Coupling Crustal Seismicity to Crustal Permeability — Empirical Theory for EGS & Hydrothermal Flow Systems
Peter C. Leary, and Peter Malin
Advanced Seismic Instrumentation and Research (ASIR), USA
Abstract: Direct association of natural and induced seismicity with crustal fluid flow properties has long been assumed, particularly for active crustal fault systems, but for a variety of reasons it has been difficult to describe the relationship in terms of subsurface properties. We present microseismicity evidence that, at least in the absence of active faulting, the relationship between microseismicity and crustal permeability can be understood in terms of the spatial correlation empirics of crustal flow properties in a critically-strained brittle crust. In summary, we introduce a theoretic construct in which the observed power-law scaling two-point spatial-correlation property of microearthquake locations, e.g., natural and induce seismicity “clouds”, are direct consequences of spatial fluctuations in crustal permeability controlled by spatially-correlated fluctuations in crustal porosity. A conceptual framework for understanding natural and induced seismicity in terms of the spatially correlated crustal porosity and permeability can significantly improve our ability to interpret microseismicity data in terms of crustal flow structures.
Evidence for a close physical relation between crustal seismicity and crustal permeability is observed at two geothermal developments: (1) large-scale fluid injection at 6 km depth at a Finnish EGS site, and (2) natural seismicity at 3 km depth in an Indonesian geothermal field. Microearthquake locations at both sites show power-law scaling two-point correlation distributions in event separation range r, Γmeq(r) ~ 1/rn, n ~ ½. Computation shows that the observed microseismicity spatial correlation systematics can be derived from a trio of crustal spatial correlation empirics for crustal porosity φ and permeability κ:
1) Well-log crustal porosity fluctuation spectral power Pφ(k) scales inversely with spatial frequency k, Pφ(k) ~ 1/k, for five to six
decades of spatial scale length, ~1/km < k < ~1/cm;
2) In well-core sequences, permeability spatial fluctuations strongly correlate with porosity fluctuations as δlogκ ~ αδφ, with empirical parameter α having values such that αφ ~ 3-4 for rock types spanning two decades of mean porosity, 0.3% < φ < 30%; the empiric αφ ~ 3-4 guarantees that normally distributed porosity φ generates lognormally distributed permeability, κ ~ exp(αφ);
3) For stationary random systems such as plausibly describe the slowly evolving ambient brittle-fracture crust, the Wiener-Khinchin theorem posits a Fourier transform pair for spatially-correlated physical-event distributions Γ(r) in offset range r and spatial fluctuation power P(k) in spatial frequency k, P(k) ~ ∫exp(ikr)Γ(r)dr and Γ(r) ~ ∫exp(-ikr)P(k)dk.
Assuming that the ambient crust is in a stationary random process state (in which stochastic parameters such as mean and variance do not change significantly with observation times), we apply the Wiener-Khinchin theorem to numerical simulations of permeability distributions κ(x,y,z) for a range of porosity spatial correlations Pφ(k) ~ 1/km, 0 < m < 2, to generate a range of two-point correlation functions Γκ(r) ~ 1/rp corresponding to the range of porosity spatial correlations. A wide range of numerical simulations show that the observed permeability spatial correlation function Γκ(r) ~ 1/r1/2 arises for the porosity spatial-correlation scaling spectral distribution for m ~ 1, corresponding to spectral scaling Pφ(k) ~ 1/k1 that is universally seen in well log data. As it is long recognised that fluid pressure effects promote seismic activity, and as fluid effects are likely to be strongest where permeability is greatest, we logically interpret the observed Γmeq(r) ~ 1/r1/2 spatial correlation as corresponding the numerical simulation permeability correlation function Γκ(r) ~ 1/r1/2. This correspondence ‘‘predicts’’ that observed seismicity at the EGS and hydrothermal sites is evidence that fundamental ambient crustal rock-fluid interactions physically link crustal porosity φ and permeability κ to induced and natural microseismicity.
Our physical interpretation of observed spatial correlation Γmeq(r) ~ 1/r1/2 for EGS and hydrothermal system seismicity has two clear practical geothermal applications. It has been extensively demonstrated that shale formations undergoing frack-stimulation emit sustained low-level seismic energy as the formation fluids are disturbed. It has been lately demonstrated that areas of sustained low-level seismic emission can be detected with 10- to 15-meter spatial resolution even before shale formations are drilled or stimulated. Our physical interpretation of microseismicity spatial correlation function Γmeq(r) ~ 1/r1/2 provides strong evidence that the demonstrated shale-formation fluid-flow-generated seismic signal generation can be extended to include discrete slip events in magnitude range -1 < M < 1 within an ambient stationary crustal state. (In contrast with a stationary ambient crustal state, crustal Coupling Crustal Seismicity to Crustal Permeability — Empirical Theory for EGS & Hydrothermal Flow Systems 660 volumes undergoing active tectonic faulting are stochastically non-stationary with no expectation that the Wiener-Khinchin theorem applies.) According to our theoretic construct, we can apply the demonstrated shale-formation fluid-flow imaging power to (i) use downhole seismic sensor arrays to monitor the mechanics of EGS permeability stimulation in deep crustal heat exchange volumes, and (ii) use surface seismic array data to map complex flow-connectivity structures in convective geothermal flow systems in order to identify suitable production-well drilling targets with greatly improved (50 meter?) spatial resolution.
Key words: EGS, convective geothermal, permeability stimulation, induced microseismicity, fractures, porosity, permeability
