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.

The strike and dip of the reflecting interfaces in the vicinity of a well can be derived from VSP data recorded with a three‐component downhole seismometer. The method relies on measuring the polarizations in the direct and reflected compressional waves. The mathematical relation which is the basis of the method is exact only when the seismometer is positioned at the depth where the interface intersects the well. At that depth the polarization of the reflected wave cannot be measured because of interference with the direct wave. The orientation of the normal to the reflector can be determined to within 2° when the polarizations of the direct and reflected waves are determined within 100 m of the reflector. If the direct and reflected waves can be identified without multidepth processing, only measurements at a single depth are required to determine the reflector orientation. Error analysis and statistical refinement can be achieved by measuring the polarizations at several seismometer depths, source azimuths, or source offsets. The method is robust in the sense that the error in the interface orientation cannot exceed the error in the measurement of the polarizations. The method should be useful in structurally complex areas provided the reflections can be observed at depths above the depths of generation.

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A new algorithm is developed for estimating the delay times and spectra in mixed wave fields. The algorithm is applicable to a spatial and temporal data window in which more than two events are present. In implementing the method it is assumed that data are recorded at equispaced hydrophones located in a spatial window in which the delay times are constant. Application of a least-squares criterion reduces the mathematics to an eigenvalue problem. The eigenvalues are complex, and their magnitude determines the frequency-dependent SNR. The phase is a linear function of frequency with a slope that determines the delay time over unit hydrophone spacing. The input data consist of the cross-power spectra between subarrays that contain the same numbers of elements and are shifted by zero or one hydrophone separation. Examples illustrate the application of the algorithm to synthetic data.