Geophysical Prospecting - Volume 64, Issue 1, 2015

Integrating migration velocity analysis and full waveform inversion can help reduce the high non‐linearity of the classic full waveform inversion objective function. The combination of inverting for the long and short wavelength components of the velocity model using a dual objective function that is sensitive to both components is still very expensive and have produced mixed results. We develop an approach that includes both components integrated to complement each other. We specifically utilize the image to generate reflections in our synthetic data only when the velocity model is not capable of producing such reflections. As a result, we get the migration velocity analysis working when we need it, and we mitigate its influence when the velocity model produces accurate reflections (possibly first for the low frequencies). This is achieved using a novel objective function that includes both objectives. Applications to a layered model and the Marmousi model demonstrate the main features of the approach.

Decomposing seismic data in local slopes is the basic idea behind velocity‐independent imaging. Using accurate moveout approximations enables computing moveout attributes such as normal moveout velocity and nonhyperbolic parameters as functions of zero‐offset travel time. Mapping of moveout attributes is performed from the pre‐stack seismic data domain into the time‐migrated image domain. The different moveout attributes have different accuracy for a given moveout approximation that depends on the corresponding order of travel‐time derivative. The most accurate attribute is the zero‐offset travel time, and the nonhyperbolic parameter has the worst accuracy, regardless of the moveout approximation. Typically, the mapping of moveout attributes is performed using a point‐to‐point procedure, whereas the generalized moveout approximation requires two point‐to‐point mappings. Testing the attribute mapping on the different models shows that the accuracy of mapped attributes is model dependent, whereas the generalized moveout approximation gives practically exact results.

Borehole seismic addresses the need for high‐resolution images and elastic parameters of the subsurface. Full‐waveform inversion of vertical seismic profile data is a promising technology with the potential to recover quantitative information about elastic properties of the medium. Full‐waveform inversion has the capability to process the entire wavefield and to address the wave propagation effects contained in the borehole data—multi‐component measurements; anisotropic effects; compressional and shear waves; and transmitted, converted, and reflected waves and multiples. Full‐waveform inversion, therefore, has the potential to provide a more accurate result compared with conventional processing methods.

We present a feasibility study with results of the application of high‐frequency (up to 60 Hz) anisotropic elastic full‐waveform inversion to a walkaway vertical seismic profile data from the Arabian Gulf. Full‐waveform inversion has reproduced the majority of the wave events and recovered a geologically plausible layered model with physically meaningful values of the medium.

Fluid depletion within a compacting reservoir can lead to significant stress and strain changes and potentially severe geomechanical issues, both inside and outside the reservoir. We extend previous research of time‐lapse seismic interpretation by incorporating synthetic near‐offset and full‐offset common‐midpoint reflection data using anisotropic ray tracing to investigate uncertainties in time‐lapse seismic observations. The time‐lapse seismic simulations use dynamic elasticity models built from hydro‐geomechanical simulation output and a stress‐dependent rock physics model. The reservoir model is a conceptual two‐fault graben reservoir, where we allow the fault fluid‐flow transmissibility to vary from high to low to simulate non‐compartmentalized and compartmentalized reservoirs, respectively. The results indicate time‐lapse seismic amplitude changes and travel‐time shifts can be used to qualitatively identify reservoir compartmentalization. Due to the high repeatability and good quality of the time‐lapse synthetic dataset, the estimated travel‐time shifts and amplitude changes for near‐offset data match the true model subsurface changes with minimal errors. A 1D velocity–strain relation was used to estimate the vertical velocity change for the reservoir bottom interface by applying zero‐offset time shifts from both the near‐offset and full‐offset measurements. For near‐offset data, the estimated P‐wave velocity changes were within 10% of the true value. However, for full‐offset data, time‐lapse attributes are quantitatively reliable using standard time‐lapse seismic methods when an updated velocity model is used rather than the baseline model.

