Prestack Reverse Time Migration Research Articles

Parallel Scalability of a Fine-Grain Prestack Reverse Time Migration Algorithm

Seismic imaging has evolved significantly due to the high demand from the oil/gas industry for hardware technological advancements, boosting the development of more sophisticated algorithms. In order to deliver the quality and accuracy required, the execution of these algorithms may lead to time infeasible solutions. Aiming at performance improvement, this work conducted the parallelization of the core of a reverse time migration (RTM) algorithm. Furthermore, analysis such as speedup and efficiency was performed in order to assess the scalability of the proposed method. While the many parallelization efforts so far deal with coarse-grain approaches, this letter tackles the intrashot fine-grain parallelization of prestack RTM, which increases the overall concurrency degree of the algorithm. Results using 2-D synthetic data show that the proposed approach is scalable, which means that an increase in hardware resources and/or in problem size will lead to a proportional increase in speed and/or accuracy.

Fracture identification based on remote detection acoustic reflection logging

Fracture identification is important for the evaluation of carbonate reservoirs. However, conventional logging equipment has small depth of investigation and cannot detect rock fractures more than three meters away from the borehole. Remote acoustic logging uses phase-controlled array-transmitting and long sound probes that increase the depth of investigation. The interpretation of logging data with respect to fractures is typically guided by practical experience rather than theory and is often ambiguous. We use remote acoustic reflection logging data and high-order finite-difference approximations in the forward modeling and prestack reverse-time migration to image fractures. First, we perform forward modeling of the fracture responses as a function of the fracture–borehole wall distance, aperture, and dip angle. Second, we extract the energy intensity within the imaging area to determine whether the fracture can be identified as the formation velocity is varied. Finally, we evaluate the effect of the fracture–borehole distance, fracture aperture, and dip angle on fracture identification.

Damage identification for composite structures using a cross-correlation reverse-time migration technique

This article presents a reverse-time migration technique to image damage by cross-correlating forward and backward propagating wavefields in composite structures using flexural wave signals. First, theory and procedures are presented for damage imaging for composite plates using a zero-lag cross-correlation imaging condition for reverse-time migration, briefly called cross-correlation-based reverse-time migration. The zero-lag cross-correlation was calculated between the forward wavefield and the backward wavefield. The forward wavefield is formed by the excitation from the actuator using a finite difference method, and the backward wavefield is generated by back-propagating the time-reversed scattered wavefield using the same finite difference method. Simulation studies were first examined to verify the capability of using the proposed zero-lag cross-correlation imaging condition to image single and multiple sites of damage. Two experiments were conducted where either the surface-mounted piezoelectric wafers or non-contact laser Doppler vibrometer was used for receiving the scattered wave signals along a linear array. The scattered wave signals were extrapolated in reverse-time to generate backward propagating wavefields. The experimental studies demonstrated that the cross-correlation-based reverse-time migration can accurately locate and image multiple sites of damage with improved resolution and higher efficiency in comparison with classical pre-stack reverse-time migration.

Acoustic Reverse-time Migration using Optimal Staggered-grid Finite-difference Operator Based on Least Squares

Reverse-time migration (RTM) directly solves the two-way wave equation for wavefield propagation; therefore, how to solve the wave equation accurately and quickly is very important for RTM. The conventional staggered-grid finite-difference (SFD) operators are usually based on the Taylor-series expansion theory. If they are used to solve wave equation on a larger frequency content, a strong dispersion will occur, which directly affects the seismic image quality. In this paper, we propose an optimal SFD operator based on least squares to solve acoustic wave equation for prestack RTM, and obtain a new antidispersion RTM algorithm that can use short spatial difference operators. The synthetic and real data tests demonstrate that the least squares SFD (LSSFD) operator can mitigate the numerical dispersion, and the acoustic RTM using the LSSFD operator can effectively improve image quality comparing with that using the Taylor-series expansion SFD (TESFD) operator. Moreover, the LSSFD method can adopt a shorter spatial difference operator to reduce the computing cost.

