Viscoelasticity expression and extension of seismic dispersion and attenuation in porous media with multiple fracture se
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RESEARCH ARTICLE - APPLIED GEOPHYSICS
Viscoelasticity expression and extension of seismic dispersion and attenuation in porous media with multiple fracture sets Jinwei Zhang1 · Renwei Ding1 · Lihong Zhao1 · Deying Wang1 Received: 22 June 2020 / Accepted: 3 October 2020 © Institute of Geophysics, Polish Academy of Sciences & Polish Academy of Sciences 2020
Abstract Intensive studies have been conducted on fluid-related seismic dispersion and attenuation in saturated anisotropic media. Most of the studies are concentrated on the transversely isotropy media. However, the fractures distribution in subsurface reservoirs is often complex. When there are multiple fracture sets developing in a porous background, the signatures of seismic dispersion and attenuation remain unclear. In this paper, we propose a method to calculate the frequency-dependent stiffness matrix of a porous medium with multiple fractures sets from a perspective of viscoelasticity. Due to the favorable approximation performance of the generalized standard linear solid model and Chapman model, we use a modified form of generalized standard linear solid model to simulate the frequency-dependent stiffness tensor of porous media with multiple fracture sets. The representation of the stiffness tensor utilizes the modulus defect to denote the effects the fractures including fracture density and geometry. With the procedure of calculating the stiffness tensors at low- and high-frequency limits, we can easily calculate the frequency-dependent stiffness tensor for media with multiple fracture sets with arbitrary orientations and directions. We then analyze the effects of the fracture parameters on the viscoelasticity characteristics taking orthotropic medium as an example. The results can help to understand the viscoelasticity and the mesoscopic seismic attenuation associated with fractures and fluids and can provide a practical rock physics model when dealing with reservoirs with complex fracture patterns. Keywords Fractured reservoirs · Seismic rock physics · Dispersion and attenuation · Viscoelasticity
Introduction Many theoretical mechanisms have been proposed to explain the fluid-related seismic dispersion and attenuation in porous media, among which wave-induced fluid flow is one of the predominant mechanisms. Commonly, there are three scales of fluid flow generating intrinsic attenuation in different frequency bands. Biot theory which laid the foundation for most studies of wave-induced fluid flow describes a macroscopic flow in the wavelength scale (Gassmann 1951; Biot 1956a, b). The squirt flow (Mavko and Nur 1975; Dvorkin et al. 1995) due to fluid pressure gradient between microcracks and pores occurs in a grain scale. Both Biot global flow and squirt flow cannot generate significant attenuation in * Jinwei Zhang [email protected] 1
College of Earth Science and Engineering, Shandong University of Science and Technology, No. 579, Qianwangang Road, Huangdao District, Qingdao, China
the seismic frequency band (Pride et al. 2004). It’s b
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