity. We see a very good match of uncorrelated time series in both amplitude and phase, demonstrating that velocity-converted distributed acoustic sensing data can be analyzed equivalent to vertical geophones. We show that distributed acoustic sensing data, when averaged over an interval comparable to typical geophone spacing, can obtain signal-to-noise ratios of 18 dB to 24 dB below clamped geophones, a result that is variable with noise spectral amplitude because the noise characteristics are not identical. With vertical seismic profile processing, we demonstrate the effectiveness of downgoing deconvolution from the large spatial sampling of distributed acoustic sensing data, along with improved upgoing reflection quality. We conclude that the extra source effort currently needed for tubing-deployed distributed acoustic sensing vertical seismic profile, as part of a modular monitoring system, is well compensated by the extra spatial sampling and lower deployment cost as compared with conventional borehole geophones.

For 3-D shallow-water seismic surveys offshore Abu Dhabi, imaging the target reflectors requires high resolution. Characterization and monitoring of hydrocarbon reservoirs by seismic amplitude-versus-offset techniques demands high pre-stack amplitude fidelity. In this region, however, it still was not clear how the survey parameters should be chosen to satisfy the required data quality. To answer this question, we applied the focal-beam method to survey evaluation and design. This subsurface- and target-oriented approach enables quantitative analysis of attributes such as the best achievable resolution and pre-stack amplitude fidelity at a fixed grid point in the subsurface for a given acquisition geometry at the surface. This method offers an efficient way to optimize the acquisition geometry for maximum resolution and minimum amplitude-versus-offset imprint. We applied it to several acquisition geometries in order to understand the effects of survey parameters such as the four spatial sampling intervals and apertures of the template geometry. The results led to a good understanding of the relationship between the survey parameters and the resulting data quality and identification of the survey parameters for reflection imaging and amplitude-versus-offset applications.

We have previously applied three-dimensional acoustic, anisotropic, full-waveform inversion to a shallow-water, wide-angle, ocean-bottom-cable dataset to obtain a high-resolution velocity model. This velocity model produced an improved match between synthetic and field data, better flattening of common-image gathers, a closer fit to well logs, and an improvement in the pre-stack depth-migrated image. Nevertheless, close examination reveals that there is a systematic mismatch between the observed and predicted data from this full-waveform inversion model, with the predicted data being consistently delayed in time. We demonstrate that this mismatch cannot be produced by systematic errors in the starting model, by errors in the assumed source wavelet, by incomplete convergence, or by the use of an insufficiently fine finite-difference mesh. Throughout these tests, the mismatch is remarkably robust with the significant exception that we do not see an analogous mismatch when inverting synthetic acoustic data. We suspect therefore that the mismatch arises because of inadequacies in the physics that are used during inversion. For ocean-bottom-cable data in shallow water at low frequency, apparent observed arrival times, in wide-angle turning-ray data, result from the characteristics of the detailed interference pattern between primary refractions, surface ghosts, and a large suite of wide-angle multiple reflected and/or multiple refracted arrivals. In these circumstances, the dynamics of individual arrivals can strongly influence the apparent arrival times of the resultant compound waveforms. In acoustic full-waveform inversion, we do not normally know the density of the seabed, and we do not properly account for finite shear velocity, finite attenuation, and fine-scale anisotropy variation, all of which can influence the relative amplitudes of different interfering arrivals, which in their turn influence the apparent kinematics. Here, we demonstrate that the introduction of a non-physical offset-variable water density during acoustic full-waveform inversion of this ocean-bottom-cable field dataset can compensate efficiently and heuristically for these inaccuracies. This approach improves the travel-time match and consequently increases both the accuracy and resolution of the final velocity model that is obtained using purely acoustic full-waveform inversion at minimal additional cost.

Most sedimentary rocks are anisotropic, yet it is often difficult to accurately incorporate anisotropy into seismic workflows because analysis of anisotropy requires knowledge of a number of parameters that are difficult to estimate from standard seismic data. In this study, we provide a methodology to infer azimuthal P-wave anisotropy from S-wave anisotropy calculated from log or vertical seismic profile data. This methodology involves a number of steps. First, we compute the azimuthal P-wave anisotropy in the dry medium as a function of the azimuthal S-wave anisotropy using a rock physics model, which accounts for the stress dependency of seismic wave velocities in dry isotropic elastic media subjected to triaxial compression. Once the P-wave anisotropy in the dry medium is known, we use the anisotropic Gassmann equations to estimate the anisotropy of the saturated medium. We test this workflow on the log data acquired in the North West Shelf of Australia, where azimuthal anisotropy is likely caused by large differences between minimum and maximum horizontal stresses. The obtained results are compared to azimuthal P-wave anisotropy obtained via orthorhombic tomography in the same area. In the clean sandstone layers, anisotropy parameters obtained by both methods are fairly consistent. In the shale and shaly sandstone layers, however, there is a significant discrepancy between results since the stress-induced anisotropy model we use is not applicable to rocks exhibiting intrinsic anisotropy. This methodology could be useful for building the initial anisotropic velocity model for imaging, which is to be refined through migration velocity analysis.

