Anisotropic Reverse Time Migration Research Articles

Reverse time migration angle gathers in acoustic anisotropic media using direction vectors

The application of direction vectors in the generation of reverse time migration (RTM) angle gathers in complex acoustic anisotropic media often encounters three main challenges: not pointing to the phase-velocity direction (PVD) of the Poynting vector, inaccuracy due to overlapping wavefields, and instability due to zero points of the direction vector. In general anisotropic media, the standard Poynting vector indicates the group-velocity direction (GVD), whereas reflection and transmission phenomena rely on the PVD. Anisotropy introduces discrepancies between the GVD and the PVD. To overcome this issue, we use the so-called PVD vector to directly calculate the PVD from anisotropic wavefields, eliminating the need for an approximated conversion from the GVD to the PVD. To mitigate the inaccuracy problem, we apply the Hilbert transform-based wavefield decomposition method to separate overlapping wavefields into their up/down components, and then we calculate the PVDs using the separated wavefields. To tackle the instability problem, we incorporate the additionally simulated quadrature wavefield during the wavefield decomposition procedure. By combining the direction vector of the quadrature wavefield with that of the original wavefield, we can eliminate the zero points and thus obtain a stabilized PVD vector. With those problems solved or alleviated, we present a scheme for the generation of anisotropic RTM angle gathers in complex areas. Two numerical examples using synthetic data sets demonstrate our method’s effectiveness.

The inverse scattering imaging condition for anisotropic reverse time migration

The inverse scattering imaging condition (ISIC) is widely used in reverse time migration (RTM), which naturally eliminates the low-wavenumber noise by combining a time-derivative imaging condition with a spatial-derivative imaging condition. However, when applying ISIC to anisotropic RTM, we observe that the low-wavenumber noise is not entirely eliminated. This phenomenon is the leakage of low-wavenumber noise caused by anisotropy. In anisotropic media, due to the deviation of the vertical velocity from the phase velocity, the spatial-derivative imaging condition does not generate correct weights to cancel the low-wavenumber noise obtained by using the time-derivative imaging condition. By adding an anisotropic correction term to compensate for this deviation, we obtain the anisotropic ISIC which can fully eliminate the low-wavenumber noise. In addition, we construct the connection between the anisotropic ISIC and the scattering function. The scattering function describes the power of the media to generate the scattering field, and it encompasses the effect of model perturbations and their scattering patterns. Under the small perturbation assumption and weak anisotropy approximation, we theoretically show that the ISIC reverses the scattering process and recovers the scattering function from the scattering field. Through three numerical examples, we demonstrate the effectiveness of our method in suppressing the low-wavenumber noise for anisotropic RTM. The anisotropic ISIC is suitable for titled transverse isotropic or orthorhombic media, and it also has potential usages in inversion-based imaging algorithms.

A new qP-wave approximation in tilted transversely isotropic media and its reverse time migration for areas with complex overburdens

During seismic imaging in anisotropic media, undesired SV waves may be detected when conventional wave equations are used for wavefield simulation, which will contaminate the final seismic image. A pure qP-wave equation that is free of S-wave artifacts is desired, such that crosstalk introduced from the interference of different waves can be eliminated. We have developed a new fully decoupled P-wave equation in transversely isotropic media with titled symmetry axis that avoids unwanted energy during migration. The qP and qSV phase velocities for the new approximations are plotted and compared with the exact solution and some other approximations and indicate high accuracy for various anisotropic models (from low to high degrees of anisotropy). During wavefield simulation, the finite-difference and pseudospectral methods also are combined to accelerate the computation. Moreover, a hybrid perfectly matched layer (H-PML) that combines two different perfectly matched layers for second-order wave equations in the wavenumber domain also is proposed and applied to eliminate the artificial boundary reflections. Comparisons of different absorbing boundary layers also are illustrated to validate the wavenumber domain H-PML. Finally, the new proposed wave approximation together with the new absorbing layer is further incorporated in a new 3D anisotropic reverse time migration (RTM). We test the RTM on the 3D synthetic SEG Advanced Modeling Corporation data and offshore field data with a complicated overburden (salt and gas overburden) and obtain seismic images with high resolution. Benchmarks against commercial implementations also are demonstrated, which proves that the positioning of the reflectors is more reliable and accurate with the new algorithm.

