Automatic well tying and wavelet phase estimation with no waveform stretching or squeezing

Abstract

Well-to-seismic tie and wavelet phase estimation are close and related steps to link geology and seismic data. Usually these processes are solved separately or alternately, diminishing the quality of the well tying procedure. Apart from trying different wavelets, the well-to-seismic tie involves shifting and, often, stretching and/or squeezing the synthetics until the correlation with the observed trace is high. These operations, which are somewhat arbitrary and prone to human errors, may lead to unrealistic velocity models and undesired waveform deformations. The automatic tying method that we propose avoids these issues allowing to adjust simultaneously the wavelet phase and the velocity log within a predefined tolerance. The problem is solved iteratively by perturbing both the observed velocity log and the wavelet phase in a way that leads to an increase of the correlation coefficient between the seismic data and synthetic seismogram. The velocity log is perturbed smoothly using afunction defined by monotonic cubic splines, while the wavelet phase is assumed to be an unknown constant. We solve the resulting optimization problem by means of differential evolution, which allows us to have complete control over the allowable velocity changes and guarantees that the measured borehole observations are honored well. By means of pseudo-synthetic and field data examples we show that the proposed automatic well-to-seismic tying method leads to high correlation values between the synthetic and the observed traces, good wavelet phase estimations, and small departures from the observed velocity log. Since it is the time scale which is stretched and/or squeezed and not the synthetic trace itself, as opposed to other automatic and manual well-tying methods, the resulting trace preserves the wavelet shape, a feature that certainly contributes to a better interpretation of the seismic data.