Based on the theory of anisotropic elasticity and observation of static mechanic measurement of transversely isotropic hydrocarbon source rocks or rock-like materials, we reasoned that one of the three principal Poisson's ratios of transversely isotropic hydrocarbon source rocks should always be greater than the other two and they should be generally positive. From these relations, we derived tight physical constraints on *c*_{13}, Thomsen parameter δ, and anellipticity parameter η. Some of the published data from laboratory velocity anisotropy measurement are lying outside of the constraints. We analysed that they are primarily caused by substantial uncertainty associated with the oblique velocity measurement. These physical constraints will be useful for our understanding of Thomsen parameter δ, data quality checking, and predicting δ from measurements perpendicular and parallel to the symmetrical axis of transversely isotropic medium. The physical constraints should also have potential application in anisotropic seismic data processing.

A better understanding of seismic dispersion and attenuation of acoustic waves in rocks is important for quantitative interpretation of seismic data, as well as for relating seismic data, sonic-log data, and ultrasonic laboratory data. In the present work, a new laboratory setup is described, allowing for combined measurements of quasistatic deformations of rocks under triaxial stress, ultrasonic velocities, and dynamic elastic stiffness (Young's modulus and Poisson's ratio) at seismic frequencies. The setup has been used mainly for the study of shales. For such rocks, it is crucial that the saturation of the samples is preserved, which requires fast sample mounting. The design of our setup, together with a technique that was developed for rapid mounting of strain gauges onto the sample and subsequent sealing of the sample, allows for sample preservation, which is of particular importance for shales. The performance of the new experimental setup and sample mounting procedure is demonstrated with test materials (aluminium and polyetheretherketone) and two different shale types (Mancos shale and Pierre shale). Furthermore, experimental results are presented that demonstrate the capability of measuring the impact of saturation, stress, and stress path on seismic dispersion. For the tests with Mancos shale and Pierre shale, large dispersion (up to 50% in Young's modulus normal to bedding) was observed. Increased water saturation of Mancos shale results in strong softening of the rock at seismic frequencies, whereas hardening is observed at ultrasonic frequencies due to an increase in dispersion, counteracting the rock softening. The Poisson's ratio of Mancos shale strongly increases with the level of saturation but appears to be nearly frequency independent. We have found that the different types of shale exhibit different stress sensitivities during hydrostatic loading and that the stress sensitivity is different at seismic and ultrasonic frequencies.

A significant portion of the world's hydrocarbon reserves are found in carbonate reservoirs, yet analysis of the petrophysical properties of these reservoirs is associated with a number of challenges. Some of these challenges stem from physical and chemical interactions between the carbonate rock matrix and pore fluids, which can affect elastic properties of the rock. Hence, the study of the pore fluid effects on the elastic properties of carbonates is important for understanding a change of the field performance properties of а carbonate reservoir caused by fluid movements during hydrocarbon extraction in producing fields. In this laboratory study, we investigate the applicability of Gassmann's model for predictions of the elastic moduli of water- and hydrocarbon-saturated Savonnières limestone and the influence of partial water saturation on elastic and anelastic properties of the rock. We present the results of two sets of laboratory experiments on the Savonnières oolitic limestone where we: (i) evaluate the effect of full water and n-decane saturation on elastic moduli and attenuation at seismic (0.1 Hz–120 Hz) and ultrasonic (0.5 MHz) frequencies; and (ii) quantify the dependence of elastic moduli and extensional attenuation on water saturation at two seismic frequencies of 1 Hz and 10 Hz. We demonstrate that the change in the bulk modulus of limestone fully saturated either with n-decane or water is in agreement with Gassmann's fluid substitution theory, whereas the shear modulus is noticeably reduced. The measurements with partial saturation show that the bulk modulus decreases with increasing water saturation to a lesser extent than the Young's and shear moduli. Our results show that extensional attenuation in the samples with closed boundaries is insignificant under dry and fully saturated conditions but is influenced greatly by the liquid content when saturation is between 0 and 20% or 95% and 100%.

The technical and economic success of a CO_{2} geological storage project requires the preservation of the site injectivity and integrity properties over its lifetime. Unlike conventional hydrocarbon gas injection, CO_{2} injection may imply geochemical reactions between acidified pore fluids and target reservoir formations, leading to modifications of their poromechanical properties. To date, the chemical effects on the host rock mechanical behaviour are not satisfactorily taken into account in site-scale numerical models of CO_{2} injection, mainly due to a lack of quantitative data. The present experimental work aims at characterizing the evolution of carbonate poromechanical properties induced by acid alteration. Unlike standard experimental approaches, the implemented alteration method induces a homogeneous dissolution pattern, which ensures reliable poromechanical measurements on altered samples. These well-controlled alteration conditions allow a proper interpretation of the test results through the macroscopic continuous approach of poromechanics. Petrophysical, geomechanical, and petroacoustic properties of outcrop carbonate samples have been measured for different levels of alteration to mimic long-term exposure to reactive brine. The obtained experimental data show clear trends of chemically induced mechanical weakening. Nuclear magnetic resonance measurements and microscanner imaging performed before and after alteration have provided complementary insights into the alteration effects at the microscopic scale.

