Postseismic Deformation Following the 2010 $M = 7.2$ El Mayor-Cucapah Earthquake: Observations, Kinematic Inversions, and Dynamic Models

Abstract

Due to its location on a transtensional section of the Pacific-North American plate boundary, the Salton Trough is a region featuring large strike-slip earthquakes within a regime of shallow asthenosphere, high heat flow, and complex faulting, and so postseismic deformation there may feature enhanced viscoelastic relaxation and afterslip that is particularly detectable at the surface. The 2010 $M = 7.2$ El Mayor-Cucapah earthquake was the largest shock in the Salton Trough since 1892 and occurred close to the US-Mexico border, and so the postseismic deformation recorded by the continuous GPS network of southern California provides an opportunity to study the rheology of this region. Three-year postseismic transients extracted from GPS displacement time-series show four key features: (1) 1–2 cm of cumulative uplift in the Imperial Valley and $\sim$1 cm of subsidence in the Peninsular Ranges, (2) relatively large cumulative horizontal displacements $>$150 km from the rupture in the Peninsular Ranges, (3) rapidly decaying horizontal displacement rates in the first few months after the earthquake in the Imperial Valley, and (4) sustained horizontal velocities, following the rapid early motions, that were still visibly ongoing 3 years after the earthquake. Kinematic inversions show that the cumulative 3-year postseismic displacement field can be well fit by afterslip on and below the coseismic rupture, though these solutions require afterslip with a total moment equivalent to at least a $M = 7.2$ earthquake and higher slip magnitudes than those predicted by coseismic stress changes. Forward modeling shows that stress-driven afterslip and viscoelastic relaxation in various configurations within the lithosphere can reproduce the early and later horizontal velocities in the Imperial Valley, while Newtonian viscoelastic relaxation in the asthenosphere can reproduce the uplift in the Imperial Valley and the subsidence and large westward displacements in the Peninsular Ranges. We present two forward models of dynamically coupled deformation mechanisms that fit the postseismic transient well: a model combining afterslip in the lower crust, Newtonian viscoelastic relaxation in a localized zone in the lower crust beneath areas of high heat flow and geothermal activity, and Newtonian viscoelastic relaxation in the asthenosphere; and a second model that replaces the afterslip in the first model with viscoelastic relaxation with a stress-dependent viscosity in the mantle. The rheology of this high-heat-flow, high-strain-rate region may incorporate elements of both these models and may well be more complex than either of them.

Appendix

See Figs. 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40.

Fig. 21

a 2 m of right-lateral slip on a vertical northwest-striking fault from 0 to 10 km depth produces surface uplift in extensional quadrants and subsidence in compressional quadrants. b, c Cross sections of coseismic displacement parallel to the dislocation show that material in extensional quadrants is extended upward as well as towards the dislocation, and material in compressional quadrants is compressed downward and away from the dislocation. Material on the left half of cross section A–A′ corresponds to the Imperial Valley in the El Mayor-Cucapah earthquake. d 2 m of right-lateral slip on a vertical northwest-striking fault from 15 to 25 km depth produces near-field subsidence in extensional quadrants and near-field uplift in compressional quadrants. e, f Material at the surface just north of the northwest end is pulled downward towards the dislocation

Fig. 22

Comparison of extracted coseismic displacements at GPS stations with coseismic displacements estimated by SOPAC. a Horizontal and vertical coseismic displacements are generally similar between the two estimates. b Time series estimated by SOPAC use only a single decay term and incorrectly ascribe some of the very early horizontal postseismic displacement in the Imperial Valley to coseismic displacement. c Comparison of vertical displacement time series at station P497 in the Imperial Valley

Fig. 23

Comparison of cumulative extracted three-year postseismic displacements at GPS stations with cumulative three-year postseismic displacements estimated by SOPAC

Fig. 24

Inversion of 3-year cumulative postseismic GPS displacements for afterslip on the main coseismic rupture planes and in the Yuha Desert. a Slip is allowed on planes F2, F3, and F4 of the Wei et al. (2011) model for the mainshock between 0 and 12 km downdip from their top edges ($\sim$0–12 km depth). Slip is also allowed on a 30-km long segment extending northwest into the Yuha Desert to fit the aftershocks and surface creep there to first order; this segment has a vertical dip and extends to 12 km depth. b–d The inversion assigns up to 1.7 m of right-lateral slip on plane F2 and up to 3.3 m of right-lateral slip and 0–1.4 m of normal slip on plane F3, equivalent in total moment to a $M=7.2$ earthquake. e The inversion produces 97 and 63 % variance reductions in horizontal and vertical displacements, respectively

