Generalized Screen Propagator Research Articles

Viscoacoustic generalized screen propagator in constant-Q model

When seismic waves propagate through the geological formation, there is a significant loss of energy and a decrease in imaging resolution, because of the viscoacoustic properties of subsurface medium. This profoundly impacts seismic wavefield propagation, imaging and interpretation. To accurately image the true structure of subsurface medium, the consensus among geophysicists is to no longer treat subsurface medium as ideal homogeneous medium, but rather to incorporate the viscoacoustic properties of subsurface medium. Based on the generalized screen propagator using conventional acoustic wave equation (acoustic GSP), our developed method introduces viscoacoustic compensation strategy, and derives a one-way wave generalized screen propagator based on time-fractional viscoacoustic wave equation (viscoacoustic GSP). In numerical experiments, we conducted tests on two-dimensional multi-layer model and the Marmousi model. When comparing with the acoustic GSP using the acoustic data, we found that the imaging results of the viscoacoustic GSP using the viscoacoustic data showed a significant attenuation compensation effect, and achieved imaging results for both algorithms were essentially consistent. However, the imaging results of acoustic GSP using viscoacoustic data showed significant attenuation effects, especially for deep subsurface imaging. This indicates that we have proposed an effective method to compensate the attenuated seismic wavefield. Our application on a set of real seismic data demonstrated that the imaging performance of our proposed method in local areas surpassed that of the conventional acoustic GSP. This suggests that our proposed method holds practical value and can more accurately image real subsurface structures while enhancing imaging resolution compared with the conventional acoustic GSP. Finally, with respect to computational efficiency, we gathered statistics on running time to compare our proposed method with conventional Q-RTM, and it is evident that our method exhibits higher computational efficiency. In summary, our proposed viscoacoustic GSP method takes into account the true properties of the medium, still achieves migration results comparable to conventional acoustic GSP.

Enhancing one-way wave equation-based migration with deep learning

One advantage of one-way wave equation-based migration is its low computational cost. However, due to the limited wavefield propagation angle, it is difficult to use one-way wave equation-based migration for high-precision imaging of structures with large inclinations due to issues such as inaccurate amplitudes and migration image artifacts. In addition, when the model has large horizontal velocity differences, it is difficult for the one-way wave propagator to calculate an accurate wavefield phase. Reverse time migration (RTM) based on the two-way wave propagator has a high resolution and avoids the issues associated with one-way wave propagators; however, it has a high computational cost in practical applications. We develop a convolutional neural network (CNN) application mode that improves one migration method by learning from another one and design a CNN with a structure similar to U-net that combines the advantages of both migration methods. The CNN label is the RTM result, and the corresponding input is the result of one-way wave migration with a generalized screen propagator (GSP). The trained CNN model improves the amplitude in the one-way wave migration image and removes the errors caused by large lateral velocity perturbations. Moreover, by maintaining the high migration calculation efficiency, our CNN model allows for a high resolution, few artifacts, and accurate images of steep structures in the one-way wave migration result. With our method, the accuracy of the one-way wave migration result is close to that of the RTM result. The use of GSP-based migration in our CNN model rather than conventional RTM to generate prospecting images can considerably reduce the calculation costs.

Two-way wave equation-based depth migration using one-way propagators on a bilayer sensor seismic acquisition system

Conventional migration uses the seismic data set recorded at a given depth as one initial condition from which to implement wavefield extrapolation in the depth domain. In using only one initial condition to solve the second-order acoustic wave equation, some approximations are used, resulting in the limitation of imaging angles and inaccurate imaging amplitudes. We use an over/under bilayer sensor seismic data acquisition system that can provide the two initial conditions required to make the second-order acoustic wave equation solvable in the depth domain, and we develop a two-way wave equation depth migration algorithm by adopting concepts from one-way propagators, called bilayer sensor migration. In this new migration method, two-way wave depth extrapolation can be achieved with two one-way propagators by combining the wavefields at two different depths. It makes it possible to integrate the advantages of one-way migration methods into the bilayer sensor system. More detailed bilayer sensor migration methods are proposed to demonstrate the feasibility. In the impulse response tests, the propagating angle of the bilayer sensor migration method can reach up to 90°, which is superior to those of the corresponding one-way propagators. To test the performance, several migration methods are used to image the salt model, including the one-way generalized screen propagator, reverse time migration (RTM), and our bilayer sensor migration methods. Bilayer sensor migration methods are capable of imaging steeply dipping structures, unlike one-way propagators; meanwhile, bilayer sensor migration methods can greatly reduce the numbers of artifacts generated by salt multiples in RTM.