Geological reservoirs can be structurally complex and can respond to CO_{2} injection both geochemically and geomechanically. Hence, predicting reservoir formation behaviour in response to CO_{2} injection and assessing the resulting hazards are important prerequisites for safe geological CO_{2} storage. This requires a detailed study of thermal-hydro-mechanical-chemical coupled phenomena that can be triggered in the reservoir formation, most readily achieved through laboratory simulations of CO_{2} injection into typical reservoir formations. Here, we present the first results from a new experimental apparatus of a steady-state drainage flooding test conducted through a synthetic sandstone sample, simulating real CO_{2} storage reservoir conditions in a shallow (∼1 km), low permeability ∼1mD, 26% porosity sandstone formation. The injected pore fluid comprised brine with CO_{2} saturation increasing in steps of 20% brine/CO_{2} partial flow rates up to 100% CO_{2} flow. At each pore fluid stage, an unload/loading cycle of effective pressure was imposed to study the response of the rock under different geomechanical scenarios. The monitoring included axial strains and relative permeability in a continuous mode (hydromechanical assessment), and related geophysical signatures (ultrasonic P-wave and S-wave velocities *V _{p}* and

A sample of Bentheim sandstone was characterized using high-resolution three-dimensional X-ray microscopy at two different confining pressures of 1 MPa and 20 MPa. The two recordings can be directly compared with each other because the same sample volume was imaged in either case. After image processing, a porosity reduction from 21.92% to 21.76% can be deduced from the segmented data. With voxel-based numerical simulation techniques, we determined apparent hydraulic transport properties and effective elastic properties. These results were compared with laboratory measurements using reference samples. Laboratory and computed volumes, as well as hydraulic transport properties, agree fairly well. To achieve a reasonable agreement for the effective elastic properties, we define pressure-dependent grain contact zones in addition to mineral phases in the digital rock images. From that, we derive a specific digital rock physics template resulting in a very good agreement between laboratory data and simulations. The digital rock physics template aims to contribute to a more standardized approach of X-ray computed tomography data analysis as a tool to determine and predict elastic rock properties.

Pore throat plugging of porous rock by fine particles causes formation damage, and thus has attracted attention in various areas such as petroleum engineering, hydrology and geothermal energy production. Despite significant efforts, the detailed pore-scale mechanisms leading to formation damage and the associated permeability reduction are not well understood. We thus investigated plugging mechanisms and characteristics with a combination of *ex situ* (i.e., coreflooding measurements and scanning electron microscopy imaging) and *in situ* (i.e., nuclear magnetic resonance and μCT) methods, with a particular focus on the effect of wettability.

The corefloods indicated that permeability drops rapidly when fines are injected; mechanistically thin pore throats are plugged first, followed by filling of adjacent pore bodies with the fine material (as evidenced by the nuclear magnetic resonance and μCT experiments, which can measure the pore size distribution evolution with fines injection). Furthermore, it is clear that wettability plays a major role: if fines and rock wettability are identical, plugging is significantly accelerated; wettability also controls the 3D distribution of the fines in the pore space. Furthermore we note that the deposited fines were tightly packed, apparently due to strong adhesion forces.

Optimizing the productivity of nonconventional, low-permeability “shale” reservoirs requires detailed knowledge of the mechanical properties of such materials. These rocks' elastic anisotropy is acknowledged but usually ignored due to difficulties in obtaining such information. Here we study in detail the dynamic and static elastic properties of a suite of calcareous mudstones from the nonconventional Duvernay reservoir of Alberta, Canada. The complete set of transversely isotropic elastic constants is obtained from strategically oriented ultrasonic transducers to confining pressures of 90 MPa. Wave speed anisotropies of up to 35% are observed at even the highest confining pressures. Furthermore, the stress sensitivity of the wave speeds, and hence moduli, is itself highly dependent on direction with speeds taken perpendicular to the bedding plane being highly nonlinearly dependent on pressure, whereas those along the bedding plane show, unexpectedly, nearly no pressure dependence. These observations are in qualitative agreement with the preferentially oriented porosity and minerals seen in scanning electron microscope images. These results may be significant to the interpretation of sonic logs and azimuthal amplitude versus offset for principal stress directions, for the concentration of stress within such formations, and for estimation of static engineering moduli from sonic log wave speeds.

