We investigate a novel way to introduce resistivity models deriving from airborne electromagnetic surveys into regional geological modelling. Standard geometrical geological modelling can be strengthened using geophysical data. Here, we propose to extract information contained in a resistivity model in the form of local slopes that constrain the modelling of geological interfaces. The proposed method is illustrated on an airborne electromagnetic survey conducted in the region of Courtenay in France. First, a resistivity contrast corresponding to the clay/chalk interface was interpreted confronting the electromagnetic soundings to boreholes. Slopes were then sampled on this geophysical model and jointly interpolated with the clay/chalk interface documented in boreholes using an implicit 3D potential-field method. In order to evaluate this new joint geophysical–geological model, its accuracy was compared with that of both pure geological and pure geophysical models for various borehole configurations. The proposed joint modelling yields the most accurate clay/chalk interface whatever the number and location of boreholes taken into account for modelling and validation. Compared with standard geological modelling, the approach introduces in between boreholes geometrical information derived from geophysical results. Compared with conventional resistivity interpretation of the geophysical model, it reduces drift effects and honours the boreholes. The method therefore improves what is commonly obtained with geological or geophysical data separately, making it very attractive for robust 3D geological modelling of the subsurface.

To better understand the effect of fluid distribution on the electric response of rocks saturated with oil and brine, we conducted experimental studies on the complex electrical impedance in a Berea sandstone, together with *in situ* acquisitions of oil distribution images employing a high-resolution medical X-ray computed tomography. We performed two tests of brine displacement by oil under high (10 MPa) and low (5 MPa) pressures, which were accompanied by fingering and stable displacement patterns, respectively. The measured complex impedance data were fitted to the Cole model to obtain the resistance, capacitance, peak frequency of the imaginary impedance, and the exponent α of the rock–fluid system. With increasing oil saturation, the resistance showed an increasing trend, whereas the other three parameters decreased. The fingering displacement exhibited lower resistance and capacitance than the stable displacement. The analysis of the resistance changes using a simple parallel connection model indicates that there are more components of residual brine in parallel connections in the fingering pattern than in the stable displacement pattern at the same saturation. We also interpreted the normalised changes in the capacitance (or apparent dielectric constant) with respect to the oil saturation via an analysis of the shape factor of fluid distribution based on the Maxwell–Wagner–Brugermann–Hanai model. The changes in the shape factor suggest that the pinch-off of the brine in parallel connection by the oil is a dominant mechanism reducing the capacitance. In the stable displacement, most of the connections in the brine phase are immediately pinched off by oil displacement front at a local oil saturation of 65%. Conversely, in the fingering displacement, there is a transition from the bulk or layered brine to the pinched-off at a local oil saturation below 60%. The analyses indicate that the difference in the fluid distribution under different fluid conditions is responsible for the non-Archie behaviour.

This paper addresses two artefacts inherent to marine towed-streamer surveys: 1) ghost reflections and 2) too sparse a sampling in the crossline direction. A ghost reflection is generated when an upcoming reflection bounces off the sea surface back into the sensors and can, in principle, be removed by decomposing the measured wavefield into its up- and downgoing constituents. This process requires a dense sampling of the wavefield in both directions along and perpendicular to the streamers. A dense sampling in the latter direction is, however, often impossible due to economical and operational constraints. Recent multi-component streamers have been designed to record the spatial gradients on top of the pressure, which not only benefits the wavefield decomposition but also facilitates a lower-than-Nyquist sampling rate of the pressure. In this paper, wavefield reconstruction and deghosting are posed as a joint inverse problem. We present two approaches to establish a system matrix that embeds both a deghosting and an interpolation operator. The first approach is derived *with* a ghost model, whereas the second approach is derived *without* a ghost model. The embodiment of a ghost model leads to an even lower sampling rate but relies on a more restrictive assumption on the sea surface.

In a multi-parameter waveform inversion, the choice of the parameterisation influences the results and their interpretations because leakages and the tradeoff between parameters can cause artefacts. We review the parameterisation selection when the inversion focuses on the recovery of the intermediate-to-long wavenumbers of the compressional velocities from the compressional body (P) waves. Assuming a transverse isotropic medium with a vertical axis of symmetry and weak anisotropy, analytical formulas for the radiation patterns are developed to quantify the tradeoff between the shear velocity and the anisotropic parameters and the effects of setting to zero the shear velocity in the acoustic approach. Because, in an anisotropic medium, the radiation patterns depend on the angle of the incident wave with respect to the vertical axis, two particular patterns are discussed: a transmission pattern when the ingoing and outgoing slowness vectors are parallel and a reflection pattern when the ingoing and outgoing slowness vectors satisfy Snell's law. When the inversion aims at recovering the long-to-intermediate wavenumbers of the compressional velocities from the P-waves, we propose to base the parameterisation choice on the transmission patterns. Since the P-wave events in surface seismic data do not constrain the background (smooth) vertical velocity due to the velocity/depth ambiguity, the preferred parameterisation contains a parameter that has a transmission pattern concentrated along the vertical axis. This parameter can be fixed during the inversion which reduces the size of the model space. The review of several parameterisations shows that the vertical velocity, the Thomsen parameter δ, or the Thomsen parameter ε have a transmission pattern along the vertical axis depending on the parameterisation choice. The review of the reflection patterns of those selected parameterisations should be done in the elastic context. Indeed, when reflection data are also inverted, there are potential leakages of the shear parameter at intermediate angles when we carry out acoustic inversion.

Single-component towed-streamer marine data acquisition records the pressure variations of the upgoing compressional waves followed by the polarity-reversed pressure variations of downgoing waves, creating sea-surface ghost events in the data. The sea-surface ghost for constant-depth towed-streamer marine data acquisition is usually characterised by a ghost operator acting on the upgoing waves, which can be formulated as a filtering process in the frequency–wavenumber domain. The deghosting operation, usually via the application of the inverse Wiener filter related to the ghost operator, acts on the signal as well as the noise. The noise power transfer into the deghosted data is proportional to the power spectrum of the inverse Wiener filter and is amplifying the noise strongly at the notch wavenumbers and frequencies of the ghost operator. For variable-depth streamer acquisition, the sea-surface ghost cannot be described any longer as a wavenumber–frequency operator but as a linear relationship between the wavenumber–frequency representation of the upgoing waves at the sea surface and the data in the space–frequency domain. In this article, we investigate how the application of the inverse process acts on noise. It turns out that the noise magnification is less severe with variable-depth streamer data, as opposed to constant depth, and is inversely proportional to the local slant of the streamer. We support this statement via application of the deghosting process to real and numerical random noise. We also propose a more general concept of a wavenumber–frequency ghost power transfer function, applicable for variable-depth streamer acquisition, and demonstrate that the inverse of the proposed variable-depth ghost power transfer function can be used to approximately quantify the action of the variable-depth streamer deghosting process on noise.