Removing smearing-effect artifacts in angle-domain common-image gathers from reverse time migration

Local plane-wave decomposition (LPWD) and local shift imaging condition (LSIC) methods for extracting angle-domain common-image gathers (ADCIGs) from prestack reverse time migration are based on the local plane-wave assumption, and both suffer from a trade-off in choosing the local window size. Small windows produce clean ADCIGs, but with low angle resolution, whereas large windows produce noisy ADCIGs, which include smearing-effect artifacts, but with high angle resolution. The cause of the smearing-effect artifacts in LPWD is the crosscorrelation of plane waves obtained by decomposition of the source and receiver wavefronts, at points that do not lie on the source wavefront excitation time trajectory. The cause of the smearing-effect artifacts in LSIC is the decomposition of curved events of offset-domain common-image gathers (ODCIGs) at incorrect depth points at zero offset. These artifacts can occur even if the migration velocity model is correct. Two methods were proposed to remove the artifacts. In the LPWD method, the smearing-effect artifacts were removed by decomposing and crosscorrelating the resulting source and receiver plane waves only at image points and excitation (image) times. In the LSIC method, the artifacts were removed by decomposing curved events in ODCIGs into planar events only at zero-offset target image points. Numerical tests with synthetic data revealed the success of the proposed methods.

Improving input/output performance in 2D and 3D angle-domain common-image gathers from reverse time migration

We have developed a new method of extracting angle-domain common-image gathers (ADCIGs) from prestack reverse time migration (RTM) that has minimal intermediate storage requirements. To include multipathing, we applied an imaging condition for prestack RTM that uses multiple excitation image times. Instead of saving the full-source snapshots at all time steps, we picked and saved only a few of the highest amplitude arrivals, and their corresponding excitation times, of the source wavefield at each grid point, and we crosscorrelated with the receiver wavefield. When extracting the ADCIGs from RTM, we calculated the source propagation direction from the gradient of the excitation times. The result was that the source time snapshots do not have to be saved or reconstructed during RTM or while extracting ADCIGs. We calculated the receiver propagation direction from Poynting vectors during the receiver extrapolation at each time step and the reflector normal direction by the phase-gradient method. With a new strategy that uses three direction vectors (the source and receiver propagation directions as well as the reflector normal direction), we provided more reliable ADCIGs that are free of low-wavenumber artifacts than any two of them do separately, when the migration velocity model was near to the correct velocity model. The 2D and 3D synthetic tests demonstrated the successful application of the new algorithms with acceptable accuracy, improved storage efficiency, and without an input/output bottleneck.

Geophysics Bright Spots

The January-February 2015 issue of Geophysics brings with it the broad diversity that we have come to expect in the journal. These include an application of integrated geophysics of landfills, a theory of shear waves in low-symmetry anisotropic media, time-lapse reservoir characterization by seismic amplitudes, a possible pitfall of confusing the seismic waves from regional earthquakes with the long-duration events associated with hydraulic fracturing, an attack on a longstanding seismological controversy — the different types of Q — a discussion of the electromagnetic response of a 1D VTI medium, tomography with RTM backscatter, a new approach to joint inversion of seismic and gravity, and finally, five ways to avoid storing source wavefield snapshots in 2D elastic prestack reverse time migration.

Five ways to avoid storing source wavefield snapshots in 2D elastic prestack reverse time migration

Five alternative algorithms were evaluated to circumvent the excessive storage requirement imposed by saving source wavefield snapshots used for the crosscorrelation image condition in 2D prestack elastic reverse time migration. We compared the algorithms on the basis of their ability, either to accurately reconstruct (not save) the source wavefield or to use an alternate image condition so that neither saving nor reconstruction of full wavefields was involved. The comparisons were facilitated by using the same (velocity-stress) extrapolator in all the algorithms, and running them all on the same hardware. We assumed that there was enough memory in a node to do an extrapolation, and that all input data were stored on disk rather than residing in random-access memory. This should provide a fair and balanced comparison. Reconstruction of the source wavefield from boundary and/or initial values reduced the required storage to a very small fraction of that needed to store source wavefield snapshots for conventional crosscorrelation, at the cost of adding an additional source extrapolation. Reverse time checkpointing avoided recursive forward recomputation. Two nonreconstructive imaging conditions do not require full snapshot storage or an additional extrapolation. Time-binning the imaging criteria removed the need for image time searching or sorting. Numerical examples using elastic data from the Marmousi2 model showed that the quality of the elastic prestack PP and PS images produced by the cost-optimized alternative algorithms were (virtually) identical to the higher cost images produced by traditional crosscorrelation.