High-order generalized screen propagator migration based on particle swarm optimization

Various migration methods have been proposed to image high-angle geological structures and media with strong lateral velocity variations; however, the problems of low precision and high computational cost remain unresolved. To describe the seismic wave propagation in media with lateral velocity variations and to image high-angle structures, we propose the generalized screen propagator based on particle swarm optimization (PSO-GSP), for the precise fitting of the single-square-root operator. We use the 2D SEG/EAGE salt model to test the proposed PSO-GSP migration method to image the faults beneath the salt dome and compare the results to those of the conventional high-order generalized screen propagator (GSP) migration and split-step Fourier (SSF) migration. Moreover, we use 2D marine data from the South China Sea to show that the PSO-GSP migration can better image strong reflectors than conventional imaging methods.

Numerical modeling of seismic waves using frequency-adaptive meshes

An improved modeling algorithm using frequency-adaptive meshes is applied to meet the computational requirements of all seismic frequency components. It automatically adopts coarse meshes for low-frequency computations and fine meshes for high-frequency computations. The grid intervals are adaptively calculated based on a smooth inversely proportional function of grid size with respect to the frequency. In regular grid-based methods, the uniform mesh or non-uniform mesh is used for frequency-domain wave propagators and it is fixed for all frequencies. A too coarse mesh results in inaccurate high-frequency wavefields and unacceptable numerical dispersion; on the other hand, an overly fine mesh may cause storage and computational overburdens as well as invalid propagation angles of low-frequency wavefields. Experiments on the Padé generalized screen propagator indicate that the Adaptive mesh effectively solves these drawbacks of regular fixed-mesh methods, thus accurately computing the wavefield and its propagation angle in a wide frequency band. Several synthetic examples also demonstrate its feasibility for seismic modeling and migration.

Prestack elastic generalized-screen migration for multicomponent data

An efficient prestack depth migration method based on the elastic one-way wave equation was developed using an improved elastic generalized-screen propagator, which effectively describes the behavior of elastic waves with mode conversion at the interfaces and efficiently computes wave propagation in media with lateral velocity variations. The elastic propagator presented in this study was improved from the elastic generalized-screen propagator. Several terms of the vertical slowness right symbol with orders are corrected from the original formulation, and the vertical slowness operator in the propagator was expanded up to the 2nd order which yields a more accurate approximation. In each screen propagation step, the multicomponent wavefields are automatically separated into the P and S wavefields by the P–S decomposition operator included in the elastic generalized-screen propagator. This process facilitates the imaging of the P and S waves separately without any additional P and S separation process after the wavefield extrapolation. Impulse response tests of the improved elastic generalized-screen propagator in a uniform-property medium proved that propagation accuracy increases with order, even when large medium perturbations are assigned. Migration tests using the developed algorithm on a simple layered model and two complex models (the SEG/EAGE salt and elastic Marmousi-2 model) demonstrated the functional advantages and capabilities of the algorithm compared with elastic migration using the scalar wave equation.

Accelerating 3D Fourier migration with graphics processing units

Computational cost is a major factor that inhibits the practical application of 3D depth migration. We have developed a fast parallel scheme to speed up 3D wave-equation depth migration on a parallel computing device, i.e., on graphics processing units (GPUs). The third-order optimized generalized-screen propagator is used to take advantage of the built-in software implementation of the fast Fourier transform. The propagator is coded as a sequence of kernels that can be called from the computer host for each frequency component. Moving the wavefield extrapolation for each depth level to the GPUs allows handling a large 3D velocity model, but this scheme can be speeded up to a limited degree over the CPU implementation because of the low-bandwidth data transfer between host and device. We have created further speedup in this extrapolation scheme by minimizing the low-bandwidth data transfer, which is done by storing the 3D velocity model and imaged data in the device memory, and reducing half the memory demand by compressing the 3D velocity model and imaged data using integer arrays instead of float arrays. By incorporating a 2D tapered function, time-shift propagator, and scaling of the inverse Fourier transform into a compact kernel, the computation time is reduced greatly. Three-dimensional impulse responses and synthetic data examples have demonstrated that the GPU-based Fourier migration typically is 25 to 40 times faster than the CPU-based implementation. It enables us to image complex media using 3D depth migration with little concern for computational cost. The macrovelocity model can be built in a much shorter turnaround time.