Fig. 25

Inversion of 3-year cumulative postseismic GPS displacements for afterslip in the lower crust and Yuha Desert. a Slip is allowed on the extensions of slip planes F2 and F3 from the Wei et al. (2011) coseismic model into the lower crust, between 12 and 24 km downdip from the top edges of those segments ($\sim$12–24 km depth; 24 km is the approximate Moho depth). Slip is also allowed on a 30-km long segment extending northwest into the Yuha Desert to fit the aftershocks and surface creep there to first order and any possible slip at greater depth; this segment has a vertical dip and extends to 24 km depth. b, c, e The inversion assigns up to 5.7 m of right-lateral slip and 3.3 m of normal slip on the lower crustal extension of plane F3, equivalent in total moment to a $M=7.3$ earthquake. d The inversion produces variance reductions of 94 and 49 % in horizontal and vertical displacements, respectively; the observed pattern of uplift and subsidence is visibly less well fit here than in models that allow for slip on the coseismic rupture

Fig. 26

Inversion of 3-year cumulative postseismic GPS displacements for afterslip on the main coseismic rupture planes, on modeled downward extensions of the coseismic rupture planes, and in the Yuha Desert. a Slip is allowed on planes F2, F3, and F4 of the Wei et al. (2011) model for the mainshock (between 0 and 12 km downdip from their top edges) and on extensions of F2 and F3 into the lower crust (between 12 and 24 km downdip). Slip is also allowed on a 30-km long segment extending northwest into the Yuha Desert to fit the aftershocks and surface creep there to first order and any possible slip at greater depth; this segment has a vertical dip and extends to 24 km depth. b, c, e The inversion assigns up to 2.2 m of right-lateral slip and 1.1 m of normal slip on plane F3 and its lower crustal extension, equivalent in total moment to a $M=7.2$ earthquake. d The inversion produces 97 and 63 % variance reductions in horizontal and vertical displacements, respectively

Fig. 27

Inversion of 3-year cumulative postseismic GPS displacements for afterslip in the lower crust, mantle lithosphere and Yuha Desert. a Slip is allowed on the extensions of slip planes F2 and F3 from the Wei et al. (2011) coseismic model into the lower crust and mantle lithosphere, at distances between 12 and 48 km downdip from the top edges of those segments. Slip is also allowed on a 30-km long segment extending northwest into the Yuha Desert to fit the aftershocks and surface creep there to first order and any possible slip at greater depth; this extension has a vertical dip and extends to 48 km depth. b, c The inversion assigns up to 3.3 m of right-lateral slip and 1.8 m of normal slip on the deep extension of plane F3, equivalent in total moment to a $M=7.3$ earthquake. d The inversion produces variance reductions of 94 and 47 % in horizontal and vertical displacements, respectively; the distribution of uplift and subsidence is visibly less well fit here than in models that allow for slip on the coseismic rupture

Fig. 28

Forward modeling of stress-driven afterslip on modeled downward extensions of coseismic slip planes F2 and F3 in the Wei et al. (2011) coseismic model into the lower crust and mantle lithosphere. The afterslip is allowed between 15 and 48 km downdip from the top edges of these planes, is driven by coseismic shear stress changes and is governed by a rate-strengthening friction law with $(a-b)\sigma = 10$ MPa. Slip is also allowed on a 30-km long segment extending northwest into the Yuha Desert; this segment has a vertical dip and extends to 48 km depth. a This afterslip model produces horizontal surface displacements with the correct azimuth but the wrong pattern of uplift and subsidence. b, c Slip decreases away from the coseismic rupture, as expected for a stress-driven mechanism

Fig. 29

a Mapview and b, c cross sections of vertical extension ($\epsilon _{zz}$) imparted by the mainshock at 22.5 km depth (Moho depth in the Salton Trough). The lower crust and mantle lithosphere beneath the northern Imperial Valley and beneath the rupture underwent vertical compression during the mainshock