Carbonate reservoirs dominated by secondary storage space: Key issues and technical strategy

Carbonate reservoirs of the Tarim Basin in China are buried deeply, with strong later diagenesis, and seldom are controlled by geologic facies. The effective storage spaces are mainly dissolution caves and fractures with few primary pores. Fluid distribution in the reservoir is extremely complicated. All these characteristics make it a world-class challenge for oil and gas exploration and production. Conventional poststack methods ignore the complexity of the reservoir medium with low accuracy of prediction results, by which the location of the dissolution cave is determined roughly. Only faults and fracture zones can be described to a certain degree instead of quantifying the fracture detection. Aiming at the key problems of the complex carbonate reservoirs in the Tarim Basin, a series of techniques has been developed to improve the successful rate of reservoir prediction, including the following aspects: the wide-azimuth and high-density data-acquisition technique to improve the quality of the original seismic data; a series of migration techniques including prestack reverse time migration; and amplitude-preserved Q migration to improve the quality of seismic gathers and the imaging precision with the matching precision of AVO gathers. The target reservoir data dominant frequency increased by more than 15% and by nearly 20 Hz. In addition, the effective DEM-Gassmann rock-physics model is proposed for velocity prediction, by which relative error of estimated shear-wave velocity reaches to less than 5%. Furthermore, an advanced inversion algorithm is introduced to improve the accuracy of extracted elastic information. By using new prestack inversion and frequency-dependent AVO inversion, the tie rate of the dissolution-cave reservoir and fluid prediction increased by more than 15%. Furthermore, the fracture-prediction tie rate can be enhanced by 20% through limited-azimuth anisotropic inversion, on the basis of which the quantitative identification of fracture fluid for actual seismic data can be realized.

Accurate Seismic Imaging Methods on Complex Fault Blocks of Subei Basin

Subei basin is well-known for its complex fault block reservoirs and has wide growth of shallow igneous rocks. These inherent geological characteristics seriously affect the accurate seismic imaging of target layers. Pre-stack depth migration is an effective imaging method for complex structure and velocity field zones. In order to verify nice imaging ability of Kirchhoff’s pre-stack depth migration (KPSDM) and reverse-time migration (RTM), imaging tests were carried out based on the velocity model for complex fault block of igneous area in Subei basin. Experimental results showed that under the condition of reliable high-frequency velocity field, RTM had obvious advantage in imaging of fault blocks, otherwise, KPSDM was a viable option. In order to verify above experimental results, by selecting seismic data with higher signal to noise ratio (SNR), a reliable high-frequency velocity field was established, and the imaging processing was carried out. The results showed that RTM has obvious advantage over KPSDM in the aspect of improving imaging results of fault blocks and target layers under igneous rocks. Therefore, the choosing of imaging methods for complex fault blocks with igneous zone depends on SNR of seismic data. If seismic data has high SNR, a more accurate high frequency velocity field can be set up. Thus RTM can achieve precise imaging for target layers. If the seismic data has low SNR, KPSDM will become a good choice. Key words: Subei basin; Complex fault block; Igneous rock; Velocity model; Reverse time migration

A normalized wavefield separation cross-correlation imaging condition for reverse time migration based on Poynting vector

Prestack reverse time migration (PSTM) is a common imaging method; however low-frequency noises reduce the structural imaging precision. Thus, the suppression of migration noises must be considered. The generation mechanism of low-frequency noises is analyzed and the up-, down-, left-, and right-going waves are separated using the Poynting vector of the acoustic wave equation. The computational complexity and memory capacitance of the proposed method are far smaller than that required when using the conventional separation algorithm of 2D Fourier transform. The normalized wavefield separation crosscorrelation imaging condition is used to suppress low-frequency noises in reverse time migration and improve the imaging precision. Numerical experiments using the Marmousi model are performed and the results show that the up-, down-, left-, and right-going waves are well separated in the continuation of the wavefield using the Poynting vector. We compared the imaging results with the conventional method, Laplacian filtering, and wavefield separation with the 2D Fourier transform. The comparison shows that the migration noises are well suppressed using the normalized wavefield separation cross-correlation imaging condition and higher precision imaging results are obtained.

Application of pre-stack reverse time migration based on FWI velocity estimation to ground penetrating radar data

Abstract Reverse-time migration (RTM) is used for subsurface imaging to handle complex velocity models including steeply dipping interfaces and dramatic lateral variations and promises better imaging results compared to traditional migration method such as Kirchhoff migration algorithm. RTM has been increasingly used in seismic surveys for hydrocarbon resource explorations. Based on the similarity of kinematics and dynamics between electromagnetic wave and elastic wave, we develop pre-stack RTM method and apply it to process ground penetrating radar (GPR) data. Finite-difference time domain (FDTD) numerical method is used to simulate the electromagnetic wave propagation including forward and backward extrapolations, the cross-correlation imaging condition is used to obtain the final image. In order to provide a velocity model with relatively higher accuracy as the initial velocity model for RTM, we apply a full waveform inversion (FWI) in time domain to estimate the subsurface velocity structure based on reflection radar data. For testing the effectiveness of the algorithm, we have constructed a complex geological model, common-offset radar data and common-shot profile (CSP) radar reflection data are synthesized. All data are migrated with traditional Kirchhoff migration method and pre-stack RTM method separately, the migration results from pre-stack RTM show better coincidence with the true model. Furthermore, we have performed a physical experiment in a sandbox where a polyvinyl chloride (PVC) box is buried in the sand, the obtained common-offset radar data and common-shot radar data are migrated by using Kirchhoff migration method and pre-stack RTM algorithm separately, the pre-stack RTM result shows that RTM algorithm could get better imaging results.