Imaging salt bodies using explicit migration operators offshore Norway

We have tested the performance of 3D shot-profile depth migration using explicit migration operators on a real 3D marine data set. The data were acquired offshore Norway in an area with a complex subsurface containing large salt bodies. We compared shot-profile migration using explicit migration operators with conventional Kirchhoff migration, split-step Fourier migration, and common-azimuth by generalized screen propagator (GSP) migration in terms of quality and computational cost. Image quality produced by the explicit migration operator approach is slightly better than with split-step Fourier migration and clearly better than in common-azimuth by GSP and Kirchhoff migrations. The main differences are fewer artifacts and better-suppressed noise within the salt bodies. Kirchhoff migration shows considerable artifacts (migration smiles) within and close to the salt bodies, which are not present in images produced by the other three wave-equation methods. Expressions for computational cost were developed for all four migration algorithms in terms of frequency content and acquisition parameters. For comparable frequency content, migration cost using explicit operators is four times the cost of the split-step Fourier method, up to 260 times the cost of common-azimuth by GSP migration, and 25 times the cost of Kirchhoff migration. Our results show that in terms of image quality, shot-profile migration using explicit migration operators is well suited for imaging in areas with complex geology and significant velocity changes. However, computational cost of the method is high and makes it less attractive in terms of efficiency.

2.5D SH Wave Propagation in Heterogeneous Crustal Wave Guides Using the Phase Screen Method

Abstract One-way approximations for regional phases slice the half-space crustal wave guide into a number of slabs perpendicular to the propagation direction; the Moho discontinuity can be easily treated as a perturbation from the crustal background. The advantage of one-way propagation methods is their great saving of computing time and memory compared to full-waveform numerical methods, especially for 3D simulations. In this article, we present general 2.5D SH formulas for the thin-slab method and a generalized screen propagator (GSP) for simulating SH wave propagation in the heterogeneous half-space crustal wave guide. Comparisons of numerical results with a finite-difference (FD) algorithm for a standard flat crustal model show excellent agreement, demonstrating the validity and accuracy of the 2.5DGSP for the half-space problem. We then compare the curves of energy attenuation calculated by the 2D and 2.5D formulas. The comparison shows that the energy attenuation of the 2.5D case is about 1.5–3 times greater than that of the 2D case when the trapped mode is formed. The SH screen propagator is also used to simulate two laterally unvarying (in the y direction) crustal models, showing the path effects on regional wave propagation.

Beamlet migration using local cosine basis

We have developed the theoretical foundation and technical details of a migration method using a local-cosine-bases (LCB) beamlet propagator. A beamlet propagator for heterogeneous media based on local perturbation theory is derived, and a fast implementation method is constructed. The use of local background velocities and local perturbations results in a two-scale decomposition of beamlet propagators: a background propagator for large-scale structures and a local phase-screen correction for small-scale local perturbations. Because of its locally adaptive nature, the beamlet propagator can handle strong lateral velocity variations with improved accuracy. For high-efficiency migration, we use a table-driven method and apply some techniques of sparse matrix operations. Compared with the Fourier finite-dif-ference and generalized screen propagator methods, the image quality and computational efficiency are similar. In some cases, we see fewer migration artifacts around and inside salt bodies with our method. We attribute this to the better high-angle accuracy of beamlet propagators in strong-contrast media. Numerical tests using synthetic data sets of the SEG-EAGE 2D salt model, Marmousi model, and Sigsbee 2A model demonstrate its high accuracy and reasonable efficiency. Another special feature of LCB beamlet migration is the availability of information in the local wavenumber domain during migration, which can be used to correct acquisition aperture effect and for other processing. Compared to beamlet migration using the Gabor-Daubechies frame (GDF) propagator, LCB migration is much more efficient because LCB is an orthonormal basis, whereas GDF has redundancy (usually greater than two) in the decomposition.