Reverse time migration with Gaussian beams using optimized ray tracing systems in transversely isotropic media

ABSTRACTPrestack depth migration is a key technology for imaging complex reservoirs in media with strong lateral velocity variations. Prestack migrations are broadly separated into ray‐based and wave‐equation‐based methods. Because of its efficiency and flexibility, ray‐based Kirchhoff migration is popular in the industry. However, it has difficulties in dealing with the multi‐arrivals, caustics and shadow zones. On the other hand, wave‐equation‐based methods produce images superior to that of the ray‐based methods, but they are expensive numerically, especially methods based on two‐way propagators in imaging large regions. Therefore, reverse time migration algorithms with Gaussian beams have recently been proposed to reduce the cost, as they combine the high computational efficiency of Gaussian beam migration and the high accuracy of reverse time migration. However, this method was based on the assumption that the subsurface is isotropic. As the acquired azimuth and maximum offsets increase, taking into account the influence of anisotropy on seismic migration is becoming more and more crucial. Using anisotropic ray tracing systems in terms of phase velocity, we proposed an anisotropic reverse time migration using the Gaussian beams method. We consider the influence of anisotropy on the propagation direction and calculate the amplitude of Gaussian beams with optimized correlation coefficients in dynamic ray tracing, which simplifies the calculations and improves the applicability of the proposed method. Numerical tests on anisotropic models demonstrate the efficiency and accuracy of the proposed method, which can be used to image complex structures in the presence of anisotropy in the overburden.

Three-dimensional passive-source anisotropic reverse time migration for imaging lithospheric discontinuities

SUMMARY The scattered teleseismic body waves have been used intensively to characterize the receiver-side lithospheric structures. The routinely used ray-theory-based methods have limitations to image complex structures and tackle strong heterogeneities. The newly developed wave-equation based, passive-source reverse time migration (RTM) approach can overcome such limitations. To date, passive-source RTM has been developed only for isotropic media. However, at least to the first-order, most lithospheric structures possess effective transverse isotropy with spatially variable symmetry directions. It is important to know the magnitudes of imaging errors that may be introduced by passive-source RTM when seismic anisotropy is treated in an incorrect way. In this paper, we investigate the influence of elastic anisotropy on teleseismic P-to-S conversions at the lithospheric discontinuities and explain why an isotropic RTM may fail to focus the converted wavefields from the perspective of relative arrival time variations with backazimuth and shear wave splitting. Accordingly, we extend the passive-source RTM approach for imaging 3-D lithospheric targets possessing transverse isotropy from the following two aspects: First, the teleseismic recordings with direct P and converted S phases are reverse-time extrapolated using rotated staggered grid (RSG) pseudospectral method, which can tackle strong heterogeneity and transverse isotropies with symmetry axes in arbitrary direction; Secondly, the backward elastic wavefields are efficiently decomposed into vector anisotropic P and S modes to support accurate imaging.

Three-Dimensional Passive-Source Anisotropic Reverse Time Migration for Imaging Lithospheric Discontinuities: The Method

Three-Dimensional Passive-Source Anisotropic Reverse Time Migration for Imaging Lithospheric Discontinuities: The Method

Pseudo-acoustic anisotropic reverse-time migration of an ocean-bottom cable dataset acquired in the North Sea

