Fracture geometry, density, and distribution control fluid and thermal transport in low porosity rocks, as well as their seismic attributes. The creation of cracks throughout the matrix can result in large and disparate reductions in P- and S-wave velocities with negligible porosity development, which breaks the classic velocity-porosity relationship. Properly interpreting these signatures in seismic surveys from stimulated geothermal, oil, and gas reservoirs or seismogenic areas requires a rock physics model that uses realistic elastic properties of fractures. Conventional models for cracked rocks employ specific inclusion shapes such as spheroids with small aspect ratios. However, all these exhibit the same normal-to-shear compliance ratio -- regardless of aspect ratio -- and therefore impact the bulk and shear moduli in the same qualitative way. As such they are inadequate for describing many of the complementary evolutions of P- and S-wave velocities that transpire with the generation of cracks. Using a differential model of decoupled compliances, we analyze published velocities for granite, basalt, and limestone to quantify typical compliance ratios and find that it is often different from that assumed in conventional crack models, which then affects crack density estimates. We also investigate how the normal and shear compliances change due to certain thermo-hydro-chemo-mechanical processes that generate large crack densities, and conclude that the final compliance ratios often still deviate from that of conventional models. Finally, we demonstrate how the model can be used to describe scatter in both P- and S-wave velocity-porosity trends. Implications for energy extraction and seismic monitoring are discussed.

Fracture geometry, density, and distribution control fluid and thermal transport in low porosity rocks, as well as their seismic attributes. The creation of cracks throughout the matrix can result in large and disparate reductions in P- and S-wave velocities with negligible porosity development, which breaks the classic velocity-porosity relationship. Properly interpreting these signatures in seismic surveys from stimulated geothermal, oil, and gas reservoirs or seismogenic areas requires a rock physics model that uses realistic elastic properties of fractures. Conventional models for cracked rocks employ specific inclusion shapes such as spheroids with small aspect ratios. However, all these exhibit the same normal-to-shear compliance ratio -- regardless of aspect ratio -- and therefore impact the bulk and shear moduli in the same qualitative way. As such they are inadequate for describing many of the complementary evolutions of P- and S-wave velocities that transpire with the generation of cracks. Using a differential model of dimensionless compliances, we analyze published velocities for granite, basalt, and limestone to quantify typical compliance ratios and find that it is often different from that assumed in conventional crack models, which then affects crack density estimates. We also investigate how the total normal and shear compliances change due to certain thermo-hydro-chemo-mechanical processes that generate large crack densities, and conclude that the final ratios often still deviate from that of conventional models. Finally, we demonstrate how the model can be used to describe scatter in both P- and S-wave velocity-porosity trends. Implications for energy extraction and seismic monitoring are discussed.