High Order Generalized Screen Propagator for Wave Equation Prestack Depth Migration

AbstractDifferent from the scattering theory used in the derivation of conventional generalized screen propagator, in this paper, a high order formula of generalized screen propagator for one‐way wave equation is proposed by using the asymptotic expansion of single‐square‐root operator. The high order generalized screen propagator improves not only the calculation precision of conventional generalized screen propagator, but also the suitability of generalized screen propagator to the media with strong lateral‐velocity variation. Applying the high order generalized screen propagator to wave equation prestack depth migration can get a better migration result than that of conventional generalized screen propagator. The higher the order number of generalized screen propagator, the higher the calculation precision, and the more the calculation amount. Using the wave equation prestack depth migration on SEG‐EAGE 2‐D salt dome model as an example, the second‐order generalized screen propagator increases 30% calculation work relative to the conventional (one‐order) generalized screen propagator. The presentation of high order generalized screen propagator is a theoretic development and improvement to the conventional generalized screen propagator.

Wave-equation-based seismic illumination analysis

We present a wave-equation-based method for seismic illumination analysis. A one-way wave-equation-based, generalized screen propagator is used to extrapolate the wavefields from sources and receivers to the subsurface target. A local plane-wave analysis is used at the target to calculate localized, directional energy fluxes for both source and receiver wavefields. We construct an illumination matrix using these energy fluxes to quantify the target illumination conditions. The target geometry information is used to manipulate the illumination matrix and generate different types of illumination measures. The wave-equation-based approach can properly handle forward multiple-scattering phenomena, including focusing/defocusing, diffraction, and interference effects. It can be directly applied to complex velocity models. Velocity-model smoothing and Fresnel-zone smoothing are not required. Different illumination measurements derived from this method can be applied to target-oriented or volumetric illumination analyses. This new method is flexible and practical for illumination analysis in complex 2D and 3D velocity models with nontrivial acquisition and target geometries.

Comparison of Different One-Way Propagators for Wave Forward Propagation in Heterogeneous Crustal Wave Guides

Crustal wave guides are usually heterogeneous on many scales, some of which can be investigated for regional phases by one-way approximation methods. The advantage of one-way propagation methods is the greater saving of computing time and memory, often up to several orders, than the full-waveform numerical methods. By slicing a half-space crustal wave guide into a number of slabs perpendicular to the propagation direction, Wu et al. (2000) formulate a wide-angle pseudoscreen method for the SH half-space problem, which leads to a generalized screen propagator (gsp) for simulating Lg propagation. In this article we introduce a broadband constant-coefficient propagator for the SH half-space problem, which accounts for wide angles in large-contrast media while allowing implementation using Fourier transforms alone. Particular attention is paid to the first-order separation-of-variables screen propagator (svsp1) that significantly improves the split-step Fourier (ssf) method for large lateral variations at the cost of one more Fourier transform in each slab. Advancing wave fields by svsp1 is actually a linear interpolation in the wavenumber domain between two split-step terms. We benchmark the ssf, gsp, and svsp1 synthetic seismograms against the full-waveform boundary-element synthetics for flat, belling, and necking crustal wave guides, which shows that the svsp1 method can model the Lg phase and the mantle wave (head wave) quite well in both travel time, energy, and waveform for most common mantle velocity perturbations. These numerical comparisons also demonstrate some limitations (especially in waveform) of the one-way propagation methods to model the Lg code attributed by forward scatterings as a result of lateral irregularities of the Moho.

