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.

Instantaneous polarization filtering focused on suppression of surface waves

“…Benhama et al (1988) introduced a filtering method based on seismic polarization analysis utilizing a moving time-window by which Rayleigh waves were filtered from body waves in multi-component recordings by calculating the eigenvalues of the covariance matrix and estimating the polarization ellipse. Many applications and improvements based on this method have been performed in the last two decades (Greenhalgh, et al, 1990;Bataille and Chiu, 1991;Cho, 1991;Cho and Spencer, 1992;Hendrick and Hearn, 1999;Wang and Teng, 1997). Perelberg and Hornbostel (1994) introduced weighting functions, although the method presents some problems when applied to field data: it is difficult to optimize a suitable time-window length to obtain real valued eigenvalues of the covariance matrix instead of complex values and the method cannot guarantee convergence in the eigenvalue computation.…”

The application of polarizing filtering with floating coordinate system in 3D3C VSP wavefield separation

“…Successful wavefield separation may considerably improve the signal-to-noise ratio (SNR) of both prestack and poststack data (Schalkwijk et al, 2003). There are two categories of wavefield separation (van der Baan, 2006): wavetheoretical methods (Robertsson, J.O.A., andCurtis, 2002, Wang et al, 2002) and parametric methods (Cho, andSpencer, 1992, Wang et al, 2009). Polarizing filtering (Morozov et al, 1997;Donno, 2006), which is commonly used for separating P-and SV-wavefield in VSP data, is a parametric method.…”

Approximate separation of pure-mode and converted waves in 3-C reflection seismics by τ-p transform

“…Broadly speaking, techniques for wavefield separation fall into two categories: wave-theoretical methods (Dankbaar, 1985;Greenhalgh et al, 1990;Wapenaar et al, 1990;Amundsen and Reitan, 1995;Wang and Singh, 2002) and parametric methods (Esmersoy, 1990;Cho and Spencer, 1992). Exact wave-theoretical methods are directly based on the physics of wave propagation but require the specification of both P-and S-wave near-surface velocities for land data and additional density parameters for ocean-bottom cable (OBC) data.…”