Natural shale samples, particularly well-preserved, drilled core samples, are extremely difficult to obtain for laboratory research. Multiple tests must be carried out on one sample, and some samples are disposed after destructive tests. Therefore, rarity and non-reusability of samples strongly restrict shale studies. In this study, based on statistical data from the world's major shale block, a new type of synthetic shale was physically constructed via a process of interfusion, stuffing, and compaction using quartz, clay, carbonate, and kerogen as the primary materials, according to statistical data from the world's major shale blocks. Further evaluation of the synthetic shale involved the use of scanning electron microscopy imagery and analysis of its anisotropic characteristics in comparison with natural shale. The synthetic shale had a laminated microstructure similar to natural shale, and its velocity anisotropy corresponded to Thomsen's anisotropy of a transversely isotropic medium. The results of tests for homogeneity and repeatability indicated that the construction process was stable and that several identical synthetic samples, which were satisfactorily similar to natural shale, could be produced for both iterative and destructive tests. The composition of each mineral, as well as the density, porosity, permeability, and anisotropy of the samples, were all variable. Therefore, a series of synthetic samples could be obtained with properties set to meet the requirements of petrophysical experimentation. Moreover, gas or oil saturation was also considered in the construction of the synthetic shale, meaning that the characteristics of gas or oil saturation (or the complete range of data from dry to saturated samples) could be tested using the synthetic shale.

Development of rock physical properties in well-sorted and poorly-sorted unconsolidated mono-quartz sands and sand–clay mixtures as a function of effective stress in both dry and brine-saturated conditions is assessed in this study. The tested samples were prepared with full control on their mineralogy, grain size, grain shape, sorting, and fabric. The experiments were performed in a high-stress uniaxial oedometer up to a maximum of 30 MPa vertical effective stress. Sand–clay samples were a mixture of sand grains and clay particles (kaolinite or smectite) in different proportions. The maximum clay volume fraction used in the experiments was at most 30%. The initial bulk density of the tested sand-dominated samples was adjusted to be close to the maximum index density expected for natural sediments (sand–clay mixtures) during deposition.

In pure sand samples, finer grained sand show higher initial porosity than relatively coarser grained sands. Moreover, sand–clay mixtures have lower initial porosity than pure sands. Porosity decreases as a function of increasing clay content. The poorly-sorted sand samples are less compaction prone than the well-sorted sand samples. Among well-sorted sand samples, coarser grained sands are more compressible than finer grained sands. At a given effective stress level, sand–clay mixtures are more compaction prone compared with their sand component alone. Pure sands and clay-poor sand–clay mixtures (either sand–kaolinite or sand–smectite) show almost the same degree of compaction when tested in both dry and brine-saturated conditions. In contrast, clay-rich sand–kaolinite and sand–smectite mixtures (clay volume >20%) are significantly more compact in brine-saturated condition. The V_{p} values of brine-saturated sand–kaolinite mixtures shows a positive correlation with the kaolinite content, whereas V_{p} starts to decrease substantially when the volume fraction of smectite exceeds 10% of the whole sand–smectite samples.

Saturated bulk moduli estimated by Gassmann's fluid substitution agree with measurements for brine-saturated clay-poor sand samples. However, the model does not yield proper predictions for sand–clay samples containing 20% clay volume and above, particularly when the clay is mainly smectite. The acoustic and physical properties derived from experimental compaction of pure sands and sand–clay mixtures show a good agreement with rock properties derived from well logs of mechanically compacted pure sands and shaly sands in progressively subsided basins such as Viking Graben in the North Sea. Thus, the outcome of this study can provide reliable constraints for rock physical properties of sands and shaly sands within the mechanical compaction domain and contribute to improved basin modelling and identification of hydrocarbon presence, overconsolidation, and/or undercompaction.

P-wave-to-S-wave ratios are important seismic characterization attributes. Velocity ratios are sensitive to the petrophysical properties of rocks and to the presence of gas. Attenuation ratios have also been shown to be sensitive to the presence of partial liquid/gas saturation. The relationship between liquid/gas saturation and P-wave and S-wave ratios has been used to distinguish gas-saturated rocks from liquid-saturated rocks. Aligned fractures are common in the Earth's crust and cause seismic anisotropy and shear wave splitting. However, most existing relationships between partial gas/liquid saturation and P-wave and S-wave ratios are for non-fractured rocks. We present experimental results comparing the effects of changing water saturation on *Q*_{s}/*Q*_{p} versus *V*_{p}/*V*_{s} ratios between a non-fractured rock and one containing fractures aligned parallel to wave propagation direction. We also study the effects of aligned fractures on the response of *V*_{p}/*V*_{s} to changing water saturation using synthetic fractured sandstones with fractures aligned at 45^{o} and parallel to the wave propagation direction. The results suggest that aligned fractures could have significant effects on the observed trends, some of which may not be obvious. Fractures aligned parallel to wave propagation could change the response of *Q*_{s}/*Q*_{p} versus *V*_{p}/*V*_{s} ratios to water saturation from previously reported trends. Shear wave splitting due to the presence of aligned fractures results in two velocity ratios (*V*_{p}/*V*_{s1} and *V*_{p}/*V*_{s2}). The fluid independence of shear wave splitting for fractures aligned parallel to wave propagation direction means the difference between *V*_{p}/*V*_{s1} and *V*_{p}/*V*_{s2} is independent of water saturation. For fractures aligned at oblique angles, shear wave splitting can be sensitive to water saturation and consequently be frequency dependent, which can lead to fluid and frequency-dependent differences between *V*_{p}/*V*_{s1} and *V*_{p}/*V*_{s2}. The effect of aligned fractures on *V*_{p}/*V*_{s} ratios not only depends on the fracture effects on both P-wave and S-wave velocities but also on the effects of water saturation distribution on the rock and fracture stiffness, and hence on the P-wave and S-wave velocities. As such, these effects can be frequency dependent due to wave-induced fluid flow. A simple modelling study combining a frequency-dependent fractured rock model, and a frequency-dependent partial saturation model was used to gain valuable interpretations of our experimental observations and possible implications, which would be useful for field seismic data interpretation.