Surface waves are often used to estimate a near-surface shear-velocity profile. The inverse problem is solved for the locally one-dimensional problem of a set of homogeneous horizontal elastic layers. The result is a set of shear velocities, one for each layer. To obtain a P-wave velocity profile, the P-guided waves should be included in the inversion scheme. As an alternative to a multi-layered model, we consider a simple smooth acoustic constant-density velocity model, which has a negative constant vertical depth gradient of the squared P-wave slowness and is bounded by a free surface at the top and a homogeneous half-space at the bottom. The exact solution involves Airy functions and provides an analytical expression for the dispersion equation. If the ratio is sufficiently small, the dispersion curves can be picked from the seismic data and inverted for the continuous P-wave velocity profile. The potential advantages of our model are its low computational cost and the fact that the result can serve as a smooth starting model for full-waveform inversion. For the latter, a smooth initial model is often preferred over a rough one. We test the inversion approach on synthetic elastic data computed for a single-layer P-wave model and on field data, both with a small ratio. We find that a single-layer model can recover either the shallow or deeper part of the profile but not both, when compared with the result of a multi-layer inversion that we use as a reference. An extension of our analytic model to two layers above a homogeneous half-space, each with a constant vertical gradient of the squared P-wave slowness and connected in a continuous manner, improves the fit of the picked dispersion curves. The resulting profile resembles a smooth approximation of the multi-layered one but contains, of course, less detail. As it turns out, our method does not degrade as gracefully as, for instance, diving-wave tomography, and we can only hope to fit a subset of the dispersion curves. Therefore, the applicability of the method is limited to cases where the ratio is small and the profile is sufficiently simple. A further extension of the two-layer model to more layers, each with a constant depth gradient of the squared slowness, might improve the fit of the modal structure but at an increased cost.

Seismic field data are often irregularly or coarsely sampled in space due to acquisition limits. However, complete and regular data need to be acquired in most conventional seismic processing and imaging algorithms. We have developed a fast joint curvelet-domain seismic data reconstruction method by sparsity-promoting inversion based on compressive sensing. We have made an attempt to seek a sparse representation of incomplete seismic data by curvelet coefficients and solve sparsity-promoting problems through an iterative thresholding process to reconstruct the missing data. In conventional iterative thresholding algorithms, the updated reconstruction result of each iteration is obtained by adding the gradient to the previous result and thresholding it. The algorithm is stable and accurate but always requires sufficient iterations. The linearised Bregman method can accelerate the convergence by replacing the previous result with that before thresholding, thus promoting the effective coefficients added to the result. The method is faster than conventional one, but it can cause artefacts near the missing traces while reconstructing small-amplitude coefficients because some coefficients in the unthresholded results wrongly represent the residual of the data. The key process in the joint curvelet-domain reconstruction method is that we use both the previous results of the conventional method and the linearised Bregman method to stabilise the reconstruction quality and accelerate the recovery for a while. The acceleration rate is controlled through weighting to adjust the contribution of the acceleration term and the stable term. A fierce acceleration could be performed for the recovery of comparatively small gaps, whereas a mild acceleration is more appropriate when the incomplete data has a large gap of high-amplitude events. Finally, we carry out a fast and stable recovery using the trade-off algorithm. Synthetic and field data tests verified that the joint curvelet-domain reconstruction method can effectively and quickly reconstruct seismic data with missing traces.

Different theoretical and laboratory studies on the propagation of elastic waves in layered hydrocarbon reservoir have shown characteristic velocity dispersion and attenuation of seismic waves. The wave-induced fluid flow between mesoscopic-scale heterogeneities (larger than the pore size but smaller than the predominant wavelengths) is the most important cause of attenuation for frequencies below 1 kHz. Most studies on mesoscopic wave-induced fluid flow in the seismic frequency band are based on the representative elementary volume, which does not consider interaction of fluid flow due to the symmetrical structure of representative elementary volume. However, in strongly heterogeneous media with unsymmetrical structures, different courses of wave-induced fluid flow may lead to the interaction of the fluid flux in the seismic band; this has not yet been explored. This paper analyses the interaction of different courses of wave-induced fluid flow in layered porous media. We apply a one-dimensional finite-element numerical creep test based on Biot's theory of consolidation to obtain the fluid flux in the frequency domain. The characteristic frequency of the fluid flux and the strain rate tensor are introduced to characterise the interaction of different courses of fluid flux. We also compare the behaviours of characteristic frequencies and the strain rate tensor on two scales: the local scale and the global scale. It is shown that, at the local scale, the interaction between different courses of fluid flux is a dynamic process, and the weak fluid flux and corresponding characteristic frequencies contain detailed information about the interaction of the fluid flux. At the global scale, the averaged strain rate tensor can facilitate the identification of the interaction degree of the fluid flux for the porous medium with a random distribution of mesoscopic heterogeneities, and the characteristic frequency of the fluid flux is potentially related to that of the peak attenuation. The results are helpful for the prediction of the distribution of oil–gas patches based on the statistical properties of phase velocities and attenuation in layered porous media with random disorder.

Using seismic attributes such as coherence and curvature to characterise faults not only can improve the efficiency of seismic interpretation but also can expand the capability to detect faults. The coherence and curvature have been widely applied to characterising faults for years. These two methods detect faults based on the similarity of seismic waveforms and shapes of the reflectors, respectively, and they are complementary to each other and both have advantages and disadvantages in fault characterisation. A recent development in fault characterisation based on reflector shapes has been the use of the rate of change of curvature. Through an application to the seismic data from Western Tazhong of the Tarim Basin, China, it was demonstrated that the rate of change of curvature is more capable of detecting subtle faults having quite small throws and heaves. However, there often exist multiple extreme values indicating the same fault when applying the rate of change of curvature, which significantly degrades the signal-to-noise ratio of the computation result for multiple extrema interfering with each other. To resolve this problem, we propose the use of a linear combination of arctangent and proportional functions as the directrix of a cylindrical surface to fit the fault model and calculate its third derivative, which can then be used to characterise the fault. Through an application to the 3D seismic data from Western Tazhong of the Tarim Basin, the results show that the proposed method not only retains the same capability to detect subtle faults having small throws as the curvature change rate but also greatly improves the signal-to-noise ratio of the calculated result.

Naturally occurring gas hydrates contain significant amounts of natural gas that might be produced as an energy resource in the foreseeable future. Thus, it is necessary to understand the pore-space characteristics of hydrate reservoirs, particularly the pore-scale distribution of the hydrate and its interaction with the sediment. Four end-member models for hydrate distribution in the pore space are pore filling, sediment-frame component, envelope cementing, and contact cementing. The goal of this study is to compare the models with pore-scale hydrate distributions obtained in laboratory-formed hydrates. Our results verify hydrate pore-scale distributions by direct, visual observations that were previously implied by indirect, elastic property measurements.

Laboratory measurements were conducted using tetrahydrofuran as a guest molecule since tetrahydrofuran hydrate can be used as a proxy for naturally occurring hydrates. We performed micro X-ray computed tomography to obtain information about the distribution of hydrate in the pore space of synthetic sediment (glass beads). We also made ultrasonic velocity measurements on the same samples. Micro X-ray computed tomography images and ultrasonic velocity measurements both indicate that the tetrahydrofuran hydrate forms in the pore space with a part of the hydrate bridging the grains without touching the grain surfaces. These hydrate-bearing sediments appear to follow a pore-filling model with a portion of the hydrate becoming a load-bearing part of the sediment frame.

