Matched catastrophe deconvolution with application to the inversion of marine seismic refraction data

Abstract

The problem of extracting accurate estimates of the travel times of unresolved arrivals (e.g., the second and third arrivals within a triplication) from a set of noisy bandlimited measurements of a time‐dependent acoustic wavefield is addressed. The method of solution presented is based on the assumption that the underlying caustic structure (or, equivalently, the travel time curve structure) of the wavefield is known. Because generic caustics associated with causal wavefields take on only certain forms, this is a weak assumption. Additionally, it is assumed that the medium structure varies as a function of depth only. This further restricts the class of observable caustic sections. These constraints are incorporated into a matched field processing approach to the deconvolution problem. The technique is demonstrated using a measured marine seismic refraction data set. A Herglotz‐Wiechert inversion of the resulting kinematic data T(R) agrees well with previously published waveform inversions of the same data set. Advantages of the new approach over linearized waveform inversions are discussed.