An improved parametric inversion methodology to separate P and Sv wavefields from VSP data

摘要

Wavefield separation is a critical and challenging step in processing multi-component VSP data. Parametric inversion is a popular approach to decompose VSP data into their four dominant downgoing and upgoing P and Sv wavefields. The conventional parametric inversion method is computationally intensive, requiring the simultaneously inversion of at least six parameters, P and Sv velocities and their respective downgoing and upgoing arrival angles, for each VSP receiver within each shot gather. Large, multi-source and multi-receiver VSP datasets, such as walkaway or 3DVSP, can take a considerable amount of time to run wavefield separation using conventional parametric inversion methodology. An additional issue with the conventional parametric method is that the six-parameter inversion might become unstable at certain frequencies and/or with receivers if the inversion condition number is too small for the parameter matrix. To minimize the instability, a damping factor is usually added to the inversion. A side effect of adding a damping factor is possible wave mode mixing in the separated wavefields at certain frequencies. We present an improved parametric inversion methodology to decompose VSP data wavefields. For many VSP data, the upgoing and downgoing wavefields can be separated easily using velocity standard filters (i.e., f-k or tau-P). Further separation of the downgoing and upcoming P and Sv waves can then be achieved more efficiently. Applying the parametric inversion using data with only upgoing (or downgoing) wavefields reduces the inverted parameters from six to four and lowers the rank of the matrix to be inverted from four to two. Consequently, the efficiency and stability of the inversion are significantly enhanced. The number of parameters to be inverted can be further reduced if the P-wave depth-velocity function is pre-determined from zero-offset VSP data. In addition, a nonlinear simulated annealing technique is employed to efficiently search for the parameters in the inversion, guaranteeing the inverted parameters are globally optimized without requiring a good initial value for each parameter. We demonstrate the effectiveness of this methodology using an offset VSP field data example.