ALBERT

Notes: In this paper, a new procedure, called the coherent-signal-subspace method (CSS), for broad-band multiple-signal detection and slowness-vector estimation is discussed and applied to a surface seismographic array. the major improvements in estimation accuracy and resolution given by the CSS method, which was developed in the fields of radar and sonar, result from the use of extended-frequency components within the data bandwidth and a high-resolution algorithm. the former is made possible through a frequency focusing transformation that for each frequency component corrects for the phase-delay difference between that frequency and a reference frequency ωo. the result is the condensation of a broad frequency band into a narrow band at ωo. the high resolution algorithm used in the CSS method is the MUSIC (multiple signal characterization; Schmidt 1986) algorithm, which is based on the eigen property of the data cross-covariance matrix that the signal phase-delay vectors lie within the subspace spanned by the signal eigenvectors. the frequency transformation improves the singularity of the estimated cross-covariance matrix and the accuracy of the estimated signal eigenvectors at ωo, which are often serious problems in seismic array analysis. Combination of these two features in CSS ensures a superior array performance over the widely used beam steering and minimum-variance (Capon 1969) methods. Approximate methods to estimate the mean and variance of the estimated slowness vector are also presented in this paper. the estimation biases introduced by deterministic arrival-time deviations of array data from a plane wavefront are derived for the single signal case. It is shown that, in the case of a single signal, significant reduction in the estimation bias may be achieved if a large enough reference frequency is used in the CSS method. Finally, with observed and synthetic ground motions, tests are performed to illustrate the utility of CSS in resolving two closely separated signals. In both cases, CSS successfully resolved two separate peaks at almost the correct slowness vectors, while the conventional beam steering and minimum variance estimation methods either failed to resolve the two signals or gave an incorrect slowness estimate.