Noda et al. (2020) computed three-dimensional shear strain energy changes caused by the 2016 Kumamoto (Japan) earthquake sequence using coseismic slip models and a background deviatoric stress level assumed equal to crustal frictional strength, and showed from the energy balance of shear faulting that the volume integral of the shear strain energy change constrains the background absolute deviatoric stress to exceed about 14 MPa at 10 km depth. Three linked questions remain open beyond these results: incorporating poroelastic and pore-fluid-pressure effects, which may explain the roughly 25% of aftershocks that occurred where shear strain energy decreased; tightening the broad lower bound on absolute stress by combining the energy-balance constraint with independently estimated radiated energy; and assessing how the resulting stress level relates to a hydrostatic pore-pressure crustal stress state. Later work partially advanced the first strand — a follow-up by co-authors found that the undrained poroelastic response is too small to explain inferred pore-pressure increases and that pre-existing overpressure plus deep fluid supply controls seismicity-rate changes — but no study has yet tightened the absolute-stress bound with radiated energy, compared it with the hydrostatic stress state, or delivered a fully coupled poroelastic account of the aftershock distribution. The problem remains open.

Background

When an earthquake ruptures a fault, the elastic stress and strain fields around the fault change, and with them the elastic strain energy stored in the crust. The shear strain energy (the part of the elastic energy associated with distortion rather than compression) is central to earthquake mechanics because fault slip can radiate seismic waves only to the extent that shear strain energy is released. To map the shear strain energy change caused by a large earthquake, one needs both the coseismic stress change (computable from a published slip distribution using elastostatic theory, e.g. Okada's formulas for a dislocation in an elastic half-space) and the pre-existing, or background, crustal stress. Earthquake focal mechanisms (the double-couple representation of the radiation pattern, retrievable for many events) constrain the orientation of the background stress, but its absolute level is one of the oldest unsolved observables in tectonophysics: no instrument measures in-situ deviatoric stress at seismogenic depth (roughly 5-15 km), and stress magnitudes must be inferred indirectly. The Coulomb failure stress change (ΔCFS), the standard metric for aftershock triggering, is the change of shear stress minus friction times the change of normal stress on a target fault plane; it depends on the coseismic stress change only, not on the absolute background stress. Energy-based metrics are more demanding because they do depend on the absolute stress. Noda et al. (2020) mapped the three-dimensional shear strain energy change for the 2016 Kumamoto earthquake sequence in southwest Japan (an Mw 6.2 foreshock on 14 April and an Mw 7.0 mainshock on 16 April 2016 on the Futagawa-Hinagu fault system), assuming the background deviatoric stress level equals the frictional strength of the crust. Their key results were that the spatial pattern of strain energy change depends strongly on that assumed level, that about 75% of aftershocks occurred where the shear strain energy increased, and — from the energy balance of shear faulting (the statement that the volume-integrated shear strain energy change must cover the radiated energy plus the energy dissipated by friction and fracture on the fault) — that the background deviatoric stress at 10 km depth must exceed roughly 14 MPa at the very least. This bound is loose because it was derived without using an actual radiated-energy estimate, which would subtract from the available energy budget and raise the required stress. The radiated energy of an earthquake (the seismic-wave energy, estimated from broadband waveform recordings) is standardly expressed relative to the seismic moment (the static measure of fault size) as the scaled energy, or via the radiation efficiency (the fraction of released energy that is radiated rather than dissipated). Three complications were left open. First, the analysis treated the crust as a purely elastic, isotropic solid, whereas crustal rocks are porous and fluid-saturated: coseismic volumetric strain changes the pore-fluid pressure (the pressure of fluid in rock pores), which alters effective normal stress and hence fault strength; in the simplest undrained approximation the pressure change equals the Skempton coefficient times the change in mean normal stress, and full poroelastic coupling also includes subsequent fluid diffusion (flow driven by pressure gradients, governed by permeability and diffusivity). Some aftershocks occurred where the shear strain energy decreased, and pore-pressure changes are a candidate explanation. Second, the energy-balance stress bound is broad and could in principle be tightened by combining it with an independently estimated radiated energy for the sequence. Third, it is unclear how the derived stress bound compares with the stress state expected if pore pressure is close to hydrostatic (the pressure of a static fluid column, which grows by about 10 MPa per kilometer of depth, reaching roughly 100 MPa at 10 km) versus overpressured. A follow-up study by co-workers (Nakagomi et al. 2021) analyzed Kumamoto seismicity-rate changes with Coulomb stresses, undrained pore-pressure changes, and a focal-mechanism pore-pressure inversion; it found that the undrained poroelastic response is an order of magnitude too small to explain the inferred post-sequence pore-pressure increases (17-20 MPa at 5-15 km depth), that seismicity rates increased mainly where pore pressure was already above hydrostatic before the sequence, and that fluid supply from greater depths appears to be required — so the poroelastic question is live but reframed rather than settled. Related methodological developments (an energetics-based failure-stress metric that includes pore-fluid pressure, applied to the 1992 Landers sequence; energy-budget models linking coseismic slip and afterslip for the 2016 Central Tottori earthquake; scaled-energy estimates for thousands of small Kumamoto events indicating fluid involvement) show the framework is active, but none has delivered an energy-balance-tightened absolute stress level for the Kumamoto source region or a complete coupled poroelastic account of its aftershocks.

Problem Statement

For the source region of the 2016 Kumamoto (Japan) earthquake sequence, determine the absolute background deviatoric stress level and its role in aftershock triggering, completing the program that remains open after Noda et al. (2020, GRL 47, e2019GL086369) in three linked facets: (1) incorporate pore-fluid-pressure and poroelastic effects — going beyond the purely elastic isotropic treatment — into the shear-strain-energy/coseismic-stress framework and quantitatively assess the extent to which the aftershocks occurring where the shear strain energy decreased (roughly one quarter of the sequence's aftershocks) are accounted for by coseismic poroelastic pressure change, post-seismic fluid diffusion, pre-existing overpressure, or a combination, quantifying any residual unexplained fraction (the undrained poroelastic branch alone has been shown by Nakagomi et al. 2021 to be insufficient); (2) combine the energy-balance constraint — the requirement that the volume integral of the coseismic shear strain energy change supply the radiated energy plus the frictional and fracture energy dissipated on the fault — with independently estimated radiated energy of the sequence, so as to tighten the lower bound of more than 14 MPa at 10-km depth into a sharper constraint on, or estimate of, the absolute in-situ deviatoric stress, with quantified uncertainty over the choices of coseismic slip model and energy-partition (radiation efficiency) assumptions; and (3) assess how the resulting absolute stress level compares with the crustal stress state expected under hydrostatic pore pressure and with the over-hydrostatic pore pressures inferred from focal-mechanism inversions in the same region. Facets (1)-(3) serve one objective: an absolute-stress-calibrated, poroelastically consistent physical account of aftershock generation in this sequence.

References

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