Array analysis of seismic signals considering an array beampattern

Seismic array data have been widely used in researches such as the discrimination of nuclear explosions, the analysis of seismic scattering, measurements of surface wave dispersion, and monitoring of the seismic activity in volcanic areas. In this study, we present a simple and high-resolution array processing method whose estimators are not pseudo but true ones. We apply the method to estimations of high-frequency rupture processes by converting temporal variations in slowness vectors and their associated amplitude into power distributions and rupture times on the fault plane. It has been shown that the minimum variance distortionless (HR) method and the multiple signal classification (MUSIC) method produce higher resolution for the location of the identified waves than the standard Fourier method (CV method). However, the estimators by the HR and MUSIC methods are pseudo ones. In order to obtain true spectral estimators with high resolutions, we propose a frequency-wavenumber method considering an array beampatterm. The observed power spectrum obtained by the CV method is a convolution of the array beampattern with the true power spectrum. Since the array beampatterm reduces the resolution of the spectral estimators, we deconvolve the observed power spectrum with the array beampattern in the wavenumber domain. The solution to this problem is determined using non-negative least squares because the power has a positive quantity. To illustrate the utility of the present method in resolving two closely separated signals, numerical tests are performed with synthetic waves. The present method successfully resolved two separate peaks at almost the correct slowness vectors. The resolution was superior to CV and HR methods and similar to MUSIC method. We then investigate the applicability of the present array processing method to estimations of high-frequency rupture processes. Using synthetic S body-wave seismograms from extended earthquake sources, we show that it is possible to image high-frequency source locations and their associated rupture times with high resolutions.