SEISMIC-WAVE SLOWNESS-VECTOR ESTIMATION FROM BROAD-BAND ARRAY DATA

In this paper, a new procedure, called the coherent-signal-subspace me thod (CSS), for broad-band multiple-signal detection and slowness-vect or estimation is discussed and applied to a surface seismographic arra y. The major improvements in estimation accuracy and resolution given by the CSS method, which was developed in the fields of radar and sona r, result from the use of extended-frequency components within the dat a bandwidth and a high-resolution algorithm. The former is made possib le through a frequency focusing transformation that for each frequency component corrects for the phase-delay difference between that freque ncy and a reference frequency omega0. The result is the condensation o f a broad frequency band into a narrow band at omega0. The high resolu tion algorithm used in the CSS method is the MUSIC (multiple signal ch aracterization; Schmidt 1986) algorithm, which is based on the eigen p roperty of the data cross-covariance matrix that the signal phase-dela y 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 eige nvectors at omega0, 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-varia nce (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 si ngle signal case. It is shown that, in the case of a single signal, si gnificant reduction in the estimation bias may be achieved if a large enough reference frequency is used in the CSS method. Finally, with ob served and synthetic ground motions, tests are performed to illustrate the utility of CSS in resolving two closely separated signals. In bot h cases, CSS successfully resolved two separate peaks at almost the co rrect slowness vectors, while the conventional beam steering and minim um variance estimation methods either failed to resolve the two signal s or gave an incorrect slowness estimate.