Reverse time migration from irregular surface by flattening surface topography

Abstract Prestack reverse time migration (RTM) is a powerful tool to provide high resolution structure images of crust and upper mantle in wide-angle seismic experiments. As a standard migration algorithm assumes that data are recorded on a flat surface, RTM meets severe challenge on the issue of complicated topography where many seismic surveys are carried out. Up till now, there are two popular techniques for handling elevation changes, i.e., elevation-static correction (or time shift) and wave equation datuming. Numerous studies demonstrate that the elevation-static correction is inaccurate for non-vertically traveling energy and subsequently may migrate reflectors to incorrect positions. Wave equation datuming is more accurate but more sophisticated and too computationally demanding for routine use. Here, we present an alternative scheme to deal with topography in prestack RTM that can migrate seismic data acquired in areas with irregular topography to the reflector positions directly without datuming or elevation static corrections. In this scheme, surface topography is flattened by a transformation of coordinates from Cartesian to curvilinear. Such a transformation is equivalent to map a rectangular grid onto a curved one, and is implemented by the introduction of boundary conforming grid. Then we use an explicit finite-difference scheme with second-order accuracy to discretize the elastic wave equations and perform the RTM in the curvilinear coordinate system. Moreover, a flux-corrected transport (FCT) algorithm, adapted from hydrodynamics, is incorporated in the RTM implementation, which can not only overcome problems of numerical dispersion that arise in finite difference algorithms, but also offer the opportunity to use a coarse grid to obtain the same accuracy as conventional finite difference methods on a dense grid. The FCTRTM method presented here has no limitations on surface irregularity, complexity of the subsurface structure, or velocity function. Extensive numerical examples demonstrate the feasibility and effectiveness of our method.

Viscoacoustic prestack reverse time migration based on the optimal time-space domain high-order finite-difference method

Prestack reverse time migration (RTM) is an accurate imaging method of subsurface media. The viscoacoustic prestack RTM is of practical significance because it considers the viscosity of the subsurface media. One of the steps of RTM is solving the wave equation and extrapolating the wave field forward and backward; therefore, solving accurately and efficiently the wave equation affects the imaging results and the efficiency of RTM. In this study, we use the optimal time-space domain dispersion high-order finite-difference (FD) method to solve the viscoacoustic wave equation. Dispersion analysis and numerical simulations show that the optimal time-space domain FD method is more accurate and suppresses the numerical dispersion. We use hybrid absorbing boundary conditions to handle the boundary reflection. We also use source-normalized cross-correlation imaging conditions for migration and apply Laplace filtering to remove the low-frequency noise. Numerical modeling suggests that the viscoacoustic wave equation RTM has higher imaging resolution than the acoustic wave equation RTM when the viscosity of the subsurface is considered. In addition, for the wave field extrapolation, we use the adaptive variable-length FD operator to calculate the spatial derivatives and improve the computational efficiency without compromising the accuracy of the numerical solution.

Simultaneous reverse time migration of primaries and free-surface related multiples without multiple prediction

Prestack reverse time migration (RTM) is usually regarded as an accurate imaging tool and has been widely used in exploration. Conventional RTM only uses primaries and treats free-surface related multiples as noise; however, free-surface related multiples can sometimes provide extra illumination of the subsurface, and this information could be used in migration procedures. There are many migration methods using free-surface related multiples, but most approaches need to predict multiples, which is time consuming and prone to error. We discovered a new RTM approach that uses the primaries and the free-surface related multiples simultaneously. Compared with migration methods that only use free-surface related multiples, the proposed approach can provide comparable migration results and does not need multiple predictions. In our approach, the source function in conventional RTM was replaced with recorded field data including primaries and free-surface related multiples, together with a synthetic wavelet; the back-propagated primaries in the conventional RTM were replaced with complete recorded field data. The imaging condition of the proposed approach was the same as the crosscorrelation imaging condition of conventional RTM. A three-layer velocity model with scatterers and the Sigsbee 2B synthetic data set were used for numerical experiments. The numerical results showed that the proposed approach can cover a wider range of the subsurface and provide better illumination compared with conventional RTM. The proposed approach was easy to implement and avoided tedious multiple prediction; it might be significant for general complex subsurface imaging.

