Wavefield reconstruction in attenuating media: A checkpointing-assisted reverse-forward simulation method

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. R349-R362 ◽  
Author(s):  
Pengliang Yang ◽  
Romain Brossier ◽  
Ludovic Métivier ◽  
Jean Virieux
Keyword(s):  
Waveform Inversion ◽  
Computational Cost ◽  
Three Dimensional ◽  
Simulation Method ◽  
Forward Modeling ◽  
Seismic Attenuation ◽  
Practical Implementation ◽  
Forward Simulation ◽  
Reverse Time ◽  
Time Migration

Three-dimensional implementations of reverse time migration (RTM) and full-waveform inversion (FWI) require efficient schemes to access the incident field to apply the imaging condition of RTM or build the gradient of FWI. Wavefield reconstruction by reverse propagation using final snapshot and saved boundaries appears quite efficient but unstable in attenuating media, whereas the checkpointing strategy is a stable alternative at the expense of increased computational cost through repeated forward modeling. We have developed a checkpointing-assisted reverse-forward simulation (CARFS) method in the context of viscoacoustic wave propagation with a generalized Maxwell body. At each backward reconstruction step, the CARFS algorithm makes a smart decision between forward modeling using checkpoints and reverse propagation based on the minimum time-stepping cost and an energy measure. Numerical experiments demonstrated that the CARFS method allows accurate wavefield reconstruction using less timesteppings than optimal checkpointing, even if seismic attenuation is very strong. For RTM and FWI applications involving a huge number of independent sources and/or applications on architectures with limited memory, CARFS will provide an efficient tool with adequate accuracy in practical implementation.

GPU Elastic Modeling Using an Optimal Staggered-Grid Finite-Difference Operator

2018 ◽  
Vol 26 (02) ◽  
pp. 1850005 ◽  
Author(s):  
Jian Wang ◽  
Xiaohong Meng ◽  
Hong Liu ◽  
Wanqiu Zheng ◽  
Zhiwei Liu
Keyword(s):  
Finite Difference ◽  
Difference Operator ◽  
Waveform Inversion ◽  
Forward Modeling ◽  
Dominant Frequency ◽  
Window Function ◽  
Numerical Dispersion ◽  
Staggered Grid ◽  
Reverse Time ◽  
Time Migration

Staggered-grid finite-difference forward modeling in the time domain has been widely used in reverse time migration and full waveform inversion because of its low memory cost and ease to implementation on GPU, however, high dominant frequency of wavelet and big grid interval could result in significant numerical dispersion. To suppress numerical dispersion, in this paper, we first derive a new weighted binomial window function (WBWF) for staggered-grid finite-difference, and two new parameters are included in this new window function. Then we analyze different characteristics of the main and side lobes of the amplitude response under different parameters and accuracy of the numerical solution between the WBWF method and some other optimum methods which denotes our new method can drive a better finite difference operator. Finally, we perform elastic wave numerical forward modeling which denotes that our method is more efficient than other optimum methods without extra computing costs.

Reducing computation cost by Lax-Wendroff methods with fourth-order temporal accuracy

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. T109-T119 ◽  
Author(s):  
Hongwei Liu ◽  
Houzhu Zhang
Keyword(s):  
Wave Equations ◽  
Numerical Solutions ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Second Order ◽  
Numerical Dispersion ◽  
Reverse Time ◽  
Time Migration ◽  
L2 Norm ◽  
Time Marching

Explicit time-marching finite-difference stencils have been extensively used for simulating seismic wave propagation, and they are the most computationally intensive part of seismic forward modeling, reverse time migration, and full-waveform inversion. The time-marching step, determined by both the stability condition and numerical dispersion, is a key factor in the computational cost. In contrast with the widely used second-order temporal stencil, the Lax-Wendroff stencil is more cost effective because the time-marching step can be much larger. It can be proved, using theory and numerical tests, that the Lax-Wendroff stencil does enable larger time steps. In terms of numerical dispersion, the time steps for second-order and Lax-Wendroff stencils are functions of the number of shortest wavelengths away from the source location. These functions are derived by evaluating the relative L2-norm of the differences between the analytical and numerical solutions. The method for determining the time-marching step is model adaptive and easy to implement. We use the pseudo spectral method for the computation of spatial derivatives, and the wave equations that we solved are for isotropic media only, but the described principles can be easily implemented for more complicated types of media.

scholarly journals Higher-order source-wavefield reconstruction for reverse time migration from stored values in a boundary strip just one point wide

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. T31-T38 ◽  
Author(s):  
Wim A. Mulder
Keyword(s):  
Waveform Inversion ◽  
Substantial Reduction ◽  
Computational Cost ◽  
Boundary Region ◽  
Reconstruction Error ◽  
Time Range ◽  
Boundary Values ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration

