Extending DFA-based multiple linear regression inference: Application to acoustic impedance models

In this paper we propose three distinct points for improving scale sensitive DFA based multiple linear regression inference: the scale dependent standardized Regression Coefficients βˆstdDFAs as a measure of dependent variables relative importance, scale dependent effect size f2(s), and Intersection-Union hypothesis test, which can handle the composite hypothesis of no cross-correlation, and of having no advantage over the standard OLS linear regression model. We applied this framework on a model for acoustic impedance of well log data, as a function of neutron effective porosity, shale volume, and resistivity. We find that the neutron effective porosity is more important for modeling acoustic impedance than resistivity and, that both are more important than the shale volume, for all scales. Results from Intersection-Union test suggest the rejection of compound null hypothesis for neutron effective porosity and resistivity for scales between 40 and 500 ft, suggesting a robust model for acoustic impedance based on neutron effective porosity and resistivity on these scales. This approach represents a novel framework for scale sensitive regression models, and we believe that it can be useful for time series studies in many diverse areas.