ABSTRACT To improve the computational efficiency of reverse-time migration (RTM) for vertically transverse isotropic (VTI) media, various acoustic approximations of the elastic wave equations have been presented. Among these, the pseudo-acoustic wave equation, which combines differential and scalar operators, has the advantage that it does not produce shear wave artefacts. In this study, we investigate the feasibility of pseudo-acoustic anisotropic RTM (PA-RTM) for the analysis of synthetic and observed ocean-bottom cable (OBC) datasets of the Volve oil field in the North Sea. To analyse the influence of anisotropic parameters on RTM images and the sensitivity of data components to seismic anisotropy, we perform PA-RTM using synthetic data by incorporating various background models, as well as pressure wavefields and vertical particle acceleration. The synthetic experiments demonstrate that the anisotropic parameter ε plays an important role, whereas δ is negligible in PA-RTM for VTI media, and that vertical particle acceleration is less affected by seismic anisotropy than the pressure wavefields. Our experiments using observed data show that reflectors are better imaged by PA-RTM than by isotropic-RTM, particularly near the reservoir below the strongly anisotropic region, which is supported by angle-domain common image gathers. These results indicate that PA-RTM using only the vertical component is a suitable option for VTI media when insufficient seismic anisotropy data are available.

Azimuth ambiguity elimination for borehole imaging using 3D borehole RTM scheme

A key technical challenge facing borehole acoustic reflection imaging is the uncertainty concerning the azimuth (i.e. the direction about the axis of the borehole) from which a reflected event arrives. In generating images of formation boundaries near the borehole this is referred to as azimuthal ambiguity. The phenomenon is comparable to the 3D out-of-plane effects encountered in imaging of 2D surface data. Systems with multiple receivers (e.g., the sonic scanner tool developed by Schlumberger) acquire sufficient information to uniquely image reflected wave energy at its correct azimuth. However, a full use of this information requires the wave data to be analyzed in the context of 3D, two-way elastic wave propagation and a suitable anisotropic medium. Here we summarize the development of a 3D anisotropic reverse time migration imaging scheme to sonic data, and demonstrate that within this imaging formulation azimuthal ambiguity is resolved for data from both monopole and dipole sources.

A feasibility study of imaging hydraulic fractures with anisotropic reverse time migration

Accurate characterization of fracture zones induced by hydraulic pressure plays a very important role in production optimization, because it may help to understand the porosity and permeability of the reservoir. During microseismic monitoring, a common technique to delineate fractures is to locate microseismic events. However, due to low signal to noise ratio (SNR) and a limited number of microseismic events, the fracturing areas may not be well described by the spatial distribution of microseismic events. Additionally, except for the inherent anisotropy of shale, fractures often show preferred orientations, which may enhance anisotropy in the formations. Therefore, in this study we propose an approach to characterize the fractured zones by applying anisotropic reverse time migration (RTM) to microseismic waveform data. During hydraulic fracturing, microseismic waveforms may include scattered wavefield due to pre-existing fractures. We shall use the scattered wavefields, P- and S-wave codas, to image fractures. We analyze the feasibility of this method by testing numerical examples with various circumstances, such as configurations of event cluster and receiver positions, different uncertainties of event locations, velocity parameters, and noises, using downhole observation in 2D models. Synthetic tests demonstrate that we can directly image the nearby fracture zones with only a small number of microseismic events. Comparison between the isotropic and anisotropic migration results indicates that the anisotropy in the shale should not be ignored for imaging.

The stability problem of reverse time migration for viscoacoustic VTI media

In real strata anisotropy and viscosity extensively exists. They degraded waveforms in amplitude, resulting in which reducing of image resolution. To obtain high-precision imaging of deep reservoirs, we extended the separated viscous and anisotropic reverse time migration (RTM) to a stable viscoacoustic anisotropic RTM for vertical transverse isotropic (VTI) media, based on single generalized standard and linear solid (GSLS) media theory.. We used a pseudo-spectral method to develop the numerical simulation. By introducing a regularization operator to eliminate the high-frequency instability problem, we built a stable inverse propagator and achieved viscoacoustic VTI media RTM. High-resolution imaging results were obtained after correcting for the effects of anisotropy and viscosity. Synthetic tests verify the validity and accuracy of algorithm.