The aim of this paper is to add confidence to existing methods using decay shape analysis to detect superparamagnetic responses in airborne electromagnetic data. While expensive to acquire, vertical spatial gradient measurements of the electromagnetic signals can discriminate near-surface superparamagnetic sources. This research investigated the use of horizontal spatial gradients and amplitude information as further indicators of superparamagnetic. High horizontal gradients were shown both theoretically and in field data to help discriminate superparamagnetic from deep mineral targets. Further, superparamagnetic responses have characteristically small amplitudes inconsistent with realistic mineral exploration targets at shallow depths.

This paper deals with the investigation of the Mars subsurface by means of data collected by the Mars Advanced Radar for Subsurface and Ionosphere Sounding working at few megahertz frequencies. A data processing strategy, which combines a simple inversion model and an accurate procedure for data selection is presented. This strategy permits to mitigate the theoretical and practical difficulties of the inverse problem arising because of the inaccurate knowledge of the parameters regarding both the scenario under investigation and the radiated electromagnetic field impinging on the Mars surface. The results presented in this paper show that it is possible to reliably retrieve the electromagnetic properties of deeper structures if such strategy is accurately applied. An example is given here, where the analysis of the data collected on Gemina Lingula, a region of the North Polar layer deposits, allowed us to retrieve permittivity values for the basal unit in agreement with those usually associated to the Earth basaltic rocks.

Statics are an effective approach to correct for complex velocity variations in the near surface, but so far, to a large extent, a general and robust automatic static correction method is still lacking. In this paper, we propose a novel two-phase automatic static correction method, which is capable of handling both primary wave statics (PP statics) and converted-wave statics (S-wave statics). Our method is purely data driven, and it aims at maximizing stacking power in the target zone of the stack image. Low-frequency components of the data are analysed first using an advanced genetic algorithm to estimate seed statics and the time structure for an event of interest, and then the original full-band data are further aligned via the back-and-forth coordinate descent method using the seed statics as initial values and the time structure for event alignment guidance. We apply our new method to two field datasets, i.e., one for 2D PP static correction and the other for 3D S-wave static correction.

To study the impact of modern coal mining on the overlying formation, a full-life-cycle four-dimensional seismic monitoring study has been carried out. Four seismic data campaigns have been performed using flexi-bin geometry with square bins, with total duration of 171 days. The four seismic datasets have been processed with the same processing workflow and parameters; major problems such as statics correction, signal-to-noise ratio, resolution, and consistency processing are addressed taking into account the geological features of the research area. This guarantees that remaining four-dimensional differences between the time-lapse datasets show mostly geological factors due to the coal mining and effects such as surface subsidence. Our four-dimensional seismic monitoring of modern coal mining shows that mined and unmined areas have significant zoning characteristics; coal mining has a direct impact on the overlying formation. The mining leads to obvious event subsidence, which reflects that overlying formations undergo subsidence during the mining process. The overlying formation appears as two zones called caving zone and fractured zone. We determine the fault dip of the overlying formation at one end of the working face to be 56°or so by calculation and conversion. We also see that, during the coal mining process, over time, the overlying formation has a self-recovery capability, which gradually strengthens from the roof siltstone upward to the Aeolian sandstone near the surface. The stability of 20-m coal pillars between working faces displays a strengthening trend and remains safe during the mining process due to both coal seam supporting and formation compaction effects.

Non-hyperbolic generalised moveout approximation is a powerful tool to approximate the travel-time function by using information obtained from two rays. The standard approach for parameter selection is using three parameters defined from zero-offset ray and two parameters obtained from a reference ray. These parameters include the travel time and travel-time derivatives of different order. The original parameter selection implies more fit at zero offset compared with offset from a reference ray. We propose an alternative approach for parameter selection within the frame of generalised moveout approximation by transferring more fit from the zero offset to a reference ray by changing in parameter selection. The modified approximation is tested against the original one in few analytical model examples, including the multi-layered model.

The automatic detection of geological features such as faults and channels is a challenging problem in today's seismic exploration industry. Edge detection filters are generally applied to locate features. It is desirable to reduce noise in the data before edge detection. The application of smoothing or low-pass filters results in noise suppression, but this causes edge blurring as well. Edge-preserving smoothing is a technique that results in simultaneous edge preservation and noise suppression. Until now, edge-preserving smoothing has been carried out on rectangular sampled seismic data. In this paper, an attempt has been made to detect edges by applying edge-preserving smoothing as a pre-processing step in the hexagonally sampled seismic-data spatial domain. A hexagonal approach is an efficient method of sampling and has greater symmetry than a rectangular approach. Here, spiral architecture has been employed to handle the hexagonally sampled seismic data. A comparison of edge-preserving smoothing on both rectangular and hexagonally sampled seismic data is carried out. The data used were provided by Saudi Aramco. It is shown that hexagonal processing results in well-defined edges with fewer computations.

We study the mechanical deformation of fractures under normal stress, via tangent and specific fracture stiffnesses, for different length scales using numerical simulations and analytical insights. First, we revisit an equivalent elastic layer model that leads to two expressions: the tangent stiffness is the sum of an “intrinsic” stiffness and the normal stress, and the specific stiffness is the tangent stiffness divided by the fracture aperture at current stress. Second, we simulate the deformation of rough fractures using a boundary element method where fracture surfaces represented by elastic asperities on an elastic half-space follow a self-affine distribution. A large number of statistically identical “parent” fractures are generated, from which sub-fractures of smaller dimensions are extracted. The self-affine distribution implies that the stress-free fracture aperture increases with fracture length with a power law in agreement with the chosen Hurst exponent. All simulated fractures exhibit an increase in the specific stiffness with stress and an average decrease with increase in length consistent with field observations. The simulated specific and tangent stiffnesses are well described by the equivalent layer model provided the “intrinsic” stiffness slightly decreases with fracture length following a power law. By combining numerical simulations and the analytical model, the effect of scale and stress on fracture stiffness measures can be easily separated using the concept of “intrinsic” stiffness. We learn that the primary reason for the variability in specific stiffness with length comes from the fact that the typical aperture of the self-affine fractures itself scales with the length of the fractures.

In this study, a new two-dimensional inversion algorithm was developed for the inversion of cross-hole direct current resistivity measurements. In the last decades, various array optimisation methods were suggested for resistivity tomography. However, researchers have still collected data by using classical electrode arrays in most cross-hole applications. Therefore, we investigated the accuracy of both the individual and the joint inversion of the classical cross-hole arrays by using both synthetic and field data with the developed algorithm. We showed that the joint inversion of bipole–bipole, pole–bipole, bipole–pole, and pole–tripole electrode arrays gives inverse solutions that are closer to the real model than the individual inversions of the electrode array datasets for the synthetic data inversion. The model resolution matrix of the suggested arrays was used to analyse the inversion results. This model resolution analysis also showed the advantage of the joint inversion of bipole–bipole, pole–bipole, bipole–pole, and pole–tripole arrays. We also used sensitivity sections from each of the arrays and their superpositions to explain why joint inversion gives better resolution than the any individual inversion result.

