Phoebe M. R. DeVries

Kinematically consistent models of viscoelastic stress evolution

Following large earthquakes, coseismic stresses at the base of the seismogenic zone may induce rapid viscoelastic deformation in the lower crust and upper mantle. As stresses diffuse away from the primary slip surface in these lower layers, the magnitudes of stress at distant locations (>1 fault length away) may slowly increase. This stress relaxation process has been used to explain delayed earthquake triggering sequences like the 1992Mw= 7.3 Landers and 1999Mw=7.1 Hector Mine earthquakes in California. However, a conceptual difficulty associated with thesemodels is that themagnitudes of stresses asymptote to constant values over long time scales. This effect introduces persistent perturbations to the total stress field over many earthquake cycles. Here we present a kinematically consistent viscoelastic stress transfer model where the total perturbation to the stress field at the end of the earthquake cycle is zero everywhere. With kinematically consistent models, hypotheses about the potential likelihood of viscoelastically triggered earthquakes may be based on the timing of stress maxima, rather than on any arbitrary or empirically constrained stress thresholds. Based on these models, we infer that earthquakes triggered by viscoelastic earthquake cycle effects may be most likely to occur during the first 50% of the earthquake cycle regardless of the assumed long-term and transient viscosities.

Geodetically constrained models of viscoelastic stress transfer and earthquake triggering along the North Anatolian fault

Over the past 80 years, 8 MW > 6.7 strike-slip earthquakes west of 40° longitude have ruptured the North Anatolian fault (NAF) from east to west. The series began with the 1939 Erzincan earthquake in eastern Turkey, and the most recent 1999 MW = 7.4 Izmit earthquake extended the pattern of ruptures into the Sea of Marmara in western Turkey. The mean time between seismic events in this westward progression is 8.5 ± 11 years (67% confidence interval), much greater than the timescale of seismic wave propagation (seconds to minutes). The delayed triggering of these earthquakes may be explained by the propagation of earthquake-generated diffusive viscoelastic fronts within the upper mantle that slowly increase the Coulomb failure stress change ( ΔCFS) at adjacent hypocenters. Here we develop three-dimensional stress transfer models with an elastic upper crust coupled to a viscoelastic Burgers rheology mantle. Both the Maxwell (ηM = 4 × 1018−1 × 1019 Pa s) and Kelvin (ηK = 1 × 1018−1 × 1019 Pa s) viscosities are constrained by studies of geodetic observations before and after the 1999 Izmit earthquake. We combine this geodetically constrained rheological model with the observed sequence of large earthquakes since 1939 to calculate the time evolution of ΔCFS changes along the North Anatolian fault due to viscoelastic stress transfer. Apparent threshold values of mean ΔCFS at which the earthquakes in the eight decade sequence occur are between ∼0.02 to ∼3.15 MPa and may exceed the magnitude of static ΔCFS values by as much as 177%. By 2023, we infer that the mean time-dependent stress change along the northern NAF strand in the Marmara Sea near Istanbul, which may have previously ruptured in 1766, may reach the mean apparent time-dependent stress thresholds of the previous NAF earthquakes.

Enabling large‐scale viscoelastic calculations via neural network acceleration

One of the most significant challenges involved in efforts to understand the effects of repeated earthquake cycle activity is the computational costs of large-scale viscoelastic earthquake cycle models. Computationally intensive viscoelastic codes must be evaluated at thousands of times and locations, and as a result, studies tend to adopt a few fixed rheological structures and model geometries and examine the predicted time-dependent deformation over short (<10 years) time periods at a given depth after a large earthquake. Training a deep neural network to learn a computationally efficient representation of viscoelastic solutions, at any time, location, and for a large range of rheological structures, allows these calculations to be done quickly and reliably, with high spatial and temporal resolutions. We demonstrate that this machine learning approach accelerates viscoelastic calculations by more than 50,000%. This magnitude of acceleration will enable the modeling of geometrically complex faults over thousands of earthquake cycles across wider ranges of model parameters and at larger spatial and temporal scales than have been previously possible.

Statistical tests of simple earthquake cycle models

A central goal of observing and modeling the earthquake cycle is to forecast when a particular fault may generate an earthquake: a fault late in its earthquake cycle may be more likely to generate an earthquake than a fault early in its earthquake cycle. Models that can explain geodetic observations throughout the entire earthquake cycle may be required to gain a more complete understanding of relevant physics and phenomenology. Previous efforts to develop unified earthquake models for strike-slip faults have largely focused on explaining both preseismic and postseismic geodetic observations available across a few faults in California, Turkey, and Tibet. An alternative approach leverages the global distribution of geodetic and geologic slip rate estimates on strike-slip faults worldwide. Here we use the Kolmogorov-Smirnov test for similarity of distributions to infer, in a statistically rigorous manner, viscoelastic earthquake cycle models that are inconsistent with 15 sets of observations across major strike-slip faults. We reject a large subset of two-layer models incorporating Burgers rheologies at a significance level of α = 0.05 (those with long-term Maxwell viscosities ηM  ~ 4.6 × 1020 Pa s) but cannot reject models on the basis of transient Kelvin viscosity ηK. Finally, we examine the implications of these results for the predicted earthquake cycle timing of the 15 faults considered and compare these predictions to the geologic and historical record.