Rock brittleness and fracability of subsurface formations are two important parameters for hydraulic fracturing in hydrocarbon reservoir production. This paper presents an effective technique to assess these parameters using the radial variation of compressional and shear velocities from borehole acoustic logging. Our technique is based on a rock mechanic phenomenon that a brittle rock with high fracability tends to leave a significant amount of drilling-induced cracks at the borehole wall, resulting in radial elastic wave velocity variation away from borehole. By determining the velocity variation, the combined effects of brittleness and fracability of formation rocks can be assessed. The compressional-wave travel-time tomography and flexural shear-wave inversion methods are respectively used to obtain compressional- and shear-velocity variations. Well-log data analysis examples demonstrate the practicability and effectiveness of this technique.

Seismic methods are commonly used to monitor the subsurface when carbon dioxide (CO_{2}) is injected into a reservoir. Besides fluid saturation and pressure changes, CO_{2}–water mixtures may cause rock alteration. In this petrophysical study, we compare the elastic property changes due to fluid replacement and those due to mineral dissolution for carbonate-cemented sandstones at the Pohokura Field, New Zealand. We quantify the effects of fluid substitution from fully brine to fully supercritical CO_{2} saturation and carbonate cement dissolution on the seismic signatures of the reservoir rocks by combining laboratory results, petrographic analyses, and geophysical well log data. We conclude that elastic property changes due to mineral dissolution are significantly greater than those due to fluid substitution alone. The northern part of the Pohokura Field has coarser-grained sandstones, which experience the largest changes in wave speeds. Our hypothesis is that these changes result from carbonate cement dissolution in the presence of CO_{2}–water–sandstone reactions. If time-lapse seismic data were to be acquired in this field, the northern area could show P-wave velocity reductions of up to 20% and a 131.7% increase in seismic amplitude from a brine-saturated rock to an altered, fully CO_{2}-saturated rock. In comparison, the southern part of the field, where sandstones are mostly fine-grained, we expect a P-wave velocity decrease of 6% if such dissolution process took place. Finally, we show that the elastic properties of the reservoir rocks can be described with the constant-cement model. The model is used to predict that the dissolution process reduces the volume of grain contact cement, on average, from 2.5% to 1.75% of the total rock mineral volume. Our analysis suggests that changes to the rock frame, which includes carbonate minerals, cannot be ignored for a CO_{2} injection scenario.

CO_{2} sequestration projects benefit from quantitative assessment of saturation distribution and plume extent for field development and leakage prevention. In this work, we carry out quantitative analysis of time-lapse seismic by using rock physics and seismic modelling tools. We investigate the suitability of Gassmann's equation for a CO_{2} sequestration project with 1600 tons of CO_{2} injected into high-porosity, brine-saturated sandstone. We analyze the observed time delays and amplitude changes in a time-lapse vertical seismic profile dataset. Both reflected and transmitted waves are analyzed qualitatively and quantitatively. To interpret the changes obtained from the vertical seismic profile, we perform a 2.5D elastic, finite-difference modelling study. The results show a P-wave velocity reduction of 750 m/s in the proximity of the injection well evident by the first arrivals (travel-time delays and amplitude change) and reflected wave amplitude changes. These results do not match with our rock physics model using Gassmann's equation predictions even when taking uncertainty in CO_{2} saturation and grain properties into account. We find that time-lapse vertical seismic profile data integrated with other information (e.g., core and well log) can be used to constrain the velocity–saturation relation and verify the applicability of theoretical models such as Gassmann's equation with considerable certainty. The study shows that possible nonelastic factors are in play after CO_{2} injection (e.g., CO_{2}–brine–rock interaction and pressure effect) as Gassmann's equation underestimated the velocity reduction in comparison with field data for all three sets of time-lapse vertical seismic profile attributes. Our work shows the importance of data integration to validate the applicability of theoretical models such as Gassmann's equation for quantitative analysis of time-lapse seismic data.

