Refraction tomography using damped monochromatic wave field

Abstract

Summary Refraction tomography requires an algorithm for efficiently computing the traveltimes and their Frechet derivatives. We have attempted to solve the damped wavefield using the frequency domain finite element modeling and then invoked the reciprocity theorem to calculate the Frechet derivative of the traveltime with respect to the subsurface parameter. Then, we used a damped least square method to invert the traveltimes of the Marmousi-2 model. Numerical tests demonstrate that the refraction tomography can be used to estimate the smooth velocity model for the prestack depth migration. Introduction Refraction survey was originally used to investigate the deep structure of the earth by seismologists in the early twentieth century. Following that, geophysicists were successful in delineating the shallow salt body for oil exploration. With the enhancement of the relevant techniques and the equipments used in conducting reflection survey, such surveying method began to replace refraction survey. Because of the depth penetrating resolution of refracted waves due to limited offset distance from a source to receivers in the reflection seismic survey, refraction survey has been mainly employed to investigate the structure of the shallow subsurface for static correction. Hampson and Russell(1984) used refraction tomography to compute a multi-layer near-surface model, though the velocity in the weathering layer was assumed to be known. Docherty(1992) have investigated the feasibility of extracting both weathering thickness and velocity information simultaneously, while Landa et al.(1995) have estimated the velocity-depth model by applying the coherence method for the estimation of the shallow subsurface. Landa et al.(1995) have inverted the velocity-depth model in the direction that the semblance coherence could be maximized. Shin et al.(1999) parameterized the subsurface model in blocky and arbitrary shaped layers, and inverted for the velocities and interface coordinates of the geologic model by calculating the Frechet derivatives of the velocity and the interface coordinate of the blocks. In this paper, we have proposed a new method for obtaining traveltime and Frechet derivative by using the monochromatic damped wave solution. For calculating the derivative of the traveltime with respect to the velocity parameter, we exploited the source-receiver reciprocity as Shin et al.(2001) did using the frequency domain modeling technique. To our knowledge, there has been little study on the issue that the velocity-depth model derived from refraction tomography was used for Kirchhoff prestack depth migration. In this paper, we have applied refraction tomography to Marmousi-2 model(Martin et al., 2002) and built the velocity model that can be used for the initial model of prestack depth migration. The migrated images demonstrate that we can obtain the velocity-depth model suitable for the migration by using the refraction tomography. Calculation of traveltime and its Frechet derivative Shin et al.(2003) introduced a new algorithm for computing the first arrival traveltime by modifying an existing frequency domain modeling technique. Before discussing how to apply their algorithm, we will briefly review their algorithm. When solving the wave equation by using the time domain finite-element method, we need to solve the discretized matrix equation given as