Traveltime and amplitude calculations using the damped wave solution

Abstract

Because of its computational efficiency, prestack Kirchhoff depth migration remains the method of choice for all but the most complicated geological depth structures. Further improvement in computational speed and amplitude estimation will allow us to use such technology more routinely and generate better images. To this end, we developed a new, accurate, and economical algorithm to calculate first‐arrival traveltimes and amplitudes for an arbitrarily complex earth model. Our method is based on numerical solutions of the wave equation obtained by using well‐established finite‐difference or finite‐element modeling algorithms in the Laplace domain, where a damping term is naturally incorporated in the wave equation. We show that solving the strongly damped wave equation is equivalent to solving the eikonal and transport equations simultaneously at a fixed reference frequency, which properly accounts for caustics and other problems encountered in ray theory. Using our algorithm, we can easily calculate first‐arrival traveltimes for given models. We present numerical examples for 2‐D acoustic models having irregular topography and complex geological structure using a finite‐element modeling code.