Comparisons Between Effects of Linear and Nonlinear Deformational Behaviors of Fractures on P-Wave Attenuation

ABSTRACT: The purpose of this paper is to study and compare the effects of linear and nonlinear normal de-formational behaviors of fractures on one-dimensional P-wave attenuation. An approach is developed, by combining the method of characteristics and the displacement discontinuity theory, to derive wave reflection and transmission coefficients for one-dimensional P-wave incidence normal to a fracture. The linear displacement discontinuity model is established by considering the linear fracture normal behavior (spring model) as the boundary conditions in the wave equation. The nonlinear displacement discontinuity model is established by considering the hyperbolic fracture normal behavior (BB model) as the boundary conditions in the wave equation. It is shown that, compared to a linear deformable fracture, a nonlinear deformable fracture can generate more wave transmission (less attenuation) in amplitudes and higher harmonics in frequencies.