Efficient Laplace-domain modeling using an axis transformation technique

Abstract

Summary We propose an axis-transformation technique for modeling wave-propagation in the Laplace-domain using a finite-difference method. This technique enables us to use small grids near the surface and large grids at depth. Accordingly, we can reduce the number of grids and attain computational efficiency in modeling in the Laplace domain. We present comparisons between modeled wavefields obtained on the regular and transformed axes. Introduction Full waveform inversion is a method used to acquire accurate subsurface parameters that are required for seismic imaging. Since publication of the research by Tarantola (1984), many geophysicists and applied mathematicians have enhanced the inversion technique in the time and frequency domains (Ben-Hadj-Ali et al., 2009; Brenders and Pratt, 2007; Operto et al., 2004; Plessix, 2009; Pratt, 1999; Shipp and Singh, 2002). Computational efficiency is one of the most important challenges in full waveform inversion (Virieux and Operto, 2009). Several authors suggested methods to reduce the computational cost of full waveform inversion. Bunks et al. (1995) proposed a multiscale inversion, and Sirgue and Pratt (2004) demonstrated an efficient strategy for selecting frequencies. Krebs et al. (2009) introduced a source encoding method in the time domain, and Ben-Hadj-Ali et al. (2009) suggested the use of a phase encoding method in the frequency domain. Recently, Shin and Cha (2008) proposed a full waveform inversion in the Laplace domain. Laplace-domain inversion could recover macro-velocity information from synthetic and real data using a simple starting model. The macro-velocity can be used for migration or subsequent frequency-domain inversion as an initial model (Shin and Cha, 2008; Shin and Ha, 2008). Large grids can be used in the Laplace-domain inversion because the inversion result is a large-scale velocity model and the error originating from the large grids is not significant (Cha and Shin, 2010). Generally, smaller grids are required to model the shallow but not the deep parts (Cha and Shin, 2010). Therefore, we can reduce the computational burden of full waveform inversion in the Laplace domain by introducing large grids at depth, thereby enabling an efficient modeling method. We can adopt an axis transformation technique to obtain the desired computational efficiency. Axis transformation techniques have been used in geophysical research for many purposes. Their applications include the improved representation of interfaces (Fornberg, 1988), the description of surface topography (Hestholm and Ruud, 1998), and the simulation of the Rayleigh wave (Kosloff and Carcione, 2010). In this study, we suggest an efficient finite-difference scheme for modeling in the Laplace domain. This method transforms the