Using Gene Expression Programming to estimate sonic log distributions based on the natural gamma ray and deep resistivity logs: A case study from the Anadarko Basin, Oklahoma

In the oil and gas industry, characterization of pore-fluid pressures and rock lithology, along with estimation of porosity, permeability, fluid saturation and other physical properties is of crucial importance for successful exploration and exploitation. Along with other well logging methods, the compressional acoustic (sonic) log (DT) is often used as a predictor because it responds to changes in porosity or compaction and, in turn, DT data are used to estimate formation porosity, to map abnormal pore-fluid pressure, or to perform petrophysical studies. However, despite its intrinsic value, the sonic log is not routinely recorded during well logging. Here we propose the use of a soft computing method — Gene Expression Programming (GEP) — to synthesize missing DT logs when only common logs (such as natural gamma ray — GR, or deep resistivity — REID) are present. The Gene Expression Programming approach can be divided into three steps: (1) supervised training of the model; (2) confirmation and validation of the model by blind-testing the results in wells containing both the predictor (GR, REID) and the target (DT) values used in the supervised training; and (3) applying the predicted model to wells containing the predictor data and obtaining the synthetic (simulated) DT log. GEP methodology offers significant advantages over traditional deterministic methods. It does not require a precise mathematical model equation describing the dependency between the predictor values and the target values. Unlike linear regression techniques, GEP does not overpredict mean values and thereby preserves original data variability. GEP also deals greatly with uncertainty associated with the data, the immense size of the data and the diversity of the data type. A case study from the Anadarko Basin, Oklahoma, involving estimating the presence of overpressured zones, is presented. The results are promising and encouraging.