Quantitative interpretation of time-lapse seismic signatures aims at assisting reservoir engineering and management operations. Time-lapse signatures are thought to be primarily induced by saturation and pressure changes. Core-flooding and reservoir flow simulations indicate that a change of the driving forces during dynamic fluid injection gives rise to a varying saturation scale. This saturation scale is yet another variable controlling the time-lapse seismic signal. In this work, we investigate the saturation scale effect on time-lapse seismic signatures by analysing simple modelling scenarios. We consider three characteristic saturation scales, ranging from few millimetres to metres, which may form during gas injection in an unconsolidated water-saturated reservoir. Using the random patchy saturation model, we compare the corresponding acoustic signatures, i.e., attenuation, reflectivity, and seismic gather associated with each saturation scale. The results show that the millimetre saturation scale produces minimum attenuation and the same seismic signatures with those obtained from the elastic modelling. The centimetre saturation scale produces maximum attenuation, whereas the metre saturation scale causes highest velocity dispersion. The analyses of the time shift and amplitude change indicate that ignoring a time-dependent saturation scale can result in biased estimation/discrimination of the saturation and the fluid pressure. In particular, the 4D signal can be strongly affected by the saturation-scale change when the reservoir gas saturation is low and the effective pressure is high. In the presence of an increasing (decreasing) saturation scale during injection, interpreting an observed time shift and amplitude change using the Gassmann model will lead to underestimation (overestimation) of the change in gas saturation and fluid pressure. We show that including the effects of capillarity and residual saturation into the rock physics modelling can potentially reduce the interpretation uncertainty due to the saturation-scale change.

Seismic attenuation and velocity dispersion are potentially able to reveal the rock physical properties of the subsurface. Conventionally, a frequency-independent quality factor (*Q*) is measured. This *Q* is equivalent to the total velocity dispersion in a seismic record and is inadequate for analysing the attenuation mechanism or rock physical properties. Here a new method is proposed to extract the velocity dispersion curves so that more attributes can be obtained from full-waveform multichannel sonic logging data, especially the critical frequency (*f _{c}*) if it is within the bandwidth of the data. This method first decomposes the seismic data into a series of frequency components, computes the semblance of each frequency component for different velocity values, cross-correlates the semblance matrices of adjacent frequency components to get the velocity gradients, and finally integrates to obtain a velocity dispersion curve. Results of this method are of satisfactory accuracy and robustness. This method is applied to the data acquired in Mallik 5L-38 gas hydrate research well in Mackenzie Delta, Northwest Territories, Canada. The observed P-wave velocity dispersion compares well with the geological setting. In the gas hydrate zone (about 900 m–1100 m), high concentration of gas hydrate causes very strong velocity dispersion and a distinct

In this study, we derived accurate and high-resolution attenuation profiles using spectral ratio, centroid frequency shift, and seismic interferometry methods. We utilized high-quality vertical seismic profiling and sonic waveform data acquired in a carbonate reservoir located in Abu Dhabi, United Arab Emirates. The scattering profile of vertical-seismic-profiling data contributes significantly to wave attenuation that can be explained by high heterogeneity of the carbonate rocks. The scattering profile also correlates well with the reservoir lithology and fractured zones imaged by the Formation MicroImager. A tar mat zone occurs within the lower part of Arab D reservoir. This zone corresponds with a decrease in scattering attenuation. The tar mat may have filled the pores and made this zone less heterogeneous. Therefore, a decrease in scattering attenuation can be considered a potential parameter for tar mat detection. After removing the scattering effect, nonphysical negative intrinsic attenuation values still exist at certain depths. The most probable explanation for this is the three-dimensional scattering effect, which is not taken into account in this paper, and short-period upgoing waves. Seismic interferometry is less sensitive to the remaining scattered upgoing wave, which is why seismic interferometry method shows fewer negative values than the spectral ratio and centroid frequency shift methods. Compared with vertical-seismic-profiling attenuation, scattering attenuation estimated from sonic waveforms recorded in the reservoir zones is insignificant, and the intrinsic attenuation is almost equivalent to the total attenuation. We attribute this underestimation of the scattering attenuation to the sparse spatial sampling of the sonic logging data at 0.1524 m, which is not sufficient to appropriately estimate the scattering effect in heterogeneous media. The cross-plots between sonic attenuation and various petrophysical properties show slight dependence between the sonic attenuation and neutron porosity and resistivity in the reservoir zones. However, we can highlight from these plots two zones belonging to the Arab reservoirs. The lower zone corresponds to Arab D reservoir and displays higher sonic intrinsic attenuation than the upper zone (Arab A–C reservoirs) due to higher oil saturation. This highlights the sensitivity of the intrinsic attenuation to the oil saturation.

Prediction of the velocity of acoustic waves in partially saturated rocks is very important in geophysical applications. The need to accurately predict acoustic velocities has resulted in a widespread popularity of Brie's effective fluid mixing law. This empirical model together with Gassmann's formula are used routinely in fluid substitution problems in petroleum geophysics and seismic monitoring of carbon capture and storage. Most attempts to justify Brie's model have been focused on interpretation in terms of patchy saturation models and attaching meaning to the Brie parameter in terms of the patch size. In this paper, using a microstructural description of the rock and a parameter relating to capillary pressure, we calculate an effective fluid modulus that is very similar to Brie's law. The fluid mixing law we propose is independent of frequency and has a solid theoretical foundation. This proposed law produces analytically harmonic and arithmetic averaging at the endpoints. Our results indicate that Brie-like behaviour may not necessarily be related to frequency- and patch-size- dependent phenomena.

The relationship between *P*-wave velocity and fluid saturation in a porous medium is of importance for reservoir rock characterization. Forced imbibition experiments in the laboratory reveal rather complicated velocity–saturation relations, including rollover-like patterns induced by injection rate changes. Poroelasticity theory-based patchy saturation models using a constant fluid patch size are not able to describe these velocity–saturation relations. Therefore, we incorporate a saturation-dependent patch size function into two models for patchy saturation. This recipe allows us to model observed velocity–saturation relations obtained for different and variable injection rates. The results reveal an increase in patch size with fluid saturation and show a reduction in the patch size for decreasing injection rate. This indicates that there can exist a distinct relation between patch size and injection rate. We assess the relative importance of capillarity on velocity–saturation relations and find that capillarity stiffening impairs the impact of patch size changes. Capillarity stiffening appears to be a plausible explanation when a decrease in the injection rate is expected to boost the importance of capillarity.

A major cause of attenuation in fluid-saturated media is the local fluid flow (or squirt flow) induced by a passing wave between pores of different shapes and sizes. Several squirt flow models have been derived for isotropic media. For anisotropic media however, most of the existing squirt flow models only provide the low- and high-frequency limits of the saturated elastic properties. We develop a new squirt flow model to account for the frequency dependence of elastic properties and thus gain some insight into velocity dispersion and attenuation in anisotropic media. In this paper, we focus on media containing aligned compliant pores embedded in an isotropic background matrix. The low- and high-frequency limits of the predicted fluid-saturated elastic properties are respectively consistent with Gassmann theory and Mukerji–Mavko squirt flow model. Results are also expressed in terms of Thomsen anisotropy parameters. It turns out that the P-wave anisotropy parameter ε tends to zero in the high-frequency limit, whereas the δ parameter remains the only indicator of P-S⊥ anisotropy. The S-wave anisotropy parameter γ is not affected by the presence of fluid and remains the same for all frequency ranges. A new definition for attenuation anisotropy parameters is also proposed to quantify the attenuation anisotropy. In the most important case of liquid saturation, analytical expressions are derived for elastic properties, velocity anisotropy parameters, quality factors, and attenuation anisotropy parameters. A companion paper considers the case of cracks with an ellipsoidal distribution of orientations resulting from the application of anisotropic stress.

A major cause of attenuation in fluid-saturated media is the local fluid flow (or squirt flow) induced by a passing wave between pores of different shapes and sizes. Several squirt flow models have been derived for isotropic media. For anisotropic media, however, most of the existing squirt flow models only provide the low- and high-frequency limits of the saturated elastic properties. We develop a new squirt flow model to account for the frequency dependence of elastic properties and thus gain some insight into velocity dispersion and attenuation in anisotropic media. In a companion paper, we focused on media containing aligned compliant pores embedded in an isotropic background matrix. In this paper, we investigate the case for which anisotropy results from the presence of cracks with an ellipsoidal distribution of orientations due to the application of anisotropic stress. The low- and high-frequency limits of the predicted fluid-saturated elastic properties are respectively consistent with Gassmann theory and Mukerji–Mavko squirt flow model. In the most important case of liquid saturation, analytical expressions are derived for elastic properties and Thomsen anisotropy parameters. The main observations drawn from this model are as follows. Crack closure perpendicular to the applied stress leads to an increase in seismic velocities as a function of stress in the direction of applied stress and a decrease in squirt-flow-induced dispersion and attenuation in this direction. The anisotropy of squirt flow dispersion engenders a decrease in the degree of anisotropy with frequency. The stress-induced anisotropy remains elliptical, even in saturated media, for all frequency ranges.

The dependence of fluid-saturated rocks' elastic properties to the measuring frequency is related to fluid-flow phenomena at different scales. In the frequency range of Hz, for fully saturated rocks, two phenomena have been experimentally documented: (i) the drained/undrained transition (i.e., global flow), and (ii) the relaxed/unrelaxed transition (i.e., local flow). When investigating experimentally those effects or comparing different measurements in rocks, one needs to account for both the boundary conditions involved and the method of measurement used. A one-dimensional poroelastic model is presented, which aims at calculating the expected poroelastic response during an experiment. The model is used to test different sets of boundary conditions, as well as the role of the measuring setup, i.e., local (strain gauges) or global (linear variable differential transformer) strain measurement. Four properties are predicted and compared with the measurements, i.e., bulk modulus, bulk attenuation, pseudo-Skempton coefficient, and pore pressure phase shift. For the drained/undrained transition, because fluid pressure may not be homogeneous in the sample, local and global measurements are predicted to differ. Furthermore, the existence of a dead volume at both sample's ends is shown to be important. Due to the existence of the dead volume, an interplay between sample's and dead volumes' storage capacity determines both the magnitudes and the frequency dependence of the dispersion/attenuation measurements. The predicted behaviours are shown to be consistent with the measurements recently reported on very compressible and porous sandstone samples.

Estimating the impact of solid pore fill on effective elastic properties of rocks is important for a number of applications such as seismic monitoring of production of heavy oil or gas hydrates. We develop a simple model relating effective seismic properties of a rock saturated with a liquid, solid, or viscoelastic pore fill, which is assumed to be much softer than the constituent minerals. A key feature of the model is division of porosity into stiff matrix pores and compliant crack-like pores because the presence of a solid material in thin voids stiffens the rock to a much greater extent than its presence in stiff pores. We approximate a typical compliant pore as a plane circular interlayer surrounded by empty pores. The effect of saturation of the stiff pores is then taken into account using generalized Gassmann's equations. The proposed model provides a good fit to measurements of the shear stiffness and loss factor of the Uvalde heavy-oil rock at different temperatures and frequencies. When the pore fill is solid, the predictions of the scheme are close to the predictions of the solid squirt model recently proposed by Saxena and Mavko. At the same time, the present scheme also gives a continuous transition to the classic Gassmann's equations for a liquid pore fill at low frequencies and the squirt theory at high frequencies.

Poroelastic modelling of micro-inhomogeneous rocks is of interest for applications in rock physics and geomechanics. Laboratory measurements from both communities indicate that the Biot poroelasticity framework is not adequate. For the case of a macroscopically homogeneous and isotropic rock, we present the most general poroelasticity framework within the scope of equilibrium thermodynamics that is able to capture the effects of micro-inhomogeneities in a natural way. Within this generalized poroelasticity framework, the concept of micro-inhomogeneity is generically related to partial localization of the deformational potential energy either in the solid phase, including the interfacial region or in the fluid phase. The former case can occur in the presence of surface roughness or multi-mineralic frame and the latter case can be related to suspended particles residing in the fluid phase. A measure for micro-inhomogeneity is the coefficient that governs the effective pressure dependence of porosity changes as described by the porosity perturbation equation of this framework. It can be therefore equivalently interpreted as porosity effective pressure coefficient or as micro-inhomogeneity parameter. We show how this parameter and the other poroelastic constants embedded in this framework can be expressed in terms of experimentally accessible poroelastic constants.

We present a generalized effective poroelastic model for periodically layered media in the mesoscopic scale range, which accounts for both Biot's global and interlayer wave-induced fluid flow, as well as for the anisotropy associated with the layering. Correspondingly, it correctly predicts the existence of the fast and slow P-waves as well as quasi and pure S-waves. The proposed analytical model is validated through comparisons of the P-wave and S-wave phase velocity dispersion and attenuation characteristics with those inferred from a one-dimensional numerical solution of Biot's poroelastic equations of motion. We also compare our model with the classical mesoscopic model of White for a range of scenarios. The results demonstrate that accounting for both wave-induced fluid flow mechanisms is essential when Biot's global flow prevails at frequencies that are comparable or smaller with respect to those governing interlayer flow. This is likely to be the case in media of high permeability, such as, for example, unconsolidated sediments, clean sandstones, karstic carbonates, or fractured rocks. Conversely, when interlayer flow occurs at smaller frequencies with respect to Biot's global flow, the predictions of this model are in agreement with White's model, which is based on quasi-static poroelasticity.

Fractures in fluid-saturated poroelastic media can be modeled as extremely thin, highly permeable, and compliant layers or by means of suitable boundary conditions that approximate the behavior of such thin layers. Since fracture apertures can be very small, the numerical simulations would require the use of extremely fine computational meshes and the use of boundary conditions would be required.

In this work, we study the validity of using boundary conditions to describe the seismic response of fractures. For this purpose, we compare the corresponding scattering coefficients to those obtained from a thin-layer representation. The boundary conditions are defined in terms of fracture apertures that, in the most general case, impose discontinuity of displacements, fluid pressures, and stresses across a fracture. Furthermore, discontinuities of either fluid pressures, stresses, or both can be removed, or displacement jumps proportional to the stresses and/or pressures can be expressed via shear and normal dry compliances in order to simplify.

In the examples, we vary the permeability, thickness, and porosity of the fracture and the type of fluid saturating the background medium and fractures. We observe good agreement of the scattering coefficients in the seismic range obtained with the two different approaches.

Relating seismic attributes to the characteristics of mesoscopic fractures is inherently challenging, yet these heterogeneities tend to dominate the mechanical and hydraulic properties of the medium. Analytical approaches linking the effects of material properties on seismic attributes, such as attenuation and velocity dispersion, tend to be limited to simple geometries, low fracture densities, and/or non-interacting fractures. Furthermore, the influence of fluid flow within interconnected fractures on P-wave and S-wave attenuation is difficult to accommodate in analytical models. One way to overcome these limitations is through numerical upscaling. In this paper, we apply a numerical upscaling approach based on the theory of quasi-static poroelasticity to fluid-saturated porous media containing randomly distributed horizontal and vertical fractures. The inferred frequency-dependent elastic moduli represent the effective behaviour of the underlying fractured medium if the considered sub-volume has at least the size of a representative elementary volume. We adapt a combined statistical and numerical approach originally proposed for elastic composites to explore wether the overall statistical properties of simple fracture networks can be captured by computationally feasible representative-elementary-volume sizes. Our results indicate that, for the considered scenarios, this is indeed possible and thus represent an important first step towards the estimation of frequency-dependent effective moduli of realistic fracture networks.