One way to deal with the storage problem for the forward source wavefield in reverse time migration and full-waveform inversion is the reconstruction of that wavefield during reverse time stepping along with the receiver wavefield. Apart from the final states of the source wavefield, this requires a strip of boundary values for the whole time range in the presence of absorbing boundaries. The width of the stored boundary strip, positioned in between the interior domain of interest and the absorbing boundary region, usually equals about half that of the finite-difference stencil. The required storage in 3D with high frequencies can still lead to a decrease in computational efficiency, despite the substantial reduction in data volume compared with storing the source wavefields at all or at appropriately subsampled time steps. We have developed a method that requires a boundary strip with a width of just one point and has a negligible loss of accuracy. Stored boundary values over time enable the computation of the second and higher even spatial derivatives normal to the boundary, which together with extrapolation from the interior provides stability and accuracy. Numerical tests show that the use of only the boundary values provides at most fourth-order accuracy for the reconstruction error in the source wavefield. The use of higher even normal derivatives, reconstructed from the stored boundary values, allows for higher orders as numerical examples up to order 26 demonstrate. Subsampling in time is feasible with high-order interpolation and provides even more storage reduction but at a higher computational cost.

scholarly journals Time-reversal checkpointing methods for RTM and FWI

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. S93-S103 ◽  
Author(s):  
John E. Anderson ◽  
Lijian Tan ◽  
Don Wang
Keyword(s):  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Forward Simulation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Step ◽  
Depth Migration ◽  
Full Waveform ◽  
Time Migration ◽  
Simulation Time

Time-domain seismic simulation can form the basis of reverse time depth migration and full-waveform inversion. These applications need to temporally crosscorrelate a forward simulation state with an adjoint simulation state and therefore need to be able to access each time step of a forward simulation in time-reverse order. This requires saving all forward states for all times (which can require more memory than is typically available on a computer system for many problems of interest), or the ability to checkpoint information and rapidly recompute forward simulation states as needed. Prior work has suggested how to do the latter by optimally choosing which forward simulation time steps to checkpoint, thereby enabling the most efficient reuse of memory buffers and minimizing recomputation. The optimal trade-off between memory usage and recomputation can be further improved under the assumption that the information needed to do temporal crosscorrelation is smaller than the information required to restart a simulation from a given time step. This assumption is true for many geophysical problems of interest. The modification can yield a reduction in the memory requirement and recomputation time. The tested examples applied to isotropic elastic reverse time migration and anisotropic viscoelastic full-waveform inversion.

scholarly journals Practical implementation of three‐dimensional poststack depth migration

Geophysics ◽  
1989 ◽  
Vol 54 (3) ◽  
pp. 309-318 ◽  
Author(s):  
Moshe Reshef ◽  
David Kessler
Keyword(s):  
Three Dimensional ◽  
Velocity Variation ◽  
Practical Implementation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Depth Migration ◽  
Time Migration ◽  
Data Volume ◽  
Migration Method ◽  
The Given

This work deals with the practical aspects of three‐dimensional (3-D) poststack depth migration. A method, based on depth extrapolation in the frequency domain, is used for the migration. This method is suitable for structures with arbitrary velocity variation, and the number of computations required can be directly related to the complexity of the given velocity function. We demonstrate the superior computational efficiency of this method for 3-D depth migration relative to the reverse‐time migration method. The computational algorithm used for the migration is designed for a multi‐processor machine (Cray-XMP/48) and takes advantage of advanced disk technologies to overcome the input/output (I/O) problem. The method is demonstrated with both synthetic and field data. The migration of a typical 3-D data volume can be accomplished in only a few hours.

First-order particle velocity equations of decoupled P- and S-wavefields and their application in elastic reverse time migration

Geophysics ◽  
2021 ◽  
pp. 1-78
Author(s):  
Zhiyuan Li ◽  
Youshan Liu ◽  
Guanghe Liang ◽  
Guoqiang Xue ◽  
Runjie Wang
Keyword(s):  
Particle Velocity ◽  
Computational Cost ◽  
Staggered Grid ◽  
Additional Stress ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Computational Accuracy ◽  
First Order ◽  
Time Migration ◽  
Stress Variable

The separation of P- and S-wavefields is considered to be an effective approach for eliminating wave-mode cross-talk in elastic reverse-time migration. At present, the Helmholtz decomposition method is widely used for isotropic media. However, it tends to change the amplitudes and phases of the separated wavefields compared with the original wavefields. Other methods used to obtain pure P- and S-wavefields include the application of the elastic wave equations of the decoupled wavefields. To achieve a high computational accuracy, staggered-grid finite-difference (FD) schemes are usually used to numerically solve the equations by introducing an additional stress variable. However, the computational cost of this method is high because a conventional hybrid wavefield (P- and S-wavefields are mixed together) simulation must be created before the P- and S-wavefields can be calculated. We developed the first-order particle velocity equations to reduce the computational cost. The equations can describe four types of particle velocity wavefields: the vector P-wavefield, the scalar P-wavefield, the vector S-wavefield, and the vector S-wavefield rotated in the direction of the curl factor. Without introducing the stress variable, only the four types of particle velocity variables are used to construct the staggered-grid FD schemes, so the computational cost is reduced. We also present an algorithm to calculate the P and S propagation vectors using the four particle velocities, which is simpler than the Poynting vector. Finally, we applied the velocity equations and propagation vectors to elastic reverse-time migration and angle-domain common-image gather computations. These numerical examples illustrate the efficiency of the proposed methods.

