Petro-seismic relations, amplitude versus angle curves, and petro-seismic inversion for sandstone properties.

摘要

A comprehensive model to calculate viscoelastic seismic parameters from petro-physical properties for sandstone is developed by combining lab measurements from published data sets and well log data. Density (rho) is calculated using the volumetric mixing equation. Velocities (Vp, V s and Vp/Vs) are empirical functions of petrophysical properties [porosity (&phis;), clay content ( C), water saturation (Sw), effective pressure (Pe), and frequency (f)] for dry, partially and fully water saturated sandstones. P-wave attenuation (100/Qp) is an empirical a function of porosity, clay content, permeability, water saturation, frequency and effective pressure. Predictions of 100/Qs are obtained from Qs/Qp and 100/Qp. Qs/Qp is a function of porosity, clay content, and frequency. These petro-seismic equations involve more parameters than any of the original individual studies did separately, and appear to be viable for predicting viscoelastic seismic parameters.; Viscoelastic displacement reflection coefficients are computed analytically to evaluate the sensitivity of reflections to petro-physical properties at a shale/sand interface. The models are defined in terms of their petrophysical variables, and the corresponding viscoelastic seismic properties are used as intermediate variables to calculate complex reflection coefficients for P-P, P-S, S-S, and S-P waves, for suites of models representing various possible sandstone reservoirs. At full saturation, AVA responses are affected, in order of significance, by porosity, clay content, effective pressure, permeability and frequency. Significant differences between viscoelastic and elastic AVA responses appear at low Q near critical incidence angles.; A petro-seismic inversion algorithm is developed based on the petro-seismic relations and some additional equations. The algorithm consists of three different approaches for finding unknown parameters; direct estimation, a grid search, and parameter approximation. This provides a tool for finding values of the unknowns when some subset of measurements is given, and for investigating causes of changing parameters. Evaluation of predictions for real samples, with optimal input combinations, show the order of the reliability in petro-seismic parameter estimation, from best to worst, as Vp, 100/Qp, rho, Vs, Sw , &phis;, Qs/Qp, Vp/V s, ln k, 100/Qs and C. Pe and f are the least reliably estimated.