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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

We suggest a new method to determine the piecewise-continuous vertical distribution of instantaneous velocities within sediment layers, using different order time-domain effective velocities on their top and bottom points. We demonstrate our method using a synthetic model that consists of different compacted sediment layers characterized by monotonously increasing velocity, combined with hard rock layers, such as salt or basalt, characterized by constant fast velocities, and low velocity layers, such as gas pockets. We first show that, by using only the root-mean-square velocities and the corresponding vertical travel times (computed from the original instantaneous velocity in depth) as input for a Dix-type inversion, many different vertical distributions of the instantaneous velocities can be obtained (inverted). Some geological constraints, such as limiting the values of the inverted vertical velocity gradients, should be applied in order to obtain more geologically plausible velocity profiles. In order to limit the non-uniqueness of the inverted velocities, additional information should be added. We have derived three different inversion solutions that yield the correct instantaneous velocity, avoiding any *a priori* geological constraints. The additional data at the interface points contain either the average velocities (or depths) or the fourth-order average velocities, or both. Practically, average velocities can be obtained from nearby wells, whereas the fourth-order average velocity can be estimated from the quartic moveout term during velocity analysis. Along with the three different types of input, we consider two types of vertical velocity models within each interval: distribution with a constant velocity gradient and an exponential asymptotically bounded velocity model, which is in particular important for modelling thick layers. It has been shown that, in the case of thin intervals, both models lead to similar results. The method allows us to establish the instantaneous velocities at the top and bottom interfaces, where the velocity profile inside the intervals is given by either the linear or the exponential asymptotically bounded velocity models. Since the velocity parameters of each interval are independently inverted, discontinuities of the instantaneous velocity at the interfaces occur naturally. The improved accuracy of the inverted instantaneous velocities is particularly important for accurate time-to-depth conversion.

When a seismic source is placed in the water at a height less than a wavelength from the water–solid interface, a prominent S-wave arrival can be observed. It travels kinematically as if it was excited at the projection point of the source on the interface. This non-geometric S-wave has been investigated before, mainly for a free-surface configuration. However, as was shown in a field experiment, the non-geometric S-wave can also be excited at a fluid–solid configuration if the S-wave speed in the solid is less than the sound speed in the water. The amplitude of this wave exponentially decreases when the source is moved away from the interface revealing its evanescent character in the fluid. In the solid, this particular converted mode is propagating as an ordinary S-wave and can be transmitted and reflected as such. There is a specific region of horizontal slownesses where this non-geometric wave exists, depending on the ratio of the S-wave velocity and the sound speed of water. Only for ratios smaller than 1, this wave appears. Lower ratios result in a wider region of appearance. Due to this property, this particular P-S converted mode can be identified and filtered from other events in the Radon domain.

Gaussian beam migration is a versatile imaging method for geologically complex land areas, which overcomes the limitation of Kirchhoff migration in imaging multiple arrivals and has no steep-dip limits of one-way wave-equation migration. However, its imaging accuracy depends on the geometry of Gaussian beam that is determined by the initial parameter of dynamic ray tracing. As a result, its applications in exploration areas with strong variations in topography and near-surface velocity are limited. Combined with the concept of Fresnel zone and the theory of wave-field approximation in effective vicinity, we present a more robust common-shot Fresnel beam imaging method for complex topographic land areas in this paper. Compared with the conventional Gaussian beam migration for irregular topography, our method improves the beam geometry by limiting its effective half-width with Fresnel zone radius. Moreover, through a quadratic travel-time correction and an amplitude correction that is based on the wave-field approximation in effective vicinity, it gives an accurate method for plane-wave decomposition at complex topography, which produces good imaging results in both shallow and deep zones. Trials of two typical models and its application in field data demonstrated the validity and robustness of our method.