An efficient symplectic reverse time migration method using a local nearly analytic discrete operator in acoustic transversely isotropic media with a vertical symmetry axis

Reverse time migration (RTM) has become an extremely important imaging method due to its ability of handling complicated velocity models. In recent years, there has been an increasing need to perform RTM with anisotropic velocity models such as transversely isotropic media with a vertical symmetry axis (VTI). Finite difference (FD) is one of the most widely used numerical methods in RTM. However, it often suffers from serious numerical dispersion, resulting in significant loss of imaging resolution. Over the years, a nearly analytic discrete operator has been developed to approximate the high-order spatial partial differential operators, which is effective in suppressing numerical dispersion. Using this operator, we developed a nearly analytic symplectic (NAS) method to numerically solve acoustic VTI wave equations, which preserves the symplectic structure. We have investigated its properties including the stability condition, numerical dispersion relation, and computational efficiency. Also, we applied the NAS method to solve wave equations in RTM in acoustic VTI media. This new method not only reduced numerical dispersion and improved computational efficiency, compared to the conventional numerical methods such as the Lax-Wendroff correction (LWC) method, but it also was symplectic. Our forward-modeling results showed that the computational efficiency of NAS is about four times and its overall memory requirement is about 75% of those of LWC. The RTM results of the 2D prestack Hess acoustic VTI model showed that RTM by using NAS obtained better image quality than that by using LWC when coarse grids were used, which demonstrated that the NAS method can be promising in large-scale anisotropic RTM.

Reverse-time migration in acoustic VTI media using a high-order stereo operator

With the capability of handling complicated velocity models, reverse-time migration (RTM) has become a powerful imaging method. Improving imaging accuracy and computational efficiency are two significant but challenging tasks in the applications of RTM. Despite being the most popular numerical technique applied in RTM, finite-difference (FD) methods often suffer from undesirable numerical dispersion, leading to a noticeable loss of imaging resolution. A new and effective FD operator, called the high-order stereo operator, has been developed to approximate the partial differential operators in the wave equation, from which a numerical scheme called the three-step stereo method (TSM) has been developed and has shown effectiveness in suppressing numerical dispersion. Numerical results show that compared with the conventional numerical methods such as the Lax-Wendroff correction (LWC) scheme and the staggered-grid (SG) FD method, this new method significantly reduces numerical dispersion and computational cost. Tests on the impulse response and the 2D prestack Hess acoustic VTI model demonstrated that the TSM achieves higher image quality than the LWC and SG methods do, especially when coarse computation grids were used, which indicated that the new method can be a promising algorithm for large-scale anisotropic RTM.

Investigation of deep-water Gulf of Mexico subsalt imaging using anisotropic model, data set and RTM — Tempest

Performing accurate depth-imaging is an essential part of deep-water Gulf of Mexico exploration and development. Over the years, depth-imaging technology has provided reliable seismic images below complicated salt bodies, and has been implemented in workflows for both prospect generation as well as reservoir development. These workflows include time domain preprocessing using various multiple elimination techniques, anisotropic model building, and depth-imaging using anisotropic reverse time migration (RTM). However, the accuracy of the depth-migrated volumes is basically unknown because they are tested only in the locations where a well is drilled. In order to learn about the accuracy of anisotropic deep water Gulf of Mexico model building, and depth-imaging tools which are used for processing and imaging of field acquired data, we created a 3D vertical transverse isotropic (VTI) anisotropic earth model and a 3D seismic data set representing subsalt Gulf of Mexico geology. The model and data set are referred to as the Tempest data set, the original being created several years ago. The recent model and data set were created incorporating upgraded technology to reflect recent developments in data acquisition, model building and depth-imaging. Our paper presents the new Tempest anisotropic model, data set, and RTM prestack depth-migration (PSDM) results. The Tempest RTM PSDM is being used to learn about the differences between the exact geological model and the RTM PSDM image, helping in the interpretation of real RTM prestack depth-migrated data.

