PP-PS registration in the reflectivity domain: A waveform-preserving approach

Joint PP-PS amplitude inversion and attribute analysis require mapping converted PS wave data to the PP time domain so that similar reflectors share the same two-way travel times. This process, known as PP-PS data registration, often results in non-stationary PS data, where wavelet spectral content varies with time and location, affecting subsequent inversion results and necessitating postprocessing to correct these issues. To address this limitation, we propose a PP-PS registration method in the reflectivity domain. The strategy consists of two steps. First, we perform sparse-spike deconvolution on both PP and PS data to transform them into the reflectivity domain, based on the hypothesis that suitable wavelets and sparse-spike reflectivities can be estimated from the data. The sparse-spike solutions are obtained by solving an inverse problem regularized with a sparsity-promoting norm and solved via proximal algorithms. In the second step, we iteratively adjust the sparse-spike PS reflectivity to match its PP counterpart using a smooth, monotonic warping function derived from the Vp/Vs ratio, represented as a cubic spline with a fixed number of knots. At each iteration, both reflectivities are convolved with a stationary replacement wavelet, and the resulting match is evaluated. Optimizing the knot values leads to a nonlinear, multimodal problem, which we solve using very fast simulated annealing. Unlike conventional methods that operate in the data domain, our approach produces stationary PP and PS seismic data with aligned reflectors in two-way travel time, eliminating waveform distortions and requiring no additional processing. Numerical tests confirm that the method preserves amplitude and outperforms techniques like dynamic time warping, yielding a cleaner spectrum and distortion-free waveforms for reliable interpretation.