Radial-trace time–frequency peak filtering filters a seismic record along the radial-trace direction rather than the conventional channel direction. It takes the spatial correlation of the reflected events between adjacent channels into account. Thus, radial-trace time–frequency peak filtering performs well in denoising and enhancing the continuity of reflected events. However, in the seismic record there is often random noise whose energy is concentrated in certain directions; the noise in these directions is correlative. We refer to this kind of random noise (that is distributed randomly in time but correlative in the space) as directional random noise. Under radial-trace time–frequency peak filtering, the directional random noise will be treated as signal and enhanced when this noise has same direction as the signal. Therefore, we need to identify the directional random noise before the filtering. In this paper, we test the linearity of signal and directional random noise in time using the Hurst exponent. The time series of signals with high linearity lead to large Hurst exponent value; however, directional random noise is a random series in time without a fixed waveform and thus its linearity is low; therefore, we can differentiate the signal and directional random noise by the Hurst exponent values. The directional random noise can then be suppressed by using a long filtering window length during the radial-trace time–frequency peak filtering. Synthetic and real data examples show that the proposed method can remove most directional random noise and can effectively recover the reflected events.

Reverse time migration backscattered events are produced by the cross-correlation between waves reflected from sharp interfaces (e.g., salt bodies). These events, along with head waves and diving waves, produce the so-called *reverse time migration* artefacts, which are visible as low wavenumber energy on migrated images. Commonly, these events are seen as a drawback for the *reverse time migration* method because they obstruct the image of the geologic structure, which is the real objective for the process. In this paper, we perform numeric and theoretical analysis to understand the *reverse time migration* backscattering energy in conventional and extended images. We show that the *reverse time migration* backscattering contains a measure of the synchronization and focusing information between the source and receiver wavefields. We show that this synchronization and focusing information is sensitive to velocity errors; this implies that a correct velocity model produces reverse time migration backscattering with maximum energy. Therefore, before filtering the reverse time migration backscattered energy, we should try to obtain a model that maximizes it.

We propose new implicit staggered-grid finite-difference schemes with optimal coefficients based on the sampling approximation method to improve the numerical solution accuracy for seismic modelling. We first derive the optimized implicit staggered-grid finite-difference coefficients of arbitrary even-order accuracy for the first-order spatial derivatives using the plane-wave theory and the direct sampling approximation method. Then, the implicit staggered-grid finite-difference coefficients based on sampling approximation, which can widen the range of wavenumber with great accuracy, are used to solve the first-order spatial derivatives. By comparing the numerical dispersion of the implicit staggered-grid finite-difference schemes based on sampling approximation, Taylor series expansion, and least squares, we find that the optimal implicit staggered-grid finite-difference scheme based on sampling approximation achieves greater precision than that based on Taylor series expansion over a wider range of wavenumbers, although it has similar accuracy to that based on least squares. Finally, we apply the implicit staggered-grid finite difference based on sampling approximation to numerical modelling. The modelling results demonstrate that the new optimal method can efficiently suppress numerical dispersion and lead to greater accuracy compared with the implicit staggered-grid finite difference based on Taylor series expansion. In addition, the results also indicate the computational cost of the implicit staggered-grid finite difference based on sampling approximation is almost the same as the implicit staggered-grid finite difference based on Taylor series expansion.

This paper describes least-squares reverse-time migration. The method provides the exact adjoint operator pair for solving the linear inverse problem, thereby enhancing the convergence of gradient-based iterative linear inversion methods. In this formulation, modified source wavelets are used to correct the source signature imprint in the predicted data. Moreover, a roughness constraint is applied to stabilise the inversion and reduce high-wavenumber artefacts. It is also shown that least-squares migration implicitly applies a deconvolution imaging condition. Three numerical experiments illustrate that this method is able to produce seismic reflectivity images with higher resolution, more accurate amplitudes, and fewer artefacts than conventional reverse-time migration. The methodology is currently feasible in 2-D and can naturally be extended to 3-D when computational resources become more powerful.

Recent advances in survey design have led to conventional common-midpoint-based analysis being replaced by subsurface-based seismic acquisition analysis, with emphasis on advanced techniques of illumination analysis. Among them is the so-called focal beam method, which is a wave-equation-based seismic illumination analysis method. The objective of the focal beam method is to provide a quantitative insight into the combined influence of acquisition geometry, overburden structure, and migration operators on the resolution and angle-dependent amplitude fidelity of the image. The method distinguishes between illumination and sensing capability of a particular acquisition geometry by computing the focal source beam and the focal detector beam, respectively. Sensing is related to the detection properties of a detector configuration, whereas illumination is related to the emission properties of a source configuration. The focal source beam analyses the incident wavefield at a specific subsurface grid point from all available sources, whereas the focal detector beam analyses the sensing wavefield reaching at the detector locations from the same subsurface grid point. In the past, this method could only address illumination by primary reflections. In this paper, we will extend the concept of the focal beam method to incorporate the illumination due to the surface and internal multiples. This in fact complies with the trend of including multiples in the imaging process. Multiple reflections can illuminate a target location from other angles compared with primary reflections, resulting in a higher resolution and an improved illumination. We demonstrate how an acquisition-related footprint can be corrected using both the surface and the internal multiples.

