Extended time-term method for identifying lateral structural variations from seismic refraction data

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A time-term method is a simple travel time inversion for seismic refraction crustal studies. Although this method is based on simple travel time calculation, it is robust in determining a basement velocity under the complicated surface structure. In the present paper, this method is extended to detect lateral velocity variation in the crystalline crust. We consider a model where a basement is composed of segments with a different velocity. Defining a likelihood function for unknown time-terms and refractor velocities, their best estimates are obtained by minimizing Akaike's Bayesian Information Criterion (ABIC). To realize accurate velocity estimation, we also incorporate an effect of vertical velocity gradient within the refractor, which was ignored in the conventional algorithms. Numerical tests undertaken for realistic crustal structures show that our method successfully detects lateral velocity variation in a basement even for a case with undulated surface layers. It is particularly stable and reliable if the surface layers are not thick and their velocities are more than 30-40% smaller than the refractor velocities. Then, the refractor velocities are almost decoupled to the time-terms in the process of inversion. The incorporation of the effect of the velocity gradient is inevitably important when travel time data at far distances are included in the inversion.

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