@phdthesis{Muldashev2017,
  author    = {Muldashev, Iskander},
  title     = {Modeling of the great earthquake seismic cycles},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-398926},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xii, 117},
  year      = {2017},
  abstract  = {The timing and location of the two largest earthquakes of the 21st century (Sumatra, 2004 and Tohoku 2011, events) greatly surprised the scientific community, indicating that the deformation processes that precede and follow great megathrust earthquakes remain enigmatic. During these phases before and after the earthquake a combination of multi-scale complex processes are acting simultaneously: Stresses built up by long-term tectonic motions are modified by sudden jerky deformations during earthquakes, before being restored by multiple ensuing relaxation processes. This thesis details a cross-scale thermomechanical model developed with the aim of simulating the entire subduction process from earthquake (1 minute) to million years' time scale, excluding only rupture propagation. The model employs elasticity, non-linear transient viscous rheology, and rate-and-state friction. It generates spontaneous earthquake sequences, and, by using an adaptive time-step algorithm, recreates the deformation process as observed naturally over single and multiple seismic cycles. The model is thoroughly tested by comparing results to those from known high- resolution solutions of generic modeling setups widely used in modeling of rupture propagation. It is demonstrated, that while not modeling rupture propagation explicitly, the modeling procedure correctly recognizes the appearance of instability (earthquake) and correctly simulates the cumulative slip at a fault during great earthquake by means of a quasi-dynamic approximation. A set of 2D models is used to study the effects of non-linear transient rheology on the postseismic processes following great earthquakes. Our models predict that the viscosity in the mantle wedge drops by 3 to 4 orders of magnitude during a great earthquake with magnitude above 9. This drop in viscosity results in spatial scales and timings of the relaxation processes following the earthquakes that are significantly different to previous estimates. These models replicate centuries long seismic cycles exhibited by the greatest earthquakes (like the Great Chile 1960 Earthquake) and are consistent with the major features of postseismic surface displacements recorded after the Great Tohoku Earthquake. The 2D models are also applied to study key factors controlling maximum magnitudes of earthquakes in subduction zones. Even though methods of instrumentally observing earthquakes at subduction zones have rapidly improved in recent decades, the characteristic recurrence interval of giant earthquakes (Mw>8.5) is much larger than the currently available observational record and therefore the necessary conditions for giant earthquakes are not clear. Statistical studies have recognized the importance of the slab shape and its surface roughness, state of the strain of the upper plate and thickness of sediments filling the trenches. In this thesis we attempt to explain these observations and to identify key controlling parameters. We test a set of 2D models representing great earthquake seismic cycles at known subduction zones with various known geometries, megathrust friction coefficients, and convergence rates implemented. We found that low-angle subduction (large effect) and thick sediments in the subduction channel (smaller effect) are the fundamental necessary conditions for generating giant earthquakes, while the change of subduction velocity from 10 to 3.5 cm/yr has a lower effect. Modeling results also suggest that having thick sediments in the subduction channel causes low static friction, resulting in neutral or slightly compressive deformation in the overriding plate for low-angle subduction zones. These modeling results agree well with observations for the largest earthquakes. The model predicts the largest possible earthquakes for subduction zones of given dipping angles. The predicted maximum magnitudes exactly threshold magnitudes of all known giant earthquakes of 20th and 21st centuries. The clear limitation of most of the models developed in the thesis is their 2D nature. Development of 3D models with comparable resolution and complexity will require significant advances in numerical techniques. Nevertheless, we conducted a series of low-resolution 3D models to study the interaction between two large asperities at a subduction interface separated by an aseismic gap of varying width. The novelty of the model is that it considers behavior of the asperities during multiple seismic cycles. As expected, models show that an aseismic gap with a narrow width could not prevent rupture propagation from one asperity to another, and that rupture always crosses the entire model. When the gap becomