Wave-induced thermal flux and scattering of P waves in a medium with aligned circular cracks

Abstract

High temperature affects the seismic properties of cracked and faulted reservoirs and can be an indicator for their detection. To this purpose, the authors study the wave-induced thermal flux (WITF) and develop two exact solutions for the scattering of compressional waves by a circular crack filled with a compressible fluid, in which the approach is based on thermally permeable and impermeable boundary conditions. The authors obtained the phase velocity and attenuation as a function of frequency, which found that there are two loss mechanisms, i.e., thermoelastic dissipation at low frequencies and elastic scattering at high frequencies. Basically, when the crack size is comparable to the thermal and elastic wavelengths, there are substantial dispersion and attenuation (anelasticity) in the WITF and scattering frequency ranges, respectively. This means that the spatial inhomogeneity scale for inducing WITF is much smaller than that of scattering and the two mechanisms can be discriminated. The dependence of the compressional-wave velocity and attenuation on the compressibility and thermal expansion of the crack-filling fluid are different depending on the thermal diffusion rates at the crack interface. The anelasticity is much higher in the fully permeable case. This model has the potential to evaluate thermoelastic properties and heterogeneity at different scales from seismic responses.