Seismic velocities and anisotropy from high‐resolution sonic logs

Abstract

High resolution sonic logs can sample formation slownesses over very short intervals, often showing considerable variation from point to point, indicative of layering as fine as or finer than the log sampling. For seismic wave propagation, this finely layered medium may be represented by an equivalent homogeneous transversely isotropic (TI) medium by the appropriate averaging scheme based on the assumption that each data point of the sonic log is representative of an isotropic layer. This assumption is not warranted in a region with many thin shale sections, but even so we obtain correct values of vertical compressional and shear slowness in the equivalent medium. Alongside segments of high resolution sonic and density logs in a section of high variability, we show computed long wavelength compressional and shear slownesses along with estimates of the anisotropy, the horizontal to vertical stress, and the sonic drift curves, i.e. the travel time based on average slownesses minus that due to the integrated sonic slownesses. This drift is positive and attains values of up to 1.5 ps/ft for compressional waves and 2.5 ps/ft for shear waves. In the presence of layering at a scale finer than log sampling, or in the presence of strong intrinsic anisotropy of some layers (such as shales), the anisotropy of the eqnivalent medium based on isotropy of the layers will tend to underestimate the true anisotropy. Data from multi-component, multi-offset VSP measurements will provide the non-vertical information necessary to construct the slowly varying equivalent TI medium most consistent with sonic and seismic observations. data, we make some preliminary assumptions: first that the formation is horizontally stratified, second that the welIis vertical, and last that the formation at any point is isotropic. Thus azimuthal variations are ignored and we are attempting to determine the best transversely isotropic (TI) background model on the seismic scale compatible with high resolution log data. The input data consist of compressional and shear sonic slowneszes, bp and s,, and density p at a rezolution equal to that of high resolution sonic logs. To know the wave behavior of much longer seismic waves in such a finely layered (compared to the seismic wavelength) medium, it is necessary to compute the best TI medium that fits the data. A TI medium is characterized by five independent elastic modnli relating stress and strain. In condensed notation, with the vertical denoted by 23, the stress-strain relation of a TI solid may be written