Refraction traveltime tomography based on damped wave equation for irregular topographic model

Abstract

Land seismic data generally have time-static issues due to irregular topography and weathered layers at shallow depths. Unless the time static is handled appropriately, interpretation of the subsurface structures can be easily distorted. Therefore, static corrections are commonly applied to land seismic data. The near-surface velocity, which is required for static corrections, can be inferred from first-arrival traveltime tomography, which must consider the irregular topography, as the land seismic data are generally obtained in irregular topography.This paper proposes a refraction traveltime tomography technique that is applicable to an irregular topographic model. This technique uses unstructured meshes to express an irregular topography, and traveltimes calculated from the frequency-domain damped wavefields using the finite element method. The diagonal elements of the approximate Hessian matrix were adopted for preconditioning, and the principle of reciprocity was introduced to efficiently calculate the Fréchet derivative. We also included regularization to resolve the ill-posed inverse problem, and used the nonlinear conjugate gradient method to solve the inverse problem.As the damped wavefields were used, there were no issues associated with artificial reflections caused by unstructured meshes. In addition, the shadow zone problem could be circumvented because this method is based on the exact wave equation, which does not require a high-frequency assumption. Furthermore, the proposed method was both robust to an initial velocity model and efficient compared to full wavefield inversions. Through synthetic and field data examples, our method was shown to successfully reconstruct shallow velocity structures. To verify our method, static corrections were roughly applied to the field data using the estimated near-surface velocity. By comparing common shot gathers and stack sections with and without static corrections, we confirmed that the proposed tomography algorithm can be used to correct the statics of land seismic data.