To investigate the vertical and horizontal impact of reservoir scale on the amplitude-versus-offset characteristics, we conduct seismic numerical simulations on models containing spatially confined lithologic units with different scales. We find that the reservoir scale has a nonlinear effect on the amplitude-versus-offset intercepts and gradients. As the reservoir width increases, amplitude-versus-offset intercept and gradient both first increase, then decrease, and finally remain stable. The amplitude-versus-offset intercept is maximum when the reservoir width is 80% larger than the Fresnel zone radius, whereas the amplitude-versus-offset gradient peaks at 1.5 times the Fresnel zone radius. Both amplitude-versus-offset intercept and gradient are approximately proportional to the reservoir width prior to reaching their maxima. When the lateral extent of the reservoir is more than three times the Fresnel zone radius, the amplitude-versus-offset attributes are constant. Modelling the reservoir thickness shows that intercept and gradient behave in a manner similar to that of tuning of thin beds. Both the amplitude-versus-offset intercept and gradient first increase and then decrease with the thickness, peaking at the tuning thickness. The thickness contribution to amplitude-versus-offset variations is negligible when the thickness is larger than 1.6 times of the tuning thickness. Considering the magnitude of the changes in amplitude-versus-offset intercept and gradient caused by reservoir scale, the width causes a maximum 433% intercept increase and a 344% gradient increase, whereas the thickness causes a maximum 100% intercept increase and a 73% gradient increase. Cross-plotting the amplitude-versus-offset intercept and gradient shows the reservoir scale change gives rise to an anti-clockwise spiraling effect. In conclusion, the lateral and vertical extents of the reservoir both play an important role in amplitude variation with offset. Our analysis shows that the lateral reservoir extent has a larger impact on the amplitude variation with offset than the vertical tuning effect.

Mechanical compaction or loss of porosity due to increase in effective stress is a fundamental geological process that governs many of the rock elastic and transport parameters, all of great importance in exploring and developing subsurface reservoirs. The ability to model the compaction process enables us to improve our understanding of the seismic signature of the basin and better relate the geology of deposition to current porosity, velocity, pore pressure, and other mechanical parameters that depend on the state of compaction of the sediment. In this paper, a set of mathematical equations that can be used to model the plastic deformation associated with primary and secondary loading curves is presented. Compaction laws are posed in terms of natural strain increment formulation often used in plasticity theory to model large deformation. Laboratory and field estimates of constitutive plastic deformation relations for sand–shale mixtures are used in a numerical model that generates estimates of porosity under various pore pressures, shale content, and loading scenarios. These estimates can be used in a variety of settings to predict various basin and reservoir properties associated with different loading conditions and/or sedimentation processes.

The possibility of a time-domain electromagnetic sounding method using excitation and measurement of vertical electric fields to search for and identify deeply buried reservoirs of hydrocarbons offshore is investigated. The method operates on source–receiver offsets, which are several times less than the depth of the reservoir. Geoelectric information is obtained from the transient responses recorded in the pauses between the pulses of electric current in the absence of the source field. The basics of the method, as well as its sensitivity, resolution, and the highest accessible depth of soundings for various geological conditions in a wide range of sea depths, are analyzed. For the analysis, 1D and 3D geoelectric models of hydrocarbon reservoirs are used. It is shown that under existing technologies of excitation and measurement of vertical electric fields, the highest accessible depth of soundings can be up to 4 km. Technology for the inversion and interpretation of transient responses is demonstrated on experimental data.

Analytical models are provided that describe how the elastic compliance, electrical conductivity, and fluid-flow permeability of rocks depend on stress and fluid pressure. In order to explain published laboratory data on how seismic velocities and electrical conductivity vary in sandstones and granites, the models require a population of cracks to be present in a possibly porous host phase. The central objective is to obtain a consistent mean-field analytical model that shows how each modeled rock property depends on the nature of the crack population. The crack populations are described by a crack density, a probability distribution for the crack apertures and radii, and the averaged orientation of the cracks. The possibly anisotropic nature of the elasticity, conductivity, and permeability tensors is allowed for; however, only the isotropic limit is used when comparing to laboratory data. For the transport properties of conductivity and permeability, the percolation effect of the crack population linking up to form a connected path across a sample is modeled. However, this effect is important only in crystalline rock where the host phase has very small conductivity and permeability. In general, the importance of the crack population to the transport properties increases as the host phase becomes less conductive and less permeable.

We propose a combination of Biot's equations for effective stress and the expression for shear failure in a rock to obtain an expression for minimum pore pressure in a stable vertical well bore. We show that a Biot's coefficient calculated from logging data in the Hejre Field, North Sea, is significantly different from 1. The log-derived Biot's coefficient is above 0.8 in the Shetland Chalk Group and in the Tyne Group, and 0.6–0.8 in the Heno Sandstone Formation. We show that the effective vertical and horizontal stresses obtained using the log-derived Biot's coefficient result in a drilling window for a vertical well larger than if approximating Biot's coefficient by 1. The estimation of the Biot's coefficient is straightforward in formations with a stiff frame, whereas in formations such as shales, caution has to be taken. We discuss the consequence of assumptions made on the mineral composition of shales as unphysical results could be obtained when choosing inappropriate mineral moduli.

We present a new method of transforming borehole gravity meter data into vertical density logs. This new method is based on the regularized spectral domain deconvolution of density functions. It is a novel alternative to the “classical” approach, which is very sensitive to noise, especially for high-definition surveys with relatively small sampling steps. The proposed approach responds well to vertical changes of density described by linear and polynomial functions. The model used is a vertical cylinder with large outer radius (flat circular plate) crossed by a synthetic vertical borehole profile. The task is formulated as a minimization problem, and the result is a low-pass filter (controlled by a regularization parameter) in the spectral domain. This regularized approach is tested on synthetic datasets with noise and gives much more stable solutions than the classical approach based on the infinite Bouguer slab approximation. Next, the tests on real-world datasets are presented. The properties and presented results make our proposed approach a viable alternative to the other processing methods of borehole gravity meter data based on horizontally layered formations.

