A semi-theoretical approach to determine shear wave velocity log using MLR method with a hypothetical test on core and well log data

Abstract

One of the most important and practical aspects of rock physics study is to make some feasible models (theoretical, empirical or semi-theoretical) which can be used to predict the body wave velocities (specifically shear wave velocity) in the fluid saturated reservoir rocks. Using of shear wave velocity information give rise to improve the hydrocarbon reservoir exploration and development. Shear wave velocity is essential to provide the amplitude versus offset studies. In this way, predicted shear wave velocity log from other well log data and core measurements is the main purpose of this study. Therefore, in addition to use of Gassmann's low frequency and Biot's high frequency models (theoretical models), Multiple Linear Regression (MLR) method with a hypothesis test were applied to create valid relations for prediction of shear wave velocity log. Hypothesis test is a procedure for determining if an assertion about a characteristic of a population is reasonable. In this way, Fisher test was used to determine whether the observed relationship between the dependent and independent variables occurs by chance or not. Student's t–test was used to determine whether each slope coefficients is useful in estimating the assessed value or not. Since acoustic data obtained from laboratory measurements at ultrasonic frequencies are used to predict S-wave velocity log, the magnitude of velocity dispersion was determined too. We applied some practical rock physics models on 31 carbonate representative core samples. Thereby, based on theoretical and empirical approaches integrated with statistical discipline (semi-theoretical approach), shear wave velocity log was constructed through a carbonate reservoir interval. Based on the semi-theoretical approach some relations were represented to predict S-wave velocity log. It is necessary to mention that MLR method used as a canned procedure is a dangerous tool, since the resulting model may include more input variables to improve only the correlation of the represented model with no physical sense. Also the input variables may be as correlated with each other as they are with the response. If this is the case, the presence of one input variable in the model may mask the effect of another (multicollinearity).