Wave-induced fluid diffusion is believed to be one of the major mechanisms in causing seismic velocity dispersion and attenuation, and it can be interpreted as scattered Biot slow wave due to mode conversion in the propagation of elastic waves scattered by inclusions. Within the framework of Biot theory, we first derive dual integral equations for the problem of elastic wave scattering by a slit crack in a fluid-saturated poroelastic medium. The integral equations are then reduced to a Cauchy-type integral equation for dislocation density, and they are verified by comparing with existing Fredholm integral equation. By combining scattering far-field solutions with Foldy-Lax homogenization scheme, we further develop an equivalent viscoelasticity model for estimation of velocity dispersion and attenuation in saturated rocks containing a sparse distribution of randomly orientated slit cracks. It is shown that wave-induced fluid diffusion, elastic scattering and Biot global flow can dominate the dispersion and attenuation at separated frequency bands. Numerical solution of Cauchy-type integrals only need 1/5 time of that of Fredholm-type integral equations. However, directly numerical solution of Cauchy-type singular integrals is still time-consuming. For the convenience of engineering applications, we further derive low- and high-frequency asymptotic solutions for effective moduli at diffusion-dominated frequencies. By using the branching function approximation method and the derived asymptotes, we present simple, explicit expressions for the effective moduli which can reveal the influences of permeability, fluid viscosity, crack width and elastic properties of background medium on velocity dispersion and attenuation due to wave-induced fluid diffusion. The most noteworthy feature of this study is that the present model can be used to estimate S-wave dispersion and attenuation, overcoming the drawback of the dual porosity model. We find that the WIFD dispersion and attenuation in S waves is comparable to that of P waves. The peak frequencies of P and S waves are the same. Analogously to the case of aligned slit cracks, the peak frequency for randomly orientated cracks occurs when the wavelength of Biot slow waves is comparable to the crack width. Specifically, the peak frequency is proportional to the first power of diffusion coefficient, but to the inverse square of crack width. The P-wave velocity is sensitive to the change of fluid bulk modulus, and it monotonously increases with fluid bulk modulus. In contrast, the S-wave velocity is insensitive to fluid bulk modulus, in particular at low frequencies. This dependence of P- and S-wave velocities on fluid bulk modulus at low frequencies can be understood by Gassmann fluid substitution theory. Unlike P-wave inverse quality factor which first increases and then decreases with the increase of fluid bulk modulus, the S-wave inverse quality will monotonously increase with fluid bulk modulus. The above results can help invert fluid parameters by using P- and S-wave properties. Moreover, we propose a concept of "equivalent incident angle" to interpret the effective properties of randomly oriented cracks. As a result, we do not need to carry out integration over every incident angle. The equivalent incident angle for P waves is 45 degrees, while 22.5 degrees or 67.5 degrees for S waves.