Wave equation GSP prestack depth migration and illumination

A heterogeneous medium with strong velocity contrast and complex subsurface structures presents a great challenge to seismic imaging. Prestack depth migrations based on the wave equation are accurate but very expensive, thereby limiting their use. However, recent advances in efficient 3D wavefield extrapolators and the continued increase in computing performance are making application of full 3D prestack wave equation depth imaging more affordable. In addition, since PreSDM was first employed for subsalt and carbonate imaging, there have been major advances in efficient and accurate 3D wavefield extrapolation technologies. The generalized screen propagator (GSP) is a one-way wave-equation-based wide-angle propagator that can provide high-resolution and high-fidelity subsurface images. GSP neglects up/down reverberations between heterogeneities and correctly handles forward multiple-scattering phenomena including focusing/defocusing, diffraction, and wave-interference effects. The algorithm alternates between the space-domain and wavenumber-domain via the fast Fourier transform (FFT). The operations within each domain are self-adaptive to the complexity of the medium, making this method robust in the presence of strong velocity contrasts. GSP can be directly applied for prestack shot-record depth migration. The forward downgoing wave from the source side and backward extrapolation of the upgoing wave from the receiver side independently use the same propagator. At each depth step, application of a correlation or deconvolution imaging condition determines a depth image. Figure 1 shows a prestack shot-record migration on the Sigsbee2 data set provided by the Smaart JV Project. Figure 1b shows that the top of salt is well imaged by the GSP migration even for the very steep-sided synclinal feature in the top salt surface. The amplitude and phase of the base salt are imaged well and have good continuity, and the diffractors beneath the salt are clearly reconstructed. The image quality in the finite-difference migration (Figure 1c) is generally comparable to the GSP result, but the …

Three‐dimensional depth imaging with generalized screens: A salt body case study

We illustrate the performance of the generalized screen propagator on real seismic data for 3D zero‐offset and prestack depth imaging. We use TotalFinaElf's L7D data set from the North Sea, a 3D marine seismic survey that contained limited azimuthal coverage. The subsurface shows significant tectonic deformation, including an intrusive salt body in sedimentary sequences. A transformation to common azimuth is applied prior to the 3D prestack depth imaging procedure. We compare the performance of the generalized screen propagator with that of a hybrid phase shift plus interpolation (PSPI)/split‐step Fourier method. Three‐dimensional prestack results confirm the generalized screen method handles multipathing more accurately. Comparisons are also made with Kirchhoff migration results. The results differ mainly in the fine‐scale irregularities of the image and not in the wavefront set of the image. Using synthetic models of similar structure (the SEG/EAGE salt model), we further illustrate the importance of multipathing and multiple scattering. Overall, our results show that our wave‐equation approach produces better images than the Kirchhoff approach to prestack depth migration; we attribute this mainly to a more complete handling of wave diffraction in the generalized screen expansion, which becomes important in strongly heterogeneous and irregular velocity models such as the ones containing salt bodies.

Wave Equation Based Pre‐Stack Depth Migration Using Generalized Screen Propagator

AbstractComputational efficiency and accuracy of seismic wave propagators are major concerns for 3‐D pre‐stack depth migration. Generalized screen propagator (GSP) is a dual‐domain one‐way propagator, which neglects reverberations between heterogeneities but correctly handles the forward multiple‐scattering including focusing, diffraction, refraction, and interference of seismic waves. Downward continuation of the wavefield using GSP is performed with a phase shift in a background medium followed by a wide‐angle correction that accommodates strong lateral velocity variations. In this paper, we implement GSP in double square root equation and propose an efficient and accurate offset domain pre‐stack depth migration method for 2‐D common offset and 3‐D common azimuth seismic data. Combined with common angle imaging (CAI) condition, offset domain GSP migration produces high quality images at a number of angles (or offset ray parameter values). Since offset ray parameter is proportional to angle of incidence at the reflector, CAI gathers provide a complete set of tools for migration velocity updating and amplitude‐versus‐offset (AVO) analysis.