]]>In many practical cases, it is necessary to characterize the explored area with a regular set of geodata. Regular matrix data (e.g., ordinary maps) are calculated via existing data interpolation and extrapolation. For low frequency (oversampled) data acquired within a dense profile net (e.g., seismic three-dimensional structural or gravity mapping), this procedure is mathematically more or less stable and, to a certain extent, unique since we might neglect discrepancies resulting from different interpolations. The situation is quite different for high-resolution and high-frequency contaminated data (e.g., raw seismic attributes or geochemistry measurements) represented by sparse profiling. Considering the variety of exploration cases, the investigation of different interpolation algorithm efficiency seems very important. Since it is impossible to compare all algorithms by means of formal mathematics, we have designed a test program. A representative set of seismic attribute maps has been artificially destroyed by introducing blank values (from 20% up to 95%) and then restored by different interpolation algorithms— bicubic, bilinear, nearest neighbor, and “smart averaging.” Smart averaging interpolation is done in a “live” window. The position, form, and size of the window are determined by some mathematical criterion on a trial-and-error basis. Discrepancies between restored and initial (true) data have been assessed and analysed. It is shown that the total (absolute) efficiency and comparative (relative) efficiency of the algorithms depend mostly upon the initial interpolant data characteristics. Identifying the best interpolation algorithm for all interpretive cases seems impossible. Some aspects of data processing are discussed in connection with interpolation accuracy.

Attenuation compensation in reverse-time migration has been shown to improve the resolution of the seismic image. In this paper, three essential aspects of implementing attenuation compensation in reverse-time migration are studied: the physical justification of attenuation compensation, the choice of imaging condition, and the choice of a low-pass filter. The physical illustration of attenuation compensation supports the mathematical implementation by reversing the sign of the absorption operator and leaving the sign of the dispersion operator unchanged in the decoupled viscoacoustic wave equation. Further theoretical analysis shows that attenuation compensation in reverse-time migration using the two imaging conditions (cross-correlation and source-normalized cross-correlation) is able to effectively mitigate attenuation effects. In numerical experiments using a simple-layered model, the source-normalized cross-correlation imaging condition may be preferable based on the criteria of amplitude corrections. The amplitude and phase recovery to some degree depend on the choice of a low-pass filter. In an application to a realistic Marmousi model with added *Q*, high-resolution seismic images with correct amplitude and kinematic phase are obtained by compensating for both absorption and dispersion effects. Compensating for absorption only can amplify the image amplitude but with a shifted phase.

Distributed acoustic sensing is a novel technology for seismic acquisition. In this technology, strain changes induced by seismic waves impinging on an optical fibre are monitored. Due to the fact that glass is relatively rigid, straight glass fibres are not sensitive to broadside waves. We suggest using distributed acoustic sensing systems with fibres helically wound around cables. One increases the fibre sensitivity to broadside waves by decreasing the fibre wrapping angle (the angle between the fibre axis and the plane normal to the cable axis). The optimal wrapping angle is chosen to minimize the impact of Rayleigh waves on the signal measured. This angle depends on the cable Poisson ratio, and it is approximately equal to 30° for cables composed of plastic. For reliable detection of seismic waves, one needs a good mechanical contact between the cable and the surrounding medium. On the other hand, the sensitivity of distributed acoustic sensing systems to primary waves can be significantly reduced if the cable is placed in a cemented borehole.

