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Multiple Regression and Modified Faust Equation on Well Logging Data in Application to Seismic Procedures: Polish Outer Carpathians Case Study

An appropriate velocity model from well logs is a key issue in the processing and interpretation of seismic data. In a deep borehole located in the central part of the Polish Outer Carpathians, the sonic measurements were inadequate for seismic purposes due to the poor quality of data and gaps in the logging. Multiple regression (MR) and a modified Faust equation were proposed to model the velocity log. MR estimated the P-wave slowness as a dependent variable on the basis of sets of various logs as independent variables. The solutions were verified by the interval velocity from Check Shots (CS) and by the convergence of synthetic seismograms and the real seismic traces. MR proved to be an effective method when a set of other logs was available. The modified Faust method allowed computation of P-wave velocity based on the shallow resistivity logs, depth, and compaction factor. Faust coefficients were determined according to the lithology and stratigraphy divisions and were calibrated with the use of the velocity previously determined in the MR analysis. The modified Faust equation may be applied in nearby old wells with limited logging data, particularly with no sonic logs, where MR could not be successfully applied.