Due to its simplicity, stability, and efficiency, the use of right rectangular prisms is still widespread for potential field modelling and inversion. It is well known that modelling the subsurface with Cartesian grids has important consequences in terms of accuracy of the results. In this paper, we review the main issues that geophysicists face in day-to-day work when trying to use right rectangular prisms for performing gravity or full tensor gravity modelling and inversions. We demonstrate the results both theoretically and through Monte Carlo simulations, also exploiting concepts from fractal geometry. We believe that the guidelines contained in this paper may suggest a good practice for the day-to-day work of geophysicists dealing with gravity and full tensor gravity data.

Under certain circumstances, seismic propagation within porous media may be associated to the conversion of mechanical energy to electromagnetic energy, which is known as a seismo-electromagnetic phenomenon. The propagation of fast compressional *P*-waves is more specifically associated to the manifestations of a seismoelectric field linked to the fluid flows within the pores. The analysis of seismoelectric phenomena, which requires the combination of the theory of electrokinetics and Biot's theory of poroelasticity, provides us with transfer function that links the coseismic seismoelectric field *E* to the seismic acceleration . To measure the transfer function, we have developed an experimental setup enabling seismoelectric laboratory observation in unconsolidated quartz sand within the kilohertz range. The investigation focused on the impact of fluid conductivity and water saturation over the coseismic seismoelectric field. During the experiment, special attention was given to the accuracy of electric field measurements. We concluded that, to obtain a reliable estimate of the electric field amplitude, the dipole from which the potential differences are measured should be of much smaller length than the wavelength of the propagating seismic field. Time-lapse monitoring of the seismic velocities and seismoelectric transfer functions were performed during imbibition and drainage experiments. In all cases, the quantitative analysis of the seismoelectric transfer function was in good agreement with theoretical predictions. While investigating saturation variations from full to residual water saturation, we showed that the ratio undergoes a switch in polarity at a particular saturation , which also implies a sign change of the filtration, traducing a reversal of the relative fluid displacement with respect to the frame. This sign change at critical saturation stresses a particular behaviour of the poroelastic medium: the dropping of the coseismic electric field to zero traduces the absence of relative pore/fluid displacements representative of a Biot dynamically compatible medium. We concluded from our experimental study in loose sand that the measurements of the coseismic seismoelectric coupling may provide information on fluid distribution within the pores and that the reversal of the seismoelectric field may be used as an indicator of the dynamically compatible state of the medium.

In the free state, Rayleigh waves are assumed to travel in the form of planar wavefronts. Under such an assumption, the propagation behaviour of the modes of Rayleigh waves in layered half-spaces is only frequency dependent. The frequency behaviour, which is often termed as dispersion, is determined by the shear wave velocity profile of layered soils within the depth related to wavelength (or frequency). According to this characteristic, the shear wave velocity profile can be back-analysed from the dispersion. The technique is widely used in the surface wave testing. However, the wavefronts of Rayleigh waves activated by the surface sources are non-planar. The geometric discrepancy could result in Rayleigh waves manifesting distance-dependent behaviour, which is referred to as spatial behaviour in this paper. Conventional analysis ignoring this spatial behaviour could introduce unexpected errors. In order to take the effects of sources on the propagation behaviour into account, a new mathematical model is established for Rayleigh waves in layered elastic media under vertical disc-like surface sources using the thin-layer method. The spatial behaviour of the activated modes and the apparent phase velocity, which is the propagation velocity of Rayleigh waves superposed by the multiple modes, are then analysed. Aspects of the spatial behaviour investigated in this paper include the equilibrium path, the particle orbit, and the geometric attenuation of the activated Rayleigh waves. The results presented in this paper can provide some guidelines for developing new inverse mathematical models and algorithms.

The horizontal transversely isotropic model, with arbitrary symmetry axis orientation, is the simplest effective representative that explains the azimuthal behaviour of seismic data. Estimating the anisotropy parameters of this model is important in reservoir characterisation, specifically in terms of fracture delineation. We propose a travel-time-based approach to estimate the anellipticity parameter η and the symmetry axis azimuth ϕ of a horizontal transversely isotropic medium, given an inhomogeneous elliptic background model (which might be obtained from velocity analysis and well velocities). This is accomplished through a Taylor's series expansion of the travel-time solution (of the eikonal equation) as a function of parameter η and azimuth angle ϕ. The accuracy of the travel time expansion is enhanced by the use of Shanks transform. This results in an accurate approximation of the solution of the non-linear eikonal equation and provides a mechanism to scan simultaneously for the best fitting effective parameters η and ϕ, without the need for repetitive modelling of travel times. The analysis of the travel time sensitivity to parameters η and ϕ reveals that travel times are more sensitive to η than to the symmetry axis azimuth ϕ. Thus, η is better constrained from travel times than the azimuth. Moreover, the two-parameter scan in the homogeneous case shows that errors in the background model affect the estimation of η and ϕ differently. While a gradual increase in errors in the background model leads to increasing errors in η, inaccuracies in ϕ, on the other hand, depend on the background model errors. We also propose a layer-stripping method valid for a stack of arbitrary oriented symmetry axis horizontal transversely isotropic layers to convert the effective parameters to the interval layer values.

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.

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.

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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