In tight gas sands, the signal-to-noise ratio of nuclear magnetic resonance log data is usually low, which limits the application of nuclear magnetic resonance logs in this type of reservoir. This project uses the method of wavelet-domain adaptive filtering to denoise the nuclear magnetic resonance log data from tight gas sands. The principles of the maximum correlation coefficient and the minimum root mean square error are used to decide on the optimal basis function for wavelet transformation. The feasibility and the effectiveness of this method are verified by analysing the numerical simulation results and core experimental data. Compared with the wavelet thresholding denoise method, this adaptive filtering method is more effective in noise filtering, which can improve the signal-to-noise ratio of nuclear magnetic resonance data and the inversion precision of transverse relaxation time *T*_{2} spectrum. The application of this method to nuclear magnetic resonance logs shows that this method not only can improve the accuracy of nuclear magnetic resonance porosity but also can enhance the recognition ability of tight gas sands in nuclear magnetic resonance logs.

Seismoelectric coupling coefficients are difficult to predict theoretically because they depend on a large numbers of rock properties, including porosity, permeability, tortuosity, etc. The dependence of the coupling coefficient on rock properties such as permeability requires experimental data. In this study, we carry out a set of laboratory measurements to determine the dependence of seismoelectric coupling coefficient on permeability. We use both an artificial porous “sandstone” sample, with cracks, built using quartz-sand and Berea sandstone samples. The artificial sample is a cube with 39% porosity. Its permeability levels are anisotropic: 14.7 D, 13.8 D, and 8.3 D in the *x*-, *y*-, and *z*-directions, respectively. Seismoelectric measurements are performed in a water tank in the frequency range of 20 kHz–90 kHz. A piezoelectric P-wave source is used to generate an acoustic wave that propagates through the sample from the three different (*x*, *y*, and *z*) directions. The amplitudes of the seismoelectric signal induced by the acoustic waves vary with the direction. The highest signal is in the direction of the highest permeability, and the lowest signal is in the direction of the lowest permeability. Since the porosity of the sample is constant, the results directly show the dependence of seismoelectric coefficients on permeability. Seismoelectric measurements with natural rocks are performed using Berea sandstone 500 and 100 samples. Because the Berea samples are nearly isotropic in permeability, the amplitudes of the seismoelectric signals induced in the different directions are the same within the measurement error. Because the permeability of Berea 500 is higher than that of Berea 100, the amplitude of the seismoelectric signals induced in Berea 500 is higher than those in Berea 100. To determine the relative contributions of porosity and permeability on seismoelectric conversion, we carried out an analysis, using Pride (1994) formulation and Kozeny–Carman relationship; the normalized amplitudes of seismoelectric coupling coefficients in three directions are calculated and compared with the experimental results. The results show that the seismoelectric conversion is related to permeability in the frequency range of measurements. This is an encouraging result since it opens the possibility of determining the permeability of a formation from seismoelectric measurements.

In theory, the streaming potential coefficient depends not only on the zeta potential but also on the permeability of the rocks that partially determines the surface conductivity of the rocks. However, in practice, it is hard to show the permeability dependence of streaming potential coefficients because of the variation of zeta potential from sample to sample. To study permeability dependence of streaming potential, including the effects of the variation of the zeta potential and surface conductance due to the difference in mineral compositions between samples, we perform measurements on 12 consolidated samples, including natural and artificial samples saturated with 7 different NaCl solutions to determine the streaming potential coefficients. The results have shown that the streaming potential coefficients strongly depend on the permeability of the samples for low fluid conductivity. When the fluid conductivity is larger than than 0.50 S/m for the natural samples or 0.25 S/m for the artificial ceramic samples, the streaming potential coefficient is independent of permeability. This behavior is quantitatively explained by a theoretical model.

This paper presents a case study of mapping basement structures in the northwestern offshore of Abu Dhabi using high-resolution aeromagnetic data. Lineament analysis was carried out on the derivatives of the reduced-to-the-pole magnetic data, along with supporting information from published geologic data. The lineament analysis suggests three well-defined basement trends in the north–south, northeast–southwest, and northwest–southeast directions. The reduced-to-the-pole magnetic data reveal high positive magnetic anomalies hypothesized to be related to intra-basement bodies in the deep seated Arabian Shield. Depth to basement was estimated using spectral analysis and Source Parameter Imaging techniques. The spectral analysis suggests that the intruded basement blocks are at the same average depth level (around 8.5 km). The estimated Source Parameter Imaging depths from gridded reduced-to-the-pole data are ranged between 4 km and 12 km with a large depth variation within small distances. These estimated depths prevent a reliable interpretation of the nature of the basement relief. However, low-pass filtering of the horizontal local wavenumber data across two profiles shows that the basement terrain is characterized by a basin-like structure trending in the northeast–southwest direction with a maximum depth of 10 km. Two-dimensional forward magnetic modelling across the two profiles suggests that the high positive magnetic anomalies over the basin could be produced by intrusion of mafic igneous rocks with high susceptibility values (0.008 to 0.016 SI.

