2.5-D forward and inverse modelling of full-waveform elastic seismic survey

Abstract

We present a two-and-half-dimensional (2.5-D) forward and inversion algorithm for the interpretation of surface seismic elastic full-waveform data. The 2-D modelling approach for elastic waves might not be sufficiently accurate because of its line-source assumption. On the other hand, a full 3-D modelling of elastic waves is still computationally very expensive for seismic exploration applications. By employing the 2.5-D modelling approach, we assume that the elastic medium is 2-D while the source is a 3-D point source. We solve the 2.5-D problem by first transforming the elastic wave equation in the spatial domain into the wavenumber domain. Then, for each wavenumber we solve a 2-D problem using the finite difference method with staggered grids. After that an inverse wavenumber transform is performed to compute the 3-D field distribution. To handle the inverse transform, we develop an efficient numerical integration scheme by subdividing the integration domain and applying different integration rules to each subinterval. We show that this approach works well for surface seismic applications. The 2.5-D approach offers a more realistic modelling of the elastic wave data, hence it produces more accurate inversion results than the 2-D inversion approach. Finally, we validate this approach by using a numerical test. In this test we used our 2.5-D full-waveform inversion algorithm to invert the synthetic data generated by a 3-D finite-difference time-domain simulation. © The Authors 2013. Published by Oxford University Press on behalf of The Royal Astronomical Society.