Localization of fractured areas is of primary interest in the study of oil and gas geology in carbonate environments. Hydrocarbon reservoirs in these environments are embedded within an impenetrable rock matrix but possess a rich system of various microheterogeneities, i.e., cavities, cracks, and fractures. Cavities accumulate oil, but its flow is governed by a system of fractures. A distinctive feature of wave propagation in such media is the excitation of the scattered/diffracted waves by the microheterogeneities. This scattering could be a reliable attribute for characterization of the fine structure of reservoirs, but it has extremely low energy and any standard data processing renders them practically invisible in comparison with images produced by specular reflections. Therefore, any attempts to use these waves for image congestion of microheterogeneities should first have a preliminary separation of the scattering and specular reflections. In this paper, the approach to performing this separation is based on the asymmetric summation. It is implemented by double focusing of Gaussian beams. To do this, the special weights are computed by propagating Gaussian beams from the target area towards the acquisition system separately for sources and receivers. The different mutual positioning of beams in each pair introduces a variety of selective images that are destined to represent some selected singular primitives of the target objects such as fractures, cavities, and edges. In this way, one can construct various wave images of a target reservoir, particularly in scattered/diffracted waves. Additional removal of remnants of specular reflections is done by means of spectral analysis of the scattered/diffracted waves' images to recognize and cancel extended lineaments. Numerical experiments with Sigsbee 2A synthetic seismic data and some typical structures of the Yurubcheno‐Tokhomskoye oil field in East Siberia are presented and discussed.

Pressure drops associated with reservoir production generate excess stress and strain that cause travel‐time shifts of reflected waves. Here, we invert time shifts of P‐, S‐, and PS‐waves measured between baseline and monitor surveys for pressure reduction and reservoir length. The inversion results can be used to estimate compaction‐induced stress and strain changes around the reservoir. We implement a hybrid inversion algorithm that incorporates elements of gradient, global/genetic, and nearest neighbour methods and permits exploration of the parameter space while simultaneously following local misfit gradients. Our synthetic examples indicate that optimal estimates of reservoir pressure from P‐wave data can be obtained using the reflections from the reservoir top. For S‐waves, time shifts from the top of the reservoir can be accurately inverted for pressure if the noise level is low. However, if noise contamination is significant, it is preferable to use S‐wave data (or combined shifts of all three modes) from reflectors beneath the reservoir. Joint wave type inversions demonstrate improvements over any single pure mode. Reservoir length can be estimated using the time shifts of any mode from the reservoir top or deeper reflectors. We also evaluate the differences between the actual strain field and those corresponding to the best‐case inversion results obtained using P‐ and S‐wave data. Another series of tests addresses the inversion of the time shifts for the pressure drops in two‐compartment reservoirs, as well as for the associated strain field. Numerical testing shows that a potentially serious source of error in the inversion is a distortion in the strain‐sensitivity coefficients, which govern the magnitude of stiffness changes. This feasibility study suggests which wave types and reflector locations may provide the most accurate estimates of reservoir parameters from compaction‐induced time shifts.

Multi‐offset phase analysis of seismic surface waves is an established technique for the extraction of dispersion curves with high spatial resolution and, consequently, for the investigation of the subsurface in terms of shear wave velocity distribution. However, field applications are rarely documented in the published literature. In this paper, we discuss an implementation of the multi‐offset phase analysis consisting of the estimation of the Rayleigh wave velocity by means of a moving window with a frequency‐dependent length. This allows maximizing the lateral resolution at high frequencies while warranting stability at the lower frequencies. In this way, we can retrieve the shallow lateral variability with high accuracy and, at the same time, obtain a robust surface‐wave velocity measurement at depth. In this paper, we apply this methodology to a dataset collected for hydrogeophysical purposes and compare the inversion results with those obtained by using refraction seismics and electrical resistivity tomography. The surface‐wave results are in good agreement with those provided by the other methods and demonstrate a superior capability in retrieving both lateral and vertical velocity variations, including inversions. Our results are further corroborated by the lithological information from a borehole drilled on the acquisition line. The availability of multi‐offset phase analysis data also allows disentangling a fairly complex interpretation of the other geophysical results.

