A Method to Increase the Convergence Rate of Surface-Wave Inversion

Abstract:

Surface-wave phase velocity data is often used to invert locally for shear wave-speed velocities as a function of depth. The standard approach involves assuming an initial velocity structure, calculating sensitivity kernels, determining linear velocity perturbations that best fit the data, and iterating this process until a final velocity structure is obtained that satisfies the phase velocity data. A common problem with this approach, however, is that poor initial guesses require iterating a large number of times so that the process can be inefficient or even non-convergent or impractically slow for a large number of such inversions. Building on a new type of 'Dix-like' surface-wave inversion method that we recently proposed, we show that a generalized 'Dix-like' approach is an iterative procedure with improved convergence rates compared to classical inversion. In particular, we find that the new approach converges quadratically whereas the classical approach only converges linearly, thus potentially speeding up inversions. This result can be understood as being related to the fact that the surface wave dispersion relation is linear in elastic modulus (density multiplied by velocity squared) rather than velocity. The new approach also clarifies the role and significance of depth sensitivity kernels and offers a new approach to computing them.