Separation of individual P and S arrivals is often a problem on three-component seismic data since P and S data are recorded on both the vertical and horizontal geophones. Due to the intrinsic response of an elastic interface, P and S waves are observed on vertical and radial geophones. A method of separating P and S waves in the Τ-p domain is presented which inverts the three-component records using the interface (or geophone) responses, thereby separating the two wavetypes. The P-S modal filter coefficients in the 2-D case are calculated from the geophone responses and the near-surface P and S wave velocities Vp and Vs .
For the 3C-2D case we consider two types of data: one acquired locating the geophone on the surface (free-surface case) and a second one considering the geophones located in the liquid-solid contact. For both cases, the geophone responses of the vertical and radial geophones are different but the modal filter method is unchanged. The P-S separation is tested using synthetic and real data showing that it is capable of separating pure P , S and converted reflections. It also appears to have low sensitivity to errors in the near-surface P and S wave velocity and to noise in the data.
Two different approaches to the 2-D Τ-p transform used in the modal filter are used: the slant stack algorithm proposed by Stoffa et al. (1981) developed in the x-t domain, and the method proposed by Wade and Gardner (1988) which works in the f-k domain. It is found that the second method provides a faster, cleaner and easier way to perform Τ-p filtering of seismic data than Stoffa's method.
A 3-D Τ-p transform is also developed. No geometric symmetry is assumed. The 3-D Τ-p transform is tested using synthetic data which includes P and converted waves, with and without random noise and ground roll added. The 3-D Τ-p transform appears to perform well by reconstructing the original data and attenuating the noise and ground roll present in the data.
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