Recently, an effective and powerful approach for simulating seismic wave propagation in elastic media with an irregular free surface was proposed. However, in previous studies, researchers used the periodic condition and/or sponge boundary condition to attenuate artificial reflections at boundaries of a computational domain. As demonstrated in many literatures, either the periodic condition or sponge boundary condition is simple but much less effective than the well‐known perfectly matched layer boundary condition. In view of this, we intend to introduce a perfectly matched layer to simulate seismic wavefields in unbounded models with an irregular free surface. We first incorporate a perfectly matched layer into wave equations formulated in a frequency domain in Cartesian coordinates. We then transform them back into a time domain through inverse Fourier transformation. Afterwards, we use a boundary‐conforming grid and map a rectangular grid onto a curved one, which allows us to transform the equations and free surface boundary conditions from Cartesian coordinates to curvilinear coordinates. As numerical examples show, if free surface boundary conditions are imposed at the top border of a model, then it should also be incorporated into the perfectly matched layer imposed at the top‐left and top‐ right corners of a 2D model where the free surface boundary conditions and perfectly matched layer encounter; otherwise, reflections will occur at the intersections of the free surface and the perfectly matched layer, which is confirmed in this paper. So, by replacing normal second derivatives in wave equations in curvilinear coordinates with free surface boundary conditions, we successfully implement the free surface boundary conditions into the perfectly matched layer at the top‐left and top‐right corners of a 2D model at the surface. A number of numerical examples show that the perfectly matched layer constructed in this study is effective in simulating wave propagation in unbounded media and the algorithm for implementation of the perfectly matched layer and free surface boundary conditions is stable for long‐time wavefield simulation on models with an irregular free surface.

We propose a method for imaging small‐scale diffraction objects in complex environments in which Kirchhoff‐based approaches may fail. The proposed method is based on a separation between the specular reflection and diffraction components of the total wavefield in the migrated surface angle domain. Reverse‐time migration was utilized to produce the common image gathers. This approach provides stable and robust results in cases of complex velocity models. The separation is based on the fact that, in surface angle common image gathers, reflection events are focused at positions that correspond to the apparent dip angle of the reflectors, whereas diffracted events are distributed over a wide range of angles. The high‐resolution radon‐based procedure is used to efficiently separate the reflection and diffraction wavefields. In this study, we consider poststack diffraction imaging. The advantages of working in the poststack domain are its numerical efficiency and the reduced computational time. The numerical results show that the proposed method is able to image diffraction objects in complex environments. The application of the method to a real seismic dataset illustrates the capability of the approach to extract diffractions.

A fluid‐saturated flat channel between solids, such as a fracture, is known to support guided waves—sometimes called Krauklis waves. At low frequencies, Krauklis waves can have very low velocity and large attenuation and are very dispersive. Because they propagate primarily within the fluid channel formed by a fracture, Krauklis waves can potentially be used for geological fracture characterization in the field. Using an analogue fracture consisting of a pair of flat slender plates with a mediating fluid layer—a trilayer model—we conducted laboratory measurements of the velocity and attenuation of Krauklis waves. Unlike previous experiments using ultrasonic waves, these experiments used frequencies well below 1 kHz, resulting in extremely low velocity and large attenuation of the waves. The mechanical compliance of the fracture was varied by modifying the stiffness of the fluid seal of the physical fracture model, and proppant (fracture‐filling high‐permeability sand) was also introduced into the fracture to examine its impact on wave propagation. A theoretical frequency equation for the trilayer model was derived using the poroelastic linear‐slip interface model, and its solutions were compared to the experimental results.

Elastic interactions between pores and cracks reflect how they are organized or spatially distributed in porous rocks. The principle goal of this paper is to understand and characterize the effect of elastic interactions on the effective elastic properties. We perform finite element modelling to quantitatively study how the spatial arrangement of inclusions affects stress distribution and the resulting overall elasticity. It is found that the stress field can be significantly altered by elastic interactions. Compared with a non‐interacting situation, stress shielding considerably stiffens the effective media, while stress amplification appreciably reduces the effective elasticity. We also demonstrate that the T‐matrix approach, which takes into account the ellipsoid distribution of pores or cracks, can successfully characterize the competing effects between stress shielding and stress amplification. Numerical results suggest that, when the concentrations of cracks increase beyond the dilute limit, the single parameter crack density is not sufficient to characterize the contribution of the cracks to the effective elasticity. In order to obtain more reliable and accurate predictions for the effective elastic responses and seismic anisotropies, the spatial distribution of pores and cracks should be included. Additionally, such elastic interaction effects are also dependent on both the pore shapes and the fluid infill.

