Seismic reflectivity of fractures: the impact of secondary connected fractures

Fractures are ubiquitous through out the Earth's upper crust and dominate the mechanical and hydraulic properties of the affected rock masses. Indeed, open fractures act as fluid conduits and, commonly, flow is controlled by larger fractures, which are, in turn, likely to be connected to smaller ones. Therefore, fracture characterization is of paramount importance for many pertinent applications, such as geothermal energy production, CO₂ sequestration, nuclear waste storage, and hydrocarbon exploration. Seismic reflection methods are useful tools for fracture characterization due to the generally high reflectivity that large fractures exhibit as a consequence of their strong mechanical contrast with the embedding intact background. The magnitude of this mechanical contrast is known to be strongly affected by fracture-to-background wave-induced fluid pressure diffusion (FPD). Conversely, the FPD effects associated with secondary connected fractures remain so far unexplored. We investigate the influence of FPD on the normal compliance and on the vertical incidence PP reflectivity of a large fracture that is hydraulically connected to smaller fractures. To this end, we use several models that consist of an infinite horizontal main fracture connected to multiple vertical secondary fractures of finite length. This fracture system is embedded in impermeable background. The individual models differ only with regard to the geometrical (e.g., length and aperture), and physical properties (e.g., permeability and bulk modulus) of the secondary fractures. For comparison, we also calculate the normal compliance and the reflectivity of an isolated infinite horizontal fracture. To assess the changes of fracture compliance due to FPD, we perform a vertical compressional oscillatory test over samples of the aforementioned models that include part of the fracture system and the embedding background. This test simulates the FPD effects that a vertically propagating P-wave generates between the main and secondary fractures. Specifically, the wave produces a pressure increase in the horizontal fracture that equilibrates as fluid flows into the secondary vertical fractures. Based on this oscillatory test, we compute the average of the vertical components of strain and stress over the main fracture, which we use to estimate its normal compliance. We then proceed to calculate the PP reflectivity at normal incidence using its inferred P-wave modulus. Our results show that both the compliance and the PP reflectivity of the main fracture increase as much as two-orders of magnitude in response to the presence of secondary fractures. We also find that the physical and geometrical properties of the secondary connected fractures have an influence on the normal compliance and reflectivity of the main fracture.