Estimation of polarization and slowness in mixed wavefields

Abstract

A new algorithm is developed for estimating the moveout velocities and polarization states in mixed wavefields recorded on multicomponent array data in the presence of random noise. The algorithm is applicable to a spatial and temporal data window in which more than two events are present. Three fundamental attributes of the waves are determined: polarization angle, apparent slowness, and the change in amplitude between adjacent detectors. In implementing the method, it is assumed that data is recorded at equispaced geophones located in a spatial window in which the three parameters are constant. Robustness is achieved by averaging the transfer matrix over all combinations of the subarrays that have the same transfer matrix. Application of a least‐squares criterion reduces the mathematics to an eigenvalue problem. The eigenvalues are complex, and their magnitude determines the amplitude change factor. The phase is a linear function of frequency with slope that determines the vertical slowness. The eigenvectors are the polarizations. The input data consists of the cross‐power spectra between subarrays that contain the same number of elements and are shifted by zero or one geophone separation. Examples illustrate the application of the algorithm to synthetic data. Numerical test results show that the performance of the method is not sensitive either to the time overlap between events or to the degree of similarity between waveforms.