Fig. 30

Synthetic three-year surface displacements at GPS stations generated by Newtonian viscoelastic relaxation in the modeled lower crustal ductile zones. All eight models produce subsidence in the Imperial Valley (Fig. 9). a Horizontal displacements from the four models with geometries that are not confined to the Salton Trough. Vertical displacements from the model prescribing viscoelastic relaxation between 10 km depth and the Moho. b Horizontal displacements from the four models with geometries localized within the Salton Trough. Vertical displacements from the model prescribing viscoelastic relaxation in the “geothermal” geometry below 10 km depth

Fig. 31

Synthetic three-year surface displacements at GPS stations generated by viscoelastic relaxation with a stress-dependent viscosity ($n=2.5$) in the modeled lower crustal ductile zones. All eight models produce subsidence in the Imperial Valley (Fig. 32). a Horizontal displacements from the four models with geometries that are not confined to the Salton Trough. Vertical displacements from the model prescribing viscoelastic relaxation between 10 km depth and the Moho. b Horizontal displacements from the four models with geometries localized within the Salton Trough. Vertical displacements from the model prescribing viscoelastic relaxation in the “geothermal” geometry below 10 km depth

Fig. 32

Synthetic time series of surface displacement at several GPS stations (locations indicated in Fig. 30) generated by viscoelastic relaxation with a stress-dependent viscosity ($n=2.5$) in the modeled lower crustal ductile zones

Fig. 33

Synthetic three-year surface displacements at GPS stations generated by viscoelastic relaxation with a stress-dependent viscosity ($n=4$) in the modeled lower crustal ductile zones. All eight models produce subsidence in the Imperial Valley (Fig. 34). a Horizontal displacements from the four models with geometries that are not confined to the Salton Trough. Vertical displacements from the model prescribing viscoelastic relaxation between 10 km depth and the Moho. b Horizontal displacements from the four models with geometries localized within the Salton Trough. Vertical displacements from the model prescribing viscoelastic relaxation in the “geothermal” geometry below 10 km depth

Fig. 34

Synthetic time series of surface displacement at several GPS stations (locations indicated in Fig. 30) generated by viscoelastic relaxation with a stress-dependent viscosity ($n=4$) in the modeled lower crustal ductile zones

Fig. 35

a Mapview and b, c cross sections of vertical extension ($\epsilon _{zz}$) imparted by the mainshock at 70 km depth, which is within the asthenosphere in all three model geometries we use. The mainshock imparted vertical extension at 70 km depth beneath the Imperial Valley and beneath the central part of the rupture

Fig. 36

Cross sections of cumulative inelastic (viscous) strain after three years of Newtonian viscoelastic relaxation in the four geometries for the asthenosphere show that although the major viscoelastic relaxation is concentrated close to the rupture, some inelastic strain does occur outside of the Salton Trough

Fig. 37

Three-year cumulative surface displacements from viscoelastic relaxation with a stress-dependent viscosity ($n=3.5$) in the four modeled geometries for the asthenosphere. This mechanism can to some extent reproduce the uplift in the Imperial Valley but does not reproduce the amplitude of subsidence observed in the Peninsular Ranges or the horizontal displacements observed anywhere in southern California

Fig. 38

Synthetic time series of surface displacement at several GPS stations (locations indicated in Fig. 37) generated by stress-dependent viscoelastic relaxation ($n=3.5$) in the modeled geometries for the asthenosphere. This mechanism can reproduce the uplift at station P497 in the Imperial Valley and possibly the rapid early eastward motion at station P473 but no other aspect of the transient

Fig. 39

a Locations of stations PJZX, PLPX and PLTX in Mexico compared to the geometry of the first coupled model. b–g Comparison of best-fit GPS time series at stations PJZX, PLPX and PLTX in Mexico with synthetic time series of surface displacement generated by the first coupled model

Fig. 40

a Locations of stations PJZX, PLPX and PLTX in Mexico compared to the geometry of the second coupled model. b–g Comparison of best-fit GPS time series at stations PJZX, PLPX and PLTX in Mexico with synthetic time series of surface displacement generated by the second coupled model