From acoustic to elastic inverse extended Born modeling: a first insight in the marine environment

Geophysics ◽  
2021 ◽  
pp. 1-73
Author(s):  
Milad Farshad ◽  
Hervé Chauris
Keyword(s):  
Least Squares ◽  
Marine Environment ◽  
Computational Cost ◽  
Physical Parameters ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Physical Density ◽  
Acoustic Approximation

Elastic least-squares reverse time migration is the state-of-the-art linear imaging technique to retrieve high-resolution quantitative subsurface images. A successful application requires many migration/modeling cycles. To accelerate the convergence rate, various pseudoinverse Born operators have been proposed, providing quantitative results within a single iteration, while having roughly the same computational cost as reverse time migration. However, these are based on the acoustic approximation, leading to possible inaccurate amplitude predictions as well as the ignorance of S-wave effects. To solve this problem, we extend the pseudoinverse Born operator from acoustic to elastic media to account for the elastic amplitudes of PP reflections and provide an estimate of physical density, P- and S-wave impedance models. We restrict the extension to marine environment, with the recording of pressure waves at the receiver positions. Firstly, we replace the acoustic Green's functions by their elastic version, without modifying the structure of the original pseudoinverse Born operator. We then apply a Radon transform to the results of the first step to calculate the angle-dependent response. Finally, we simultaneously invert for the physical parameters using a weighted least-squares method. Through numerical experiments, we first illustrate the consequences of acoustic approximation on elastic data, leading to inaccurate parameter inversion as well as to artificial reflector inclusion. Then we demonstrate that our method can simultaneously invert for elastic parameters in the presence of complex uncorrelated structures, inaccurate background models, and Gaussian noisy data.

An exact adjoint operation pair in time extrapolation and its application in least-squares reverse-time migration

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. H27-H33 ◽  
Author(s):  
Jun Ji
Keyword(s):  
Least Squares ◽  
Adjoint Operator ◽  
Synthetic Data ◽  
Forward Modeling ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Product Test ◽  
Least Squares Migration ◽  
Time Extrapolation

To reduce the migration artifacts arising from incomplete data or inaccurate operators instead of migrating data with the adjoint of the forward-modeling operator, a least-squares migration often is considered. Least-squares migration requires a forward-modeling operator and its adjoint. In a derivation of the mathematically correct adjoint operator to a given forward-time-extrapolation modeling operator, the exact adjoint of the derived operator is obtained by formulating an explicit matrix equation for the forward operation and transposing it. The programs that implement the exact adjoint operator pair are verified by the dot-product test. The derived exact adjoint operator turns out to differ from the conventional reverse-time-migration (RTM) operator, an implementation of wavefield extrapolation backward in time. Examples with synthetic data show that migration using the exact adjoint operator gives similar results for a conventional RTM operator and that least-squares RTM is quite successful in reducing most migration artifacts. The least-squares solution using the exact adjoint pair produces a model that fits the data better than one using a conventional RTM operator pair.

Efficient 3D elastic full-waveform inversion using wavefield reconstruction methods

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. R45-R55 ◽  
Author(s):  
Espen Birger Raknes ◽  
Wiktor Weibull
Keyword(s):  
Particle Velocity ◽  
Large Scale ◽  
Waveform Inversion ◽  
Transversely Isotropic ◽  
Reconstruction Method ◽  
Full Waveform Inversion ◽  
Reverse Time ◽  
Full Waveform ◽  
Time Migration ◽  
Reconstruction Methods

In reverse time migration (RTM) or full-waveform inversion (FWI), forward and reverse time propagating wavefields are crosscorrelated in time to form either the image condition in RTM or the misfit gradient in FWI. The crosscorrelation condition requires both fields to be available at the same time instants. For large-scale 3D problems, it is not possible, in practice, to store snapshots of the wavefields during forward modeling due to extreme storage requirements. We have developed an approximate wavefield reconstruction method that uses particle velocity field recordings on the boundaries to reconstruct the forward wavefields during the computation of the reverse time wavefields. The method is computationally effective and requires less storage than similar methods. We have compared the reconstruction method to a boundary reconstruction method that uses particle velocity and stress fields at the boundaries and to the optimal checkpointing method. We have tested the methods on a 2D vertical transversely isotropic model and a large-scale 3D elastic FWI problem. Our results revealed that there are small differences in the results for the three methods.

Sign in / Sign up

Export Citation Format

Share Document