Seismic physical modeling based on the physical similitudes: application in isotropic media

Abstract

Throughout the decades seismic physical modeling has been used to help the geophysicists to understand the phenomena related to the elastic wave propagation on isotropic and anisotropic media. Most of the published works related to physical modeling, use physical similitudes between model and field (geological environment) only in the geometric, and sometimes, in the kinematics sense. The dynamic similitude is approximately or, most of the time, not obeyed due to the difficulty to reproduce, in laboratory, the forces and tensions that exist inside the earth when elastic waves propagate. In this work, an analytical expression for dynamic similitude in isotropic media in the sense of dynamic stress (stress due wave propagation) was derived. The resulting expression for dynamic similitude shows that this type of similitude has multiple solutions in context of dynamic stress (non-unicity problem). However, the regularization of this problem can be reached by controlling porosity and clay content. Ultrassonic measurements(elastic) as well as petrophysical measurements (density, porosity and clay content) in synthetic sandstone samples show how difficult it is to reproduce in the laboratory the three physical similarities studied in this work. Other important result of our analysis (from the kinematic similitude), is the achievement of an expression that relates the seismic frequency source with ultrasonic sources which are used in laboratory.