Earthquake deformation cycle driven by elastic lithosphere or
Earthquake deformation cycle driven by elastic lithosphere or a coupled lithosphereasthenosphere ? Thatcher (JGR, 1983)
Strain rate observations of strike slip faults 1. Shear strain rates at surface near the fault monotonically decrease with time. 2. Surface strain gradually spreads away from the zone, particularly later in the earthquake cycle.
Two models of earthquake deformation cycle Elastic half-space model Viscoelastic model A region of time-dependent slip for realistic modeling and has exponential dependence with time. Fault may extend all the way through lithosphere or not. Relaxation time is directly comparable to T in the elastic half-space model.
Comparison of shear strain rates from models near fault 1. Shear strain rates at monotonically decrease with time. 2. Parameters can be adjusted to achieve similar profiles.
Spreading of strain away from the fault The half maximum points of the curve all move outward and almost similarly for both models.
Application to the San Andreas Fault Viscoelastic model Modified elastic half-space model Lessons: 1. Hard to distinguish between deformation mechanisms from these observations. 2. Using rate information alone may be insufficient.
Postseismic deformation after Parkfield Earthquake : Purely Afterslip ? Freed (GRL, 2007)
Parkfield Earthquake (2004) 1. First small earthquake (Mw = 6) to be observed using continuous GPS. 2. Post-seismic deformation mechanisms. • Afterslip (aseismic slip) • Poroelastic relaxation (fluid pressure) • Viscoelastic relaxation (lower crust and upper mantle interactions). 3. Unusual: Vigorous post-seismic response within first few months. Not observed with larger Earthquakes. 4. Claims by Freed • The earthquake is too small to load the mantle and to initiate visco-elastic response. • Afterslip is a sufficient mechanism to describe all postseismic deformation.
Comparison of Elastic and coupled models 1. The estimated viscoelastic displacements are not aligned with the observed GPS displacements. 2. The magnitude of viscoelastic displacements are an order of magnitude smaller than observed near the fault. 3. Far field observations do not match up.
Freed’s Viscoelastic model 1. Assumed uniform linear viscosity for the lower crust (20 -30 km) and upper mantle (30 -100 km). 2. Assumed viscosity of (10^17 Pa s), to allow for complete relaxation within 2 years of observation. 3. This estimate represents the maximum deformation due to viscoelastic response. This is order of magnitude smaller than that observed. 4. Allowing afterslip to load the lower crust and mantle made little difference. Coseismic shear stress argument 1. From inverting coseismic data, estimated shear stress of 0. 05 MPa at 20 Km and 0. 01 MPa at 30 Km. 2. 300 times smaller than 2002 Denali Earthquake. 3. Too small to drive detectable viscoelastic reponse? 4. Conclusion: Too hard to resolve viscoelastic component.
Freed’s Afterslip model Peak of inferred coseismic slip model 1. Determined from the cumulative GPS surface displacement. 2. Three different areas of peak slip. 3. 10 -12 cm peak afterslip. Coseismic slip is 50 cm. But distributed afterslip leads to a moment of 6. 3 Mw (greater than the Earthquake itself). 4. Time-evolution of deformation is not used in the model. 5. Vertical GPS displacements not used due to low SNR.
Postseismic deformation after Parkfield earthquake : afterslip or viscous flow? Bruhat , Barbot and Avouac (2011)
Parkfield postseismic deformation: afterslip or viscous flow? Is inferred afterslip real or a bias from viscoelastic relaxation? Is viscoelastic relaxation in lower crust and mantle compatible with geodetic data? barbot et al. , 2009 a
Trade-offs between deep afterslip and viscoelastic flow Great trade-off in inferences of deep afterslip and viscoelastic flow in low-resolution fault areas. elastic (fault slip) viscoelastic (bulk flow)
Design of inverse problem: a linear solution? 93. 4% 4% Post-Landers viscoelastic relaxation in the radar line of sight (LOS) is dominated by a time-space separable signal.
Design of inverse problem: linearize viscoelastic flow GPS In. SAR data vector effect of unit slip on fault patch i effect viscoelastic flow amplitude of slip amplitude of viscoelastic deformation
Design of inverse problem: linearize viscoelastic flow GPS In. SAR minimize the misfit data vector with non-negativity constraint n io s er slip inversion v in and regularization Slip and viscous amplitude inversion include a bilinear function to compensate for imprecise knowledge of orbits.
Comparing strong-crust and weak lower-crust models A. Afterslip model of In. SAR+GPS data B. Joint afterslip/viscoelastic inversion Given problems of trade-offs and non-uniqueness, how may one find the most realistic model?
Comparing strong-crust and weak lower-crust models • Inclusion of viscoelastic relaxation systematically improves fit to In. SAR and GPS data. • The null hypothesis that improved fit is non significant is rejected with 99% confidence. • Geodetic data requires the presence of lower-crustal
Time evolution of viscoelastic amplitude (only GPS) maximum flow some viscoelastic flow weak viscoelastic flow no flow Only a class of models is mechanically viable. The time evolution is compatible with expected response of a viscoelastic material.
Conclusions and further challenges • In. SAR and GPS data are compatible with the presence of viscoelastic flow in the lower crust. • What are the implications for loading of the seismogenic zone and earthquake cycles at Parkfield? • Can we infer anything about the period of the earthquake cycle? tremors
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