Existing and commonly used in industry nowadays, closed-form approximations for a P-wave reflection coefficient in transversely isotropic media are restricted to cases of a vertical and a horizontal transverse isotropy. However, field observations confirm the widespread presence of rock beds and fracture sets tilted with respect to a reflection boundary. These situations can be described by means of the transverse isotropy with an arbitrary orientation of the symmetry axis, known as tilted transversely isotropic media. In order to study the influence of the anisotropy parameters and the orientation of the symmetry axis on P-wave reflection amplitudes, a linearised 3D P-wave reflection coefficient at a planar weak-contrast interface separating two weakly anisotropic tilted tranversely isotropic half-spaces is derived. The approximation is a function of the incidence phase angle, the anisotropy parameters, and symmetry axes tilt and azimuth angles in both media above and below the interface. The expression takes the form of the well-known amplitude-versus-offset “Shuey-type” equation and confirms that the influence of the tilt and the azimuth of the symmetry axis on the P-wave reflection coefficient even for a weakly anisotropic medium is strong and cannot be neglected. There are no assumptions made on the symmetry-axis orientation angles in both half-spaces above and below the interface. The proposed approximation can be used for inversion for the model parameters, including the orientation of the symmetry axes. Obtained amplitude-versus-offset attributes converge to well-known approximations for vertical and horizontal transverse isotropic media derived by Rüger in corresponding limits. Comparison with numerical solution demonstrates good accuracy.

Image gathers as a function of subsurface offset are an important tool for the inference of rock properties and velocity analysis in areas of complex geology. Traditionally, these gathers are thought of as multidimensional correlations of the source and receiver wavefields. The bottleneck in computing these gathers lies in the fact that one needs to store, compute, and correlate these wavefields for all shots in order to obtain the desired image gathers. Therefore, the image gathers are typically only computed for a limited number of subsurface points and for a limited range of subsurface offsets, which may cause problems in complex geological areas with large geologic dips. We overcome increasing computational and storage costs of extended image volumes by introducing a formulation that avoids explicit storage and removes the customary and expensive loop over shots found in conventional extended imaging. As a result, we end up with a matrix–vector formulation from which different image gathers can be formed and with which amplitude-versus-angle and wave-equation migration velocity analysis can be performed without requiring prior information on the geologic dips. Aside from demonstrating the formation of two-way extended image gathers for different purposes and at greatly reduced costs, we also present a new approach to conduct automatic wave-equation-based migration-velocity analysis. Instead of focusing in particular offset directions and preselected subsets of subsurface points, our method focuses every subsurface point for all subsurface offset directions using a randomized probing technique. As a consequence, we obtain good velocity models at low cost for complex models without the need to provide information on the geologic dips.

Various models have been proposed to link partial gas saturation to seismic attenuation and dispersion, suggesting that the reflection coefficient should be frequency-dependent in many cases of practical importance. Previous approaches to studying this phenomenon typically have been limited to single-interface models. Here, we propose a modelling technique that allows us to incorporate frequency-dependent reflectivity into convolutional modelling. With this modelling framework, seismic data can be synthesised from well logs of velocity, density, porosity, and water saturation. This forward modelling could act as a basis for inversion schemes aimed at recovering gas saturation variations with depth. We present a Bayesian inversion scheme for a simple thin-layer case and a particular rock physics model and show that, although the method is very sensitive to prior information and constraints, both gas saturation and layer thickness theoretically can be estimated in the case of interfering reflections.

Spectral decomposition is a powerful tool that can provide geological details dependent upon discrete frequencies. Complex spectral decomposition using inversion strategies differs from conventional spectral decomposition methods in that it produces not only frequency information but also wavelet phase information. This method was applied to a time-lapse three-dimensional seismic dataset in order to test the feasibility of using wavelet phase changes to detect and map injected carbon dioxide within the reservoir at the Ketzin carbon dioxide storage site, Germany. Simplified zero-offset forward modelling was used to help verify the effectiveness of this technique and to better understand the wavelet phase response from the highly heterogeneous storage reservoir and carbon dioxide plume. Ambient noise and signal-to-noise ratios were calculated from the raw data to determine the extracted wavelet phase. Strong noise caused by rainfall and the assumed spatial distribution of sandstone channels in the reservoir could be correlated with phase anomalies. Qualitative and quantitative results indicate that the wavelet phase extracted by the complex spectral decomposition technique has great potential as a practical and feasible tool for carbon dioxide detection at the Ketzin pilot site.

Reverse-time migration gives high-quality, complete images by using full-wave extrapolations. It is thus not subject to important limitations of other migrations that are based on high-frequency or one-way approximations. The cross-correlation imaging condition in two-dimensional pre-stack reverse-time migration of common-source data explicitly sums the product of the (forward-propagating) source and (backward-propagating) receiver wavefields over all image times. The primary contribution at any image point travels a minimum-time path that has only one (specular) reflection, and it usually corresponds to a local maximum amplitude. All other contributions at the same image point are various types of multipaths, including prismatic multi-arrivals, free-surface and internal multiples, converted waves, and all crosstalk noise, which are imaged at later times, and potentially create migration artefacts. A solution that facilitates inclusion of correctly imaged, non-primary arrivals and removal of the related artefacts, is to save the depth versus incident angle slice at each image time (rather than automatically summing them). This results in a three-parameter (incident angle, depth, and image time) common-image volume that integrates, into a single unified representation, attributes that were previously computed by separate processes. The volume can be post-processed by selecting any desired combination of primary and/or multipath data before stacking over image time. Separate images (with or without artifacts) and various projections can then be produced without having to remigrate the data, providing an efficient tool for optimization of migration images. A numerical example for a simple model shows how primary and prismatic multipath contributions merge into a single incident angle versus image time trajectory. A second example, using synthetic data from the Sigsbee2 model, shows that the contributions to subsalt images of primary and multipath (in this case, turning wave) reflections are different. The primary reflections contain most of the information in regions away from the salt, but both primary and multipath data contribute in the subsalt region.

Reservoir history matching is assuming a critical role in understanding reservoir characteristics, tracking water fronts, and forecasting production. While production data have been incorporated for matching reservoir production levels and estimating critical reservoir parameters, the sparse spatial nature of this dataset limits the efficiency of the history matching process. Recently, gravimetry techniques have significantly advanced to the point of providing measurement accuracy in the microgal range and consequently can be used for the tracking of gas displacement caused by water influx. While gravity measurements provide information on subsurface density changes, i.e., the composition of the reservoir, these data do only yield marginal information about temporal displacements of oil and inflowing water. We propose to complement gravimetric data with interferometric synthetic aperture radar surface deformation data to exploit the strong pressure deformation relationship for enhancing fluid flow direction forecasts. We have developed an ensemble Kalman-filter-based history matching framework for gas, gas condensate, and volatile oil reservoirs, which synergizes time-lapse gravity and interferometric synthetic aperture radar data for improved reservoir management and reservoir forecasts. Based on a dual state–parameter estimation algorithm separating the estimation of static reservoir parameters from the dynamic reservoir parameters, our numerical experiments demonstrate that history matching gravity measurements allow monitoring the density changes caused by oil–gas phase transition and water influx to determine the saturation levels, whereas the interferometric synthetic aperture radar measurements help to improve the forecasts of hydrocarbon production and water displacement directions. The reservoir estimates resulting from the dual filtering scheme are on average 20%–40% better than those from the joint estimation scheme, but require about a 30% increase in computational cost.

