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

Abstract

Well-to-seismic tie and wavelet phase estimation are closely related steps that 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 synthetic data 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 us to simultaneously adjust the wavelet phase and the velocity log within a predefined tolerance. The problem is solved iteratively by perturbing 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 the synthetic seismogram. The velocity log is perturbed smoothly using a function defined by monotonic cubic splines, whereas 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 well-honored. By means of pseudosynthetic and field data examples, we found that our automatic well-to-seismic tying method leads to high correlation values between the synthetic and the observed traces, accurate wavelet phase estimations, and small departures from the observed velocity log. Because it is the time scale that 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 improves seismic data interpretation.