Multiwavelet seismic-wave gradiometry

Abstract

A new technique to determine uncertainty estimates for wave parameters obtained by seismic-wave gradiometry is established using the multiwavelet transform. Wave gradiometry uses spatial gradients as measured by a small-scale seismicarray to estimate the wave parameters of propagation azimuth, slowness, geometrical spreading, and radiation pattern. The advantage of wave gradiometry is that the wave parameters are estimated on a point-by-point basis for the entire seismogram. Previous work on wave gradiometery employed the continuous wavelet transform to decompose the wave field into narrow-band realizations prior to gradiometric analysis so that the wave parameters are resolved as functions of both time and frequency. To build on this approach, I incorporated the multiwavelet transform. The multiwavelet transform decomposes the wave field into a series of mutually orthogonal wavelet coefficients,which can then be analyzed by wave gradiometry. Each result can then be treated as asample from a statistical population. The method is tested on synthetic data, with and without noise. A relatively low degree of uncorrelated noise can have a significant impact on the quality of the results. Finally, multiwavelet gradiometry is applied to a single earthquake recorded by a small subset of USArray stations and shows that the method accurately and robustly determines the wave parameters.