A slowly moving loess landslide along the River Danube in South Hungary was studied using electrical resistivity tomography. Our aim was to determine the fracture system of the study site. Due to the homogeneous composition of the loess, it seems to be the only possibility to get information about the landslide and its further evolution. The applicability of the electrical resistivity tomography technique for such a supposedly dense fracture system was studied by numerical modelling, and the results have been verified in the field. The dip of the fractures could not always been observed, and they could not be explored deeply. However, it was possible to map their surface projection to get the desired information about the structure of the landslide. Fracture zones could have been especially well localized, enabling the prediction of the positions of future rupture surfaces and thus the delineation of the endangered zone. Although the area outside of the already subsided one is not endangered yet, the area which has already started to move is going to break into two. Parts of the about 5 m wide blocks at the front of the landslide may fall or slide down anytime. A large area was assumed to move as one unit. Most of our predictions have been verified by the mass movements that occurred about one and half years after the measurements. The electrical resistivity tomography method proved to be a good tool to characterize the fracture system of such a landslide area, enabling the prediction of future rupture surfaces and also delineation of the endangered area. Its use is therefore highly recommended to monitor landslides to provide early risk warnings to avoid damage to constructions or endangering human life.

Linear prediction filters are an effective tool for reducing random noise from seismic records. Unfortunately, the ability of prediction filters to enhance seismic records deteriorates when the data are contaminated by erratic noise. Erratic noise in this article designates non-Gaussian noise that consists of large isolated events with known or unknown distribution. We propose a robust *f*-*x* projection filtering scheme for simultaneous erratic noise and Gaussian random noise attenuation. Instead of adopting the ℓ_{2}-norm, as commonly used in the conventional design of *f*-*x* filters, we utilize the hybrid -norm to penalize the energy of the additive noise. The estimation of the prediction error filter and the additive noise sequence are performed in an alternating fashion. First, the additive noise sequence is fixed, and the prediction error filter is estimated via the least-squares solution of a system of linear equations. Then, the prediction error filter is fixed, and the additive noise sequence is estimated through a cost function containing a hybrid -norm that prevents erratic noise to influence the final solution. In other words, we proposed and designed a robust M-estimate of a special autoregressive moving-average model in the *f*-*x* domain. Synthetic and field data examples are used to evaluate the performance of the proposed algorithm.

Using both image and data domains to perform velocity inversion can help us resolve the long and short wavelength components of the velocity model, usually in that order. This translates to integrating migration velocity analysis into full waveform inversion. The migration velocity analysis part of the inversion often requires computing extended images, which is expensive when using conventional methods. As a result, we use pre-stack wavefield (the double-square-root formulation) extrapolation, which includes the extended information (subsurface offsets) naturally, to make the process far more efficient and stable. The combination of the forward and adjoint pre-stack wavefields provides us with update options that can be easily conditioned to improve convergence. We specifically use a modified differential semblance operator to split the extended image into a residual part for classic differential semblance operator updates and the image (Born) modelling part, which provides reflections for higher resolution information. In our implementation, we invert for the velocity and the image simultaneously through a dual objective function. Applications to synthetic examples demonstrate the features of the approach.

Hydrocarbon production and fluid injection affect the level of subsurface stress and physical properties of the subsurface, and can cause reservoir-related issues, such as compaction and subsidence. Monitoring of oil and gas reservoirs is therefore crucial. Time-lapse seismic is used to monitor reservoirs and provide evidence of saturation and pressure changes within the reservoir. However, relative to background velocities and reflector depths, the time-lapse changes in velocity and geomechanical properties are typically small between consecutive surveys. These changes can be measured by using apparent displacement between migrated images obtained from recorded data of multiple time-lapse surveys. Apparent displacement measurements by using the classical cross-correlation method are poorly resolved. Here, we propose the use of a phase-correlation method, which has been developed in satellite imaging for sub-pixel registration of the images, to overcome the limitations of cross-correlation. Phase correlation provides both vertical and horizontal displacements with a much better resolution. After testing the method on synthetic data, we apply it to a real dataset from the Norne oil field and show that the phase-correlation method can indeed provide better resolution.

We present here a comparison between two statistical methods for facies classifications: Bayesian classification and expectation–maximization method. The classification can be performed using multiple seismic attributes and can be extended from well logs to three-dimensional volumes. In this work, we propose, for both methods, a sensitivity study to investigate the impact of the choice of seismic attributes used to condition the classification. In the second part, we integrate the facies classification in a Bayesian inversion setting for the estimation of continuous rock properties, such as porosity and lithological fractions, from the same set of seismic attributes. The advantage of the expectation–maximization method is that this algorithm does not require a training dataset, which is instead required in a traditional Bayesian classifier and still provides similar results. We show the application, comparison, and analysis of these methods in a real case study in the North Sea, where eight sedimentological facies have been defined. The facies classification is computed at the well location and compared with the sedimentological profile and then extended to the 3D reservoir model using up to 14 seismic attributes.

Between the years 2008 and 2013, approximately 67 kilotons of CO_{2} have been injected at the Ketzin site, Germany. As part of the geophysical monitoring programme, time-lapse electrical resistivity tomography has been applied using crosshole and surface-downhole measurements of electrical resistivity tomography. The data collection of electrical resistivity tomography is partly based on electrodes that are permanently installed in three wells at the site (one injection well and two observation wells). Both types of ERT measurements consistently show the build-up of a CO_{2}-related resistivity signature near the injection point. Based on the imaged resistivity changes and a petrophysical model, CO_{2} saturation levels are estimated. These CO_{2} saturations are interpreted in conjunction with CO_{2} saturations inferred from neutron-gamma loggings. Apart from the CO_{2}–brine substitution response in the observed resistivity changes, significant imprints from the dynamic behaviour of the CO_{2} in the reservoir are observed.

We have studied three-dimensional fault geometries through a geologically integrated analysis of fault seismic attribute volumes. We used a series of coherence (semblance) and filtered coherence attribute volumes with parameters optimised for imaging faults in the studied seismic volumes. Fault geometric attributes such as along strike segment length and displacement were measured on fault seismic attributes. The scaling relationships of fault geometric attributes were studied using statistical methods such as the Bayesian information criterion, the likelihood ratio test, and the bootstrap method. Univariate distributions of fault segment length and maximum displacement show a truncated power law for most of the fault data. The statistical results indicate a piecewise-linear relation with two slopes between depth and fault segments lengths: depth and mean displacement. For these relations, we observe consistent increases in fault segment lengths and mean displacements from the lower tip of the fault at depth toward a point of inflection at shallower depth at the vertical section. From that point, a reduction in fault segment lengths and mean displacements toward the upper tip of the fault at the shallower depth occurs. Fault segmentation along strike increases toward the lower and upper tips of the fault, but the maximum number of segments are located near the lower tip of the fault in two of the studied faults. The fault segment length is maximum, where the number of segments (along strike) is least close to the middle of the fault in the vertical section.