Simulating propagation of separated wave modes in general anisotropic media, Part I: qP-wave propagators

Wave propagation in an anisotropic medium is inherently described by elastic wave equations with P- and S-wave modes intrinsically coupled. We present an approach to simulate propagation of separated wave modes for forward modeling, migration, waveform inversion, and other applications in general anisotropic media. The proposed approach consists of two cascaded computational steps. First, we simulate equivalent elastic anisotropic wavefields with a minimal second-order coupled system (that we call here a pseudo-pure-mode wave equation), which describes propagation of all wave modes with a partial wave mode separation. Such a system for qP-wave is derived from the inverse Fourier transform of the Christoffel equation after a similarity transformation, which aims to project the original vector displacement wavefields onto isotropic references of the polarization directions of qP-waves. It accurately describes the kinematics of all wave modes and enhances qP-waves when the pseudo-pure-mode wavefield components are summed. The second step is a filtering to further project the pseudo-pure-mode wavefields onto the polarization directions of qP-waves so that residual qS-wave energy is removed and scalar qP-wave fields are accurately separated at each time step during wavefield extrapolation. As demonstrated in the numerical examples, pseudo-pure-mode wave equation plus correction of projection deviation provides a robust and flexible tool for simulating propagation of separated wave modes in transversely isotropic and orthorhombic media. The synthetic example of a Hess VTI model shows that the pseudo-pure-mode qP-wave equation can be used in prestack reverse-time migration applications.

Corrigendum to “Acoustic VTI modeling and pre-stack reverse-time migration based on the time-space domain staggered-grid finite-difference method” [J. Appl. Geophys. 90 (2013) 41–52

Corrigendum to “Acoustic VTI modeling and pre-stack reverse-time migration based on the time-space domain staggered-grid finite-difference method” [J. Appl. Geophys. 90 (2013) 41–52

Multi-Component Seismic Wave Field Prestack Reverse-Time Depth Migration

Based on the elastic wave equation, high-order finite-difference schemes for reverse-time extrapolation in the space of staggered grid and the perfectly matched layer (PML) absorbing boundary condition for the equation are derived. Prestack reverse-time depth migration (RTM) of elastic wave equation using the excitation time imaging condition and normalized cross-correlation imaging condition is carried out. Numerical experiments show that reverse-time migration is not limited for the angle of incidence and dramatic changes in lateral velocity. The reverse-time migration results of normalized cross-correlation imaging condition give the better effect than that of excitation time imaging condition.

Polarization-based wave-equation migration velocity analysis in acoustic media

The source extrapolation step in wave-equation prestack reverse-time migration gives wavefield polarization information, which can be used to generate angle-domain common-image gathers (ADCIGs) from seismic reflection data from acoustic media. Concatenation of P-wave polarization segments gives wavefield propagation paths (“wavepaths”), which are similar to the raypaths in ray-based velocity tomography. The ADCIGs provide residual depth moveout (RMO) information, from which a system of linear equations is constructed for tomography to solve for the velocity ratio used for velocity updating. An empirical relation between the RMO data and the velocity ratio updates reduces the amount of computation, and is stabilized by the feedback provided by the iterative loop through prestack migration, to RMO, to velocity update, to prestack migration. Correcting the RMOs to flatten the ADGIGs is the convergence condition. Synthetic data for a layered model with a fault successfully illustrates the method.

Direct pre-stack depth migration on rugged topography

Engineering seismic exploration aims at shallow imaging which is confused by statics if the surface is uneven. Direct pre-stack depth migration (DPDM) is based on accurate elevations of sources and receivers, by which static correction is completely abandoned before migration and surely the imaging quality is remarkably improved. To obtain some artificial shot gathers, high-order staggered-grid finite-difference (FD) method is adapted to model acoustic wave propagation. Since the shot gathers are always disturbed by regular interferences, the statics still must be applied to supporting the interference elimination by apparent velocity filtering method. Then all the shot gathers should be removed back to their original positions by reverse statics. Finally, they are migrated by pre-stack reverse-time depth migration and imaged. The numerical experiments show that the DPDM can ideally avoid the mistakes caused by statics and increase imaging precision.