Transport-healing scaling for Omori exponents: A minimal model and its limits
Abstract
The temporal decay of triggered seismicity is commonly described by the Omori law r(t ) ∼ (t + c) -p . I introduce a minimal phenomenological framework that relates this temporal decay to two concurrent processes: the spatial spreading of a triggering perturbation and the progressive depletion of elements that remain susceptible to failure. The model yields the scaling relation p = 1 -αd/2 + γ , where α characterizes spreading, d is an effective spatial dimension, and γ describes depletion or healing. This relation provides a joint consistency test rather than a unique inversion of the Omori exponent for material healing. Numerical simulations recover the predicted scaling. A comparison with published earthquake-pair statistics illustrates that slow spatial spreading can be identified, but also that spatial and temporal exponents cannot be combined unless their underlying observables and event selections are compatible. The main implication is that the Omori exponent alone cannot generally be interpreted as a direct measure of fault or reservoir healing; testing the proposed relation requires compatible estimates of spatial spreading, event-rate decay, effective geometry, and, where possible, an independent recovery observable.
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BibTeX
@article{petrillo2026transporthealing,
title = {{Transport-healing scaling for Omori exponents: A minimal model and its limits}},
author = {Giuseppe Petrillo},
journal = {APS Open Science},
year = {2026},
month = sep,
doi = {10.1103/fgw2-2sxn},
url = {https://hal.science/hal-05773540v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Transport-healing scaling for Omori exponents: A minimal model and its limits
AU - Giuseppe Petrillo
PY - 2026
DA - 2026/09/24
JO - APS Open Science
DO - 10.1103/fgw2-2sxn
UR - https://hal.science/hal-05773540v1
AB - The temporal decay of triggered seismicity is commonly described by the Omori law r(t ) ∼ (t + c) -p . I introduce a minimal phenomenological framework that relates this temporal decay to two concurrent processes: the spatial spreading of a triggering perturbation and the progressive depletion of elements that remain susceptible to failure. The model yields the scaling relation p = 1 -αd/2 + γ , where α characterizes spreading, d is an effective spatial dimension, and γ describes depletion or healing. This relation provides a joint consistency test rather than a unique inversion of the Omori exponent for material healing. Numerical simulations recover the predicted scaling. A comparison with published earthquake-pair statistics illustrates that slow spatial spreading can be identified, but also that spatial and temporal exponents cannot be combined unless their underlying observables and event selections are compatible. The main implication is that the Omori exponent alone cannot generally be interpreted as a direct measure of fault or reservoir healing; testing the proposed relation requires compatible estimates of spatial spreading, event-rate decay, effective geometry, and, where possible, an independent recovery observable.
SN - 3070-2240
SN - 3070-2240
ER -