We developed a reverse-time migration scheme that can image regions with rugged topography without requiring any approximations by adopting an irregular, unstructured-grid modelling scheme. This grid, which can accurately describe surface topography and interfaces between high-velocity-contrast regions, is generated by Delaunay triangulation combined with the centroidal Voronoi tessellation method. The grid sizes vary according to the migration velocities, resulting in significant reduction of the number of discretized nodes compared with the number of nodes in the conventional regular-grid scheme, particularly in the case wherein high near-surface velocities exist. Moreover, the time sampling rate can be reduced substantially. The grid method, together with the irregular perfectly matched layer absorbing boundary condition, enables the proposed scheme to image regions of interest using curved artificial boundaries with fewer discretized nodes. We tested the proposed scheme using the 2D SEG Foothill synthetic dataset.

The existence of fractures not only provides space for oil and gas to reside in but also creates pathways for their migration. Accurate description of a fractured reservoir is thus an important subject of exploration for geophysicists and petroleum engineers. In reflection seismology, a reservoir of parallel vertical fractures is often considered a transversely isotropic medium with its symmetry axis horizontally oriented and its physical properties varying in azimuth on the horizontal symmetry-axis plane. In the history of fractured reservoir exploration, azimuthal variation in the *P*-wave amplitude, velocity, and fractional difference of the split *S*-waves have been popular seismic attributes used to delineate characteristics and extract information from the reservoir. Instead of analysing the reflection signatures of *P*-wave and *S*-wave, the objective of this study is to demonstrate the azimuthal variation of the converted wave (*C*-wave) amplitude in a fractured reservoir. To facilitate our objective, both common offset and end-on shooting reflection experiments were conducted in different azimuths on the horizontal symmetry-axis plane of a horizontal transverse isotropic model. In the acquired profile, reflections of *P*-wave, *PS _{1}*-wave (

Imaging using dipole acoustic logging reflections has become a research topic of increasing interest in recent years. Extracting reflections from the whole waveform is both important and extremely difficult because the reflections are obscured by large-amplitude direct waves. A method of wavefield separation based on high-resolution Radon transforms has been applied to separate the reflected waves. First, an analysis of the common offset gathers shows that the linear Radon transform can be used to separate the direct and reflected wave fields. However, traditional linear Radon transforms cannot focus the wave event using the least squares method. An improved high-resolution linear Radon transform is achieved using the principles of maximum entropy and Bayesian methods based on previous studies. The separation method is tested using synthetic data for hard and soft formations, a void model, and a fault model. The high-resolution Radon transform method is used to process a field dataset and exhibits improved results compared with those of the standard method.

Current models for unconformity-associated uranium deposits predict fluid flow and ore deposition along reactivated faults in >1.76 Ga basement beneath Mesoproterozoic siliciclastic basins. In frontier regions such as the Thelon Basin in the Kivalliq region of Nunavut, little is known about the sub-basin distribution of units and structures, making exploration targeting very tenuous. We constructed a geological map of the basement beneath the unconformity by extrapolating exposed features into the subsurface. The new map is constrained by detailed geological, geophysical, and rock property observations of outcrops adjacent to the basin and by aeromagnetic and gravity data over the geophysically transparent sedimentary basin. From rock property measurements, it is clear that the diverse magnetic and density characteristics of major rock packages provide quantitative three-dimensional constraints. Gravity profiles forward modelled in four cross sections define broad synforms of the Amer Belt and Archean volcanic rocks that are consistent with the structural style outside the basin. Major lithotectonic entities beneath the unconformity include: supracrustal rocks of the Archean Woodburn Lake group and Marjorie Hills meta sedimentary gneiss and associated mixed granitoid and amphibolitic gneiss; the Amer Mylonite Zone and inferred mafic intrusions oriented parallel and sub-parallel; other igneous intrusions of 2.6 Ga, 1.83 Ga, and 1.75 Ga vintage; and the <2.3 Ga to >1.84 Ga Amer Group. Four main brittle regional fault arrays (040°–060°, 075°–90°, 120°, and 150°) controlled development and preservation of the basin. The reactivated intersections of such faults along fertile basement units such as the Rumble assemblage, Marjorie Hills assemblage, Nueltin igneous rocks, and Pitz formation are the best targets for uranium exploration.

The analysis of seismic ambient noise acquired during temporary or permanent microseismic monitoring campaigns (e.g., improved/enhanced oil recovery monitoring, surveillance of induced seismicity) is potentially well suited for time-lapse studies based on seismic interferometry. No additional data acquisition required, ambient noise processing can be automatized to a high degree, and seismic interferometry is very sensitive to small medium changes. Thus there is an opportunity for detection and monitoring of velocity variations in a reservoir at negligible additional cost and effort.

Data and results are presented from an ambient noise interferometry study applied to two wells in a producing oil field in Romania. Borehole microseismic monitoring on three component geophones was performed for four weeks, concurrent with a water-flooding phase for improved oil recovery from a reservoir in ca. 1 km depth. Both low-frequency (2 Hz–50 Hz) P- and S-waves propagating through the vertical borehole arrays were reconstructed from ambient noise by the virtual source method. The obtained interferograms clearly indicate an origin of the ambient seismic energy from above the arrays, thus suggesting surface activities as sources. It is shown that ambient noise from time periods as short as 30 seconds is sufficient to obtain robust interferograms. Sonic log data confirm that the vertical and horizontal components comprise first arrivals of P-wave and S-waves, respectively. The consistency and high quality of the interferograms throughout the entire observation period further indicate that the high-frequency part (up to 100 Hz) represents the scattered wave field. The temporal variation of apparent velocities based on first-arrival times partly correlates with the water injection rate and occurrence of microseismic events. It is concluded that borehole ambient noise interferometry in production settings is a potentially useful method for permanent reservoir monitoring due to its high sensitivity and robustness.

I derive the kinematic properties of single-mode P, S1, and S2 waves as well as converted PS1, PS2, and S1S2 waves in elastic orthorhombic media including vertical velocity, two normal moveout velocities defined in vertical symmetry planes, and three anelliptic parameters (two of them are defined in vertical symmetry plane and one parameter is the cross-term one). I show that the azimuthal dependence of normal moveout velocity and anellipticity is different in phase and group domains. The effects on-vertical-axis singularity and on-vertical-axis triplication are considered for pure-mode S1 and S2 waves and converted-mode S1S2 waves. The conditions and properties of on-vertical-axis triplication are defined in terms of kinematic parameters. The results are illustrated in four homogeneous orthorhombic models and one multilayered orthorhombic model with no variation in azimuthal orientation for all the layers.

Diffractions play a vital role in seismic processing as they can be utilized for high-resolution imaging applications and analysis of subsurface medium properties like velocity. They are particularly valuable for anisotropic media as they inherently possess a wide range of dips necessary to resolve the angular dependence of velocity. However, until recently, the focus of diffraction imaging or inversion algorithms have been only on the isotropic approximation of the subsurface. Using diffracted waves, we develop a framework to invert for the effective η model. This effective model is obtained through scanning over possible effective η values and selecting the one that best fits the observed moveout curve for each diffractor location. The obtained effective η model is then converted to an interval η model using a Dix-type inversion formula. The inversion methodology holds the potential to reconstruct the true η model with sufficiently high accuracy and resolution properties. However, it relies on an accurate estimation of diffractor locations, which in turn requires good knowledge of the background velocity model. We test the effectiveness and applicability of our method on the vertical transverse isotropic Marmousi model. The inversion results yield a reasonable match even for the complex Marmousi model.