Borehole fluid injections are accompanied by microseismic activity not only during but also after termination of the fluid injection. Previously, this phenomenon has been analysed, assuming that the main triggering mechanism is governed by a linear pressure diffusion in a hydraulically isotropic medium. In this context the so‐called back front of seismicity has been introduced, which allows to characterize the hydraulic transport from the spatiotemporal distribution of post‐injection induced events. However, rocks are generally anisotropic, and in addition, fluid injections can strongly enhance permeability. In this case, permeability becomes a function of pressure. For such situations, we carry out a comprehensive study about the behaviour and parametrization of the back front. Based on a model of a factorized anisotropic pressure dependence of permeability, we present an approach to reconstruct the principal components of the diffusivity tensor. We apply this approach to real microseismic data and show that the back front characterizes the least hydraulic transport. To investigate the back front of non‐linear pore‐fluid pressure diffusion, we numerically consider a power‐law and an exponential‐dependent diffusivity. To account for a post‐injection enhanced hydraulic state of the rock, we introduce a model of a frozen (i.e., nearly unchanged after the stimulation) medium diffusivity and generate synthetic seismicity. We find that, for a weak non‐linearity and 3D exponential diffusion, the linear diffusion back front is still applicable. This finding is in agreement with microseismic data from Ogachi and Fenton Hill. However, for a strong non‐linear fluid–rock interaction such as hydraulic fracturing, the back front can significantly deviate from a time dependence of a linear diffusion back front. This is demonstrated for a data set from the Horn River Basin. Hence, the behaviour of the back front is a strong indicator of a non‐linear fluid–rock interaction.

The increased application of airborne electromagnetic surveys to hydrogeological studies is driving a demand for data that can consistently be inverted for accurate subsurface resistivity structure from the near surface to depths of several hundred metres. We present an evaluation of three commercial airborne electromagnetic systems over two test blocks in western Nebraska, USA. The selected test blocks are representative of shallow and deep alluvial aquifer systems with low groundwater salinity and an electrically conductive base of aquifer. The aquifer units show significant lithologic heterogeneity and include both modern and ancient river systems. We compared the various data sets to one another and inverted resistivity models to borehole lithology and to ground geophysical models. We find distinct differences among the airborne electromagnetic systems as regards the spatial resolution of models, the depth of investigation, and the ability to recover near‐surface resistivity variations. We further identify systematic biases in some data sets, which we attribute to incomplete or inexact calibration or compensation procedures.

The Catalão I alkaline–carbonatite complex, which is located in Central Brazil, is one of the main producers of niobium and phosphates in the world. It has been intensely studied geologically and geochemically for its economic potential. This work presents a geophysical analysis over this complex, identifying its behaviour in the subsurface and in portions that have not been explored yet. Different geophysical methods and techniques were applied to achieve the most reliable results possible: at the surface, through radiometric, geological, and topographic data, and at depth, by geological, magnetic, and gravimetric data. The analysis was successfully completed with inversions of gravity and magnetic data that resulted in quite similar models, both in volume and shape. Their density and magnetic susceptibility contrasts were consistent with the expected dunite–pyroxenite lithology from the original mafic intrusion and indicated (by exclusion) the volume of the carbonatite body, which along with the known contents of phosphates and niobium allowed an indirect estimate of the reserves and resources of the complex.

In the traditional inversion of the Rayleigh dispersion curve, layer thickness, which is the second most sensitive parameter of modelling the Rayleigh dispersion curve, is usually assumed as correct and is used as fixed a priori information. Because the knowledge of the layer thickness is typically not precise, the use of such a priori information may result in the traditional Rayleigh dispersion curve inversions getting trapped in some local minima and may show results that are far from the real solution. In this study, we try to avoid this issue by using a joint inversion of the Rayleigh dispersion curve data with vertical electric sounding data, where we use the common‐layer thickness to couple the two methods. The key idea of the proposed joint inversion scheme is to combine methods in one joint Jacobian matrix and to invert for layer S‐wave velocity, resistivity, and layer thickness as an additional parameter, in contrast with a traditional Rayleigh dispersion curve inversion. The proposed joint inversion approach is tested with noise‐free and Gaussian noise data on six characteristic, synthetic sub‐surface models: a model with a typical dispersion; a low‐velocity, half‐space model; a model with particularly stiff and soft layers, respectively; and a model reproduced from the stiff and soft layers for different layer‐resistivity propagation. In the joint inversion process, the non‐linear damped least squares method is used together with the singular value decomposition approach to find a proper damping value for each iteration. The proposed joint inversion scheme tests many damping values, and it chooses the one that best approximates the observed data in the current iteration. The quality of the joint inversion is checked with the relative distance measure. In addition, a sensitivity analysis is performed for the typical dispersive sub‐surface model to illustrate the benefits of the proposed joint scheme. The results of synthetic models revealed that the combination of the Rayleigh dispersion curve and vertical electric sounding methods in a joint scheme allows to provide reliable sub‐surface models even in complex and challenging situations and without using any a priori information.