**Author details**

30 Wave Processes in Classical and New Solids

material (equations 1a~g).

dependent P- and S- speed expressions are presented. We discuss the reductions from current theoretical approach to the traditional works of acoustoelasticity in pure solid material. Neglecting solid/fluid differences both in a large static part of strain induced by confining pressure and in a small dynamic part of strain induced by wave's propagation and vibration, the velocity equations in this paper (equations 21, 26, 31, 34, 38, 41 & 44) are completely compatible with the expressions of acoustoelasticity theory in pure solid

We design a virtual rock sample with seven assumed 3rd-order elastic constants. We perform four numerical tests on this virtual rock sample with different considerations: openpore jacketed sample under hydrostatic loading, open-pore jacketed sample under uniaxial loading, closed-pore jacketed sample under hydrostatic loading and closed-pore jacketed sample under uniaxial loading. Numerical results show that fast P wave's inverse quality factor is both sensitive to the confining pressure and wave centre frequency, which agrees with the laboratory observations of our former studies [47] in the aspect that P wave's inverse quality factors are more sensitive to pressure than S wave's. For the virtual rock sample, velocities of fast P waves and S waves seem to be more sensitive to pressure change than to changes in wave centre frequency, while slow P wave shows an opposite feature. In closed-pore jacketed uniaxial loading configuration, fast P wave's velocity in transverse direction is in decreasing trend with the rise of loading pressure, which is completely contrary to other three configurations. In all test configurations of this paper, S inverse quality factors share the same value which is independent to confining loading. S inverse

We perform the "open-pore jacketed" and "closed-pore jacketed" P-velocity measurements on a sandstone sample under hydrostatic loading. The observed P-velocity differences between the "open-pore jacketed" and "closed-pore jacketed" tests are getting larger as the confining pressure is increased in the range of 10~35 MPa, which agrees well with theoretical prediction, while in a higher confining loading range (>40MPa), the tested "openpore jacketed" velocity approaches to the "closed-pore jacketed" velocity. When hydrostatic confining pressure is increased and pore pressure keeps constant in an "open-pore" experiment, fluid will continue to flow out and microscopic connections between pores tend to close. When effective pressure reaches a high level, the rock in an "open-pore" test will approach to the theoretical configuration of the "closed-pore" system, where the pore fluid will actually stop flowing out under loading. The basic assumptions of the theoretical "open-pore jacketed" configuration is violated. A rock under high effective pressure in an "open-pore jacketed" test is actually "closed". In a high confining loading, the crack-like fraction will become gradually closed while the visible pores remain almost affected. Mostly the equant pores remain survived for which the compressibility weakly depend on the presence of the fluid (does not matter "closed-" or "open-pore"). The theory presented in this paper can give reasonable predictions for wave speeds in a confining pressure range lower than 50 MPa.

Moreover, in this work, the mechanism of "local fluid flow" have been neglected when we theoretically derive the nonlinear wave equations. The heterogeneity in pore structures and

quality factor can be influenced by wave centre frequency.

Jing Ba and Hong Cao *Geophysical Department, Research Institute of Petroleum Exploration and Development, PetroChina, Beijing, China Key Laboratory of Geophysics, PetroChina, Beijing, China* 

Qizhen Du *School of Geosciences, China University of Petroleum (East China), Qingdao, China* 