TTI reverse time migration using the pseudo-analytic method

Reverse time migration (RTM) was first introduced in the early 1980s (Whitmore, 1983), but was seemingly dormant until recent advances in computer hardware helped propel it onto the stage as a powerful depth-imaging method. RTM is now standard for areas where large velocity contrasts and/or steep dips pose a challenge, for instance below salt in the Gulf of Mexico. In recent years, where called for by the data, the migration tool of choice has gone from isotropic RTM to anisotropic RTM. The most common representations of anisotropy in sedimentary rocks are VTI (transverse isotropy with a vertical axis of symmetry) and TTI (tilted transverse isotropy). While isotropic and VTI RTM have become somewhat routine, TTI RTM remains challenging due to the complexity, stability, computational cost, and the difficulty in estimating the anisotropic parameters for TTI media.

Reverse time migration in tilted transversely isotropic (TTI) media

Reverse time migration (RTM) exhibits great advantages over other imaging methods because it is based on computing numerical solutions to a two-way wave equation. It does not suffer from dip limitation like one-way downward continuation techniques do, thus enabling overturned reflections to be imaged. As well as correctly handling multipathing, RTM has the potential to image internal multiples when the boundaries responsible for generating the multiples are present in the model. In isotropic media, one can use a scalar acoustic wave equation for RTM of pressure data. In anisotropic media, P- and SV-waves are coupled together so, formally, elastic wave equations must be used for RTM. A new wave equation for P-waves is proposed in tilted transversely isotropic (TTI) media that can be solved as part of an acoustic anisotropic RTM algorithm, using standard explicit finite differencing. If the shear velocity along the axis of symmetry is set to zero, stable numerical solutions can be computed for media with a vertical axis of symmetry and [Formula: see text] not less than [Formula: see text]. In TTI media with rapid variations in the direction of the axis of symmetry, setting the shear velocity along the axis of symmetry to zero can cause numerical solutions to become unstable. A solution to this problem is proposed that involves using a small amount of nonzero shear velocity. The amount of shear velocity added is chosen to remove triplications from the SV wavefront and to minimize the anisotropic term of the SV reflection coefficient. We show modeling and high-quality RTM results in complex TTI media using this equation.

Application of reverse time migration to complex imaging problems

Paul A. Farmer, Ian F. Jones, Hongbo Zhou, Robert I. Bloor, and Mike C. Goodwin explain the revival of interest in reverse time migration with some examples from the North Sea of model building and migrating with the full acoustic two-way wave equation. Standard shot-based one-way wavefield extrapolation (WE) preSDM techniques image the subsurface by downward continuing the source and receiver wave-fields for each shot. The imaging condition is invoked by cross correlating these two wave-fields at each depth level, and then summing the contributions from all shots in the aperture to form the image. One of the assumptions made in using this technique is that the wave-fields travel along the direction of extrapolation only in one direction: downwards for the source wave-field, and upwards for the receiver or scattered wave-field. In practice, each of these wave-fields will generally travel both up and down when the velocity model is complex, when turning (diving) ray-paths are involved, or when multiples are being generated. In addition, approximations in the extrapolation techniques usually limit the dips present in the final image to less than seventy degrees. Steeper dips, and turning rays are usually imaged using Kirchhoff techniques, but these fail to deliver acceptable images once we have a multi-pathing problem. One technique which can address all these issues is migration using the two-way wave equation. Here, we have used an anisotropic reverse time migration (RTM) algorithm to achieve this. RTM properly propagates the wave-field through velocity structures of arbitrary complexity, correctly imaging dips greater than 90 degrees. It even has the potential to image with internal multiples when the boundaries responsible for the multiple are present in the model. Although hitherto considered economically impracticable, recent enhancements to computing capacity, both in terms of CPU speeds and highly efficient hardware infrastructure, have made RTM commercially viable. Following an historical review of the approximations used in migration, we will show anisotropic RTM examples from the North Sea, outlining the potential benefit of model building and migrating with the full acoustic two-way wave equation.