Seismic-to-well ties by smooth dynamic time warping

Tianci Cui, Gary F. Margrave

Without knowledge of Q or a check-shot/VSP survey, synthetic seismogram has to be manually stretched or squeezed to tie the seismic traces in practice, which is a tedious process and always involves human errors. Dynamic time warping (DTW) can reliably estimate the time shifts between two signals, but it returns unsmooth integer lags. The improved algorithm, smooth dynamic time warping (SDTW), can accurately estimate smooth time shifts, which are more realistic to represent the drift time in seismic-to-well ties. Taking the place of the interpretive stretch-squeeze process, SDTW is applied to estimate the time shifts between the synthetic seismogram and seismic traces of the Hussar field data. The estimated time shifts are used to calibrate the timing of the reflectivity instead of warping the synthetic seismogram, to reserve the embedded zero-phase wavelets but making the time calibration adequate only after two iterations. Both the residual drift time and overestimated sonic overburden cause theses time shifts, which have similar slops at the three well locations attributed from the flat subsurface geological structure in the Hussar area. The time-variant constant-phase difference and time-variant amplitude scalar function are calculated between the time calibrated synthetic seismogram and the seismic traces. They are linearly interpolated and extrapolated from the three wells to other CDP locations horizontally to rotate the phase and balance the amplitude of the whole seismic section. After seismic-to-well ties, the same well tops are tied to the same seismic events, making major seismic horizons easy to be identified. The bandlimited impedance inversion of the Hussar seismic data using a low-frequency cut-off of 3 Hz and a high-end frequency of 75 Hz is shown to be a good approximation to the subsurface properties. The second iteration of time calibration significantly reduces the percent errors around well 12-27 between the seismic inversion and well impedance, verifying better seismic-to-well ties