Why seismic-to-well ties are difficult

Gary F. Margrave

Tying seismic data to well control is a crucial step in seismic inversion and interpretation. This is where key ambiguities that prevent the interpretation of a seismic image as bandlimited reflectivity are resolved. Reflectivity can be calculated directly from suitable well logs while the estimation of reflectivity from seismic data requires the unambiguous determination of the seismic wavelet and the removal of the same. However, due to the unavoidable presence of anelastic attenuation, the very notion of a single seismic wavelet is not robust. Instead, constant-Q theory predicts that the source waveform evolves continuously as it propagates in the subsurface. It progressively loses frequency content and undergoes continual phase changes. This evolution means that each reflecting structure in the subsurface is illuminated by a unique waveform. The use of stationary (standard) deconvolution methods leads to a trace with unbalanced amplitude, in both time and frequency, and time-variant residual phase. Attempts to remedy this by time-variant balancing leads to a trace that can, at best, be tied to a well in a local time zone but which has misties above and below that zone. Nonstationary deconvolution or inverse Q filtering can potentially address these effects but the former relies on a statistical reflectivity model while the latter requires knowledge of Q. The theoretical advantage of inverse Q filtering over nonstationary deconvolution largely vanishes with the presence of even small noise levels. Processes that successfully address nonstationarity must also be data adaptive to successfully deal with noise. Well tying can be improved by using deconvolution algorithms and well-tying methodologies that are consistent with constant-Q theory.