Ground-penetrating radar is one of the most effective methods of detecting shallow buried objects. Ground-penetrating radar radargram is a vertical map of the radar pulse reflections that returns from subsurface objects, and in the case of cylindrical objects, it would be a hyperbola. In order to get clear and accurate information on the presence, location, and geometry of the buried objects, the radargrams need to be interpreted. Interpretation of the results is a time-consuming task and needs an expert with vast knowledge. Development of an automatic interpretation method of B-scan ground-penetrating radar images would be an effective and efficient solution to this problem. A novel automatic interpretation method of ground-penetrating radar images, based on simultaneous perturbation artificial bee colony algorithm using tournament selection strategy, simultaneous perturbation stochastic approximation method, and new search equations, is introduced in this paper. The proposed algorithm is used to extract geometrical parameters, i.e. depth, location, and radius, of buried cylindrical objects in order to assess its accuracy. Synthetic data, simulated using GprMax2D forward modelling program, and real data, surveyed in the campus of Isfahan University of Technology, are used in the assessment. The performance of the proposed method in detecting synthetic hyperbolas is compared with that of the original artificial bee colony algorithm, genetic algorithm, and modified Hough transform. The results show superiority of the proposed algorithm, in detecting synthetic hyperbolas. Furthermore, the performance of the proposed method in estimating depth and radius of pipes in real ground-penetrating radar images is compared with that of the modified Hough transform. The results indicate higher accuracy of the proposed method in estimating geometrical parameters of the buried cylindrical objects.

The seismic industry is increasingly acquiring broadband data in order to reap the benefits of extra low- and high-frequency contents. At the low end, as the sharp low-cut decay gets closer to zero frequency, it becomes harder for a well tie to estimate the low-frequency response correctly. The fundamental difficulty is that well logs are too short to allow accurate estimation of the long-period content of the data. Three distinctive techniques, namely parametric constant phase, frequency-domain least squares with multi-tapering, and Bayesian time domain with broadband priors, are introduced in this paper to provide a robust solution to the wavelet estimation problem for broadband seismic data. Each of these techniques has a different mathematical foundation that would enable one to explore a wide range of solutions that could be used on a case-by-case basis depending on the problem at hand. A case study from the North West Shelf Australia is used to analyse the performance of the proposed techniques. Cross-validation is proposed as a robust quality control measure for evaluating well-tie applications. It is observed that when the seismic data are carefully processed, then the constant phase approach would likely offer a good solution. The frequency-domain method does not assume a constant phase. This flexibility makes it prone to over-fitting when the phase is approximately constant. Broadband priors for the time-domain least-squares method are found to perform well in defining low-frequency side lobes to the wavelet.

Distributed vibration sensing, also known as distributed acoustic sensing, is a relatively new method for recording vertical seismic profile data using a fibre optic cable as the sensor. The signal obtained from such systems is a distributed measurement over a length of fibre referred to as the gauge length. In this paper, we show that gauge length selection is one of the most important acquisition parameters for a distributed vibration sensing survey. If the gauge length is too small, then the signal-to-noise ratio will be poor. If the gauge length is too large, resolution will be reduced and the shape of the wavelet will be distorted. The optimum gauge length, as derived here, is a function of the velocity and frequencies of the seismic waves being measured. If these attributes vary considerably over the depth of a survey, then the use of different gauge lengths is recommended. The significant increases in data quality resulting from the use of multiple gauge length values are demonstrated using field data.

A new method for the calculation of the depth, location, and dip of thin dykes from pole-reduced magnetic data is introduced. The depth can be obtained by measuring the distance between chosen values of a tilt angle that is based upon the ratio of the magnetic field and its Hilbert transform over the dyke. Alternatively, it can be obtained from the horizontal derivative of the ratio of the Hilbert transform of the field to the field itself, over the dyke. The latter method also allows the dip of the dyke to be estimated from the gradient of the depth estimates.

We introduce the signal dependent time–frequency distribution, which is a time–frequency distribution that allows the user to optimize the tradeoff between joint time–frequency resolution and suppression of transform artefacts. The signal-dependent time–frequency distribution, as well as the short-time Fourier transform, Stockwell transform, and the Fourier transform are analysed for their ability to estimate the spectrum of a known wavelet used in a tuning wedge model. Next, the signal-dependent time–frequency distribution, and fixed- and variable-window transforms are used to estimate spectra from a zero-offset synthetic seismogram. Attenuation is estimated from the associated spectral ratio curves, and the accuracy of the results is compared. The synthetic consisted of six pairs of strong reflections, based on real well-log data, with a modeled intrinsic attenuation value of 1000/*Q* = 20. The signal-dependent time–frequency distribution was the only time–frequency transform found to produce spectra that estimated consistent attenuation values, with an average of 1000/*Q* = 26±2; results from the fixed- and variable-window transforms were 24±17 and 39±10, respectively. Finally, all three time–frequency transforms were used in a pre-stack attenuation estimation method (the pre-stack *Q* inversion algorithm) applied to a gather from a North Sea seismic dataset, to estimate attenuation between nine different strong reflections. In this case, the signal-dependent time-frequency distribution produced spectra more consistent with the constant-Q model of attenuation assumed in the pre-stack attenuation estimation algorithm: the average L1 residuals of the spectral ratio surfaces from the theoretical constant-Q expectation for the signal-dependent time-frequency distribution, short-time Fourier transform, and Stockwell transform were 0.12, 0.21, and 0.33, respectively. Based on the results shown, the signal-dependent time-frequency distribution is a time–frequency distribution that can provide more accurate and precise estimations of the amplitude spectrum of a reflection, due to a higher attainable time–frequency resolution.

To simulate the seismic signals that are obtained in a marine environment, a coupled system of both acoustic and elastic wave equations is solved. The acoustic wave equation for the fluid region simulates the pressure field while minimizing the number of degrees of freedom of the impedance matrix, and the elastic wave equation for the solid region simulates several elastic events, such as shear waves and surface waves. Moreover, by combining this coupled approach with the waveform inversion technique, the elastic properties of the earth can be inverted using the pressure data obtained from the acoustic region. However, in contrast to the pure acoustic and elastic cases, the complex impedance matrix for the coupled media does not have a symmetric form because of the boundary (continuity) condition at the interface between the acoustic and elastic elements. In this study, we propose a manipulation scheme that makes the complex impedance matrix for acoustic–elastic coupled media to take a symmetric form. Using the proposed symmetric matrix, forward and backward wavefields are identical to those generated by the conventional approach; thus, we do not lose any accuracy in the waveform inversion results. However, to solve the modified symmetric matrix, LDLT factorization is used instead of LU factorization for a matrix of the same size; this method can mitigate issues related to severe memory insufficiency and long computation times, particularly for large-scale problems.

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

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

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

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

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

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

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

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

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

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

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.

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 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.

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.

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.

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.

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.

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.

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.

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 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.

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.