Adaptive finite difference for seismic wavefield modelling in acoustic media.

Gang Yao,Henry Alexander Debens,Di Wu

doi:10.1038/srep30302

Gang Yao, Henry Alexander Debens + Show 1 more

Open Access

https://doi.org/10.1038/srep30302

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Abstract

Efficient numerical seismic wavefield modelling is a key component of modern seismic imaging techniques, such as reverse-time migration and full-waveform inversion. Finite difference methods are perhaps the most widely used numerical approach for forward modelling, and here we introduce a novel scheme for implementing finite difference by introducing a time-to-space wavelet mapping. Finite difference coefficients are then computed by minimising the difference between the spatial derivatives of the mapped wavelet and the finite difference operator over all propagation angles. Since the coefficients vary adaptively with different velocities and source wavelet bandwidths, the method is capable to maximise the accuracy of the finite difference operator. Numerical examples demonstrate that this method is superior to standard finite difference methods, while comparable to Zhang’s optimised finite difference scheme.

Highlights

Efficient numerical seismic wavefield modelling is a key component of modern seismic imaging techniques, such as reverse-time migration and full-waveform inversion
Seismic wavefield modelling based on the wave equation has evolved to become an essential component of advanced seismic imaging[1,2,3,4,5] and model building techniques, such as full waveform inversion[6,7,8]
We have presented here an improved method for calculating finite difference coefficients

Summary

Introduction

Efficient numerical seismic wavefield modelling is a key component of modern seismic imaging techniques, such as reverse-time migration and full-waveform inversion. For standard finite difference based on Taylor series expansion, the higher the frequency is, the stronger the dispersion it suffers To mitigate this numerical dispersion, optimisation strategies are often employed to find improved finite difference coefficients (FDCs) that cover a wider frequency bandwidth and wavenumber range, but with limited errors. One such strategy is to seek optimised FDCs for spatial derivatives that are able to decrease dispersion of the spatial terms and compensate somewhat for dispersion of the temporal terms, thereby reducing the overall dispersion errors[11,12,13,14,15]. In this manner we can hope to exploit the maximum potential of finite difference

Methods

Findings

Conclusion