Empiric Comparison of Relationships of Sandstones Velocity with Their Porosity, Volume of Clay and Pressure

At the first stage, we choose the model equation (In most areas of knowledge epistemic aspects of creative activity are amongst the most controversial ones and rarely analyzed in detail. .Relationships, that analysts apply as instruments of well data petrophysical interpretation, are usually justified in one of three ways. The model approach employs relationships based on the idealized model of the rock. The statistical approach justifies relationships by well data. The model-statistical approach employs both model and statistical data obtained from similar wells. The report elaborates on the constraints and opportunities of the latter approach with regard to the relationships of elastic waves interval time and component composition. The author singles out three successive stages of this activity. on example of continuous mixing equation, the possibility of which was predicted in publications of the author and MM Ellansky (1973.1978) and was recently analysed by Tenchov (2016). It is shown that this equation meets the limit transitions better than Gardner equation). At the second stage we examine empirical evidence to specify the constants to include in the equation. At the third stage we investigate equivalent transformations of this nonlinear equation, that allow to simplify the procedure of nonlinear estimation of these coefficients. The coefficients of the transformed nonlinear equation are identified using search methods. Limited coefficients provide a sustainable solution with greater accuracy than one obtained by linear regression. We also analyze impact of criterion to minimize residuals (least squares and the smallest units) on the coefficients.

For simple generalizations of several well-known petrophysical relationships of interval time with porosity, clay content and the pressure we compare fitting parameters