A Hybrid BE-GS Method for Modeling Regional Wave Propagation

— We present a hybrid boundary-element (BE) and generalized screen propagator (GSP) method for the 2-D SH problem to model the combined effects of arbitrarily irregular topography, large-scale crustal variation, and the associated small-scale heterogeneities on regional wave propagation. We develop a boundary connection technique to couple the wave fields calculated by the BE method with those of the GSP method. Its validity is tested by numerical experiments. For a long crustal waveguide, the relatively short sections with severe surface topography can be modeled by the time-consuming BE method to high frequencies, and the exterior field in the relatively weak heterogeneous media of large volume can be calculated by the GSP method. For the waveguide with severe topography, the BE method can be used section by section via the boundary connection technique to model the combined effects of rough topography and large-scale structural variation on Lg wave propagation at extended regional distances.¶Numerical comparisons with independent methods showed that the hybrid method is relatively accurate for Lg simulation. We apply the hybrid method to Lg wave propagation in two real crustal waveguides in the Tibet region; one with Lg blockage and another without blockage. We found that the most characteristic effect from the irregular topography is the strong scattering by the topographic structures. The scattering by local irregular topographies leads to anomalous near-receive effects and tends to remove energy from the guided waves, which causes decay of amplitude and waveform distortion. It can be expected that rough surface topography and random heterogeneities with scale length close to the dominant wavelength will be very efficient in attenuating regional waves. The dramatic lateral variation of the topography-Moho large-scale structure combined with the small-scale rough topography and random heterogeneities could be the cause of Lg anomalous attenuation and blockage observed in this region. More quantitative assessment of the topographic effects must be conducted in the future.

Energy partition and attenuation of Lg waves by numerical simulations using screen propagators

Energy partition and attenuation of Lg waves in complex crustal waveguides with both large-scale structures and small-scale random heterogeneities are studied by numerical simulations. A newly developed screen propagator method (half-space generalized screen propagators) is tested and applied to this problem. The screen method is two to three orders of magnitude faster than finite difference (FD) method and uses much less internal memory. The method has no numerical dispersion and can easily incorporate various Q models into the codes. After analyzing different attenuation mechanisms, this paper is concentrated in simulating the leakage attenuation of Lg waves caused by forward large-angle scattering from random heterogeneities, which scatters the guided waves out of the trapped modes and leaking into the mantle. In addition to energy attenuation curves, variations of angular spectra of Lg waves along the path are also shown to give insight on the energy partition and scattering effects. The curve of equivalent Q for leakage attenuation as a function of normalized scale length ( ka) of the random heterogeneities agrees well with the scattering theory. The comparisons of the method with wavenumber integration and FD method, and the results of the numerical simulations demonstrate the validity and capacity of the screen propagator method in studying Lg attenuation.

Seismic Wave Propagation and Scattering in Heterogeneous Crustal Waveguides Using Screen Propagators: I SH Waves

The great advantages of one-way propagation methods, such as the gen- eralized screen propagators (GSP) method, are the fast speed of computation, often several orders of magnitude faster than the full-wave finite difference and finite element methods, and the huge savings in internal memory. In this article, a half- space GSP is formulated for the SH half-space problem. Two versions of the half- space GSP are derived: the wide-angle pseudo-screen and the phase-screen. The Moho discontinuity is treated as parameter perturbations from the crustal back- ground. The validity and limitations of this treatment are discussed. It is shown that half-space screen propagators can accurately propagate guided crustal waves that are composed of small-angle waves with respect to the horizontal direction. Comparisons of numerical results with a wavenumber integration method for flat crustal models and a finite difference algorithm for heterogeneous models show excellent agree- ments. For a model with propagation distance of 250 km, dominant frequency at 0.5 Hz, the GSP method is about 300 times faster than a finite difference algorithm with a similar accuracy. These comparisons demonstrate the accuracy and efficiency of the method. We apply our method to simulate regional wave propagation in different types of complex crustal waveguides including those with small-scale random het- erogeneities. The influence of these heterogeneities on Lg amplitude attenuation and Lg coda formation is significant.

Seismic depth migration with pseudo-screen propagator

The generalized screen propagator (GSP) is a fast and accurate method for computing wave propagation in laterally varying velocity media. The method solves the acoustic one-way wave equation by shuffling FFTs between frequency-space and frequency-wavenumber domain. The velocity model is decomposed into a vertically varying reference velocity and a laterally varying perturbation. Downward continuation of the wavefield is performed with a phase shift in a background medium followed by a correction that accommodates the lateral velocity variations. All frequencies of interest are migrated and summed to produce an image at each depth level. The screen propagators are applicable to both poststack and prestack depth migrations. We illustrate the method with the SEG-EAGE salt model and Marmousi data set. The image results show that the pseudo-screen propagator is a big improvement over the phase-screen propagator for steeply dipping events in strong-contrast heterogeneous media.