Modern airborne transient electromagnetic surveys typically produce datasets of thousands of line kilometres, requiring careful data processing in order to extract as much and as reliable information as possible. When surveys are flown in populated areas, data processing becomes particularly time consuming since the acquired data are contaminated by couplings to man-made conductors (power lines, fences, pipes, etc.). Coupled soundings must be removed from the dataset prior to inversion, and this is a process that is difficult to automate. The signature of couplings can be both subtle and difficult to describe in mathematical terms, rendering removal of couplings mostly an expensive manual task for an experienced geophysicist.

Here, we try to automate the process of removing couplings by means of an artificial neural network. We train an artificial neural network to recognize coupled soundings in manually processed reference data, and we use this network to identify couplings in other data. The approach provides a significant reduction in the time required for data processing since one can directly apply the network to the raw data. We describe the neural network put to use and present the inputs and normalizations required for maximizing its effectiveness. We further demonstrate and assess the training state and performance of the network before finally comparing inversions based on unprocessed data, manually processed data, and artificial neural network automatically processed data. The results show that a well-trained network can produce high-quality processing of airborne transient electromagnetic data, which is either ready for inversion or in need of minimal manual processing. We conclude that the use of artificial neural network scan significantly reduce the processing time and its costs by as much as 50%.

A detailed magnetotelluric survey was conducted in 2013 in the Sehqanat oil field, southwestern Iran to map the geoelectrical structures of the sedimentary Zagros zone, particularly the boundary between the Gachsaran Formation acting as cap rock and the Asmari Formation as the reservoir. According to the electrical well logs, a large resistivity contrast exists between the two formations. The Gachsaran Formation is formed by tens to hundreds of metres of evaporites and it is highly conductive (ca. 1 Ωm–10 Ωm), and the Asmari Formation consists of dense carbonates, which are considerably more resistive (more than 100 Ωm). Broadband magnetotelluric data were collected along five southwest–northeast directed parallel lines with more than 600 stations crossing the main geological trend. Although dimensionality and strike analysis of the magnetotelluric transfer functions showed that overall they satisfied local 2D conditions, there were also strong 3D conditions found in some of the sites. Therefore, in order to obtain a more reliable image of the resistivity distribution in the Sehqanat oil field, in addition to standard 2D inversion, we investigated to what extent 3D inversion of the data was feasible and what improvements in the resistivity image could be obtained. The 2D inversion models using the determinant average of the impedance tensor depict the main resistivity structures well, whereas the estimated 3D model shows significantly more details although problems were encountered in fitting the data with the latter. Both approaches resolved the Gachsaran–Asmari transition from high conductivity to moderate conductivity. The well-known Sehqanat anticline could also be delineated throughout the 2D and 3D resistivity models as a resistive dome-shaped body in the middle parts of the magnetotelluric profiles.

To reduce the numerical errors arising from the improper enforcement of the artificial boundary conditions on the distant surface that encloses the underground part of the subsurface, we present a finite-element–infinite-element coupled method to significantly reduce the computation time and memory cost in the 2.5D direct-current resistivity inversion. We first present the boundary value problem of the secondary potential. Then, a new type of infinite element is analysed and applied to replace the conventionally used mixed boundary condition on the distant boundary. In the internal domain, a standard finite-element method is used to derive the final system of linear equations. With a novel shape function for infinite elements at the subsurface boundary, the final system matrix is sparse, symmetric, and independent of source electrodes. Through lower upper decomposition, the multi-pole potentials can be swiftly obtained by simple back-substitutions. We embed the newly developed forward solution to the inversion procedure. To compute the sensitivity matrix, we adopt the efficient adjoint equation approach to further reduce the computation cost. Finally, several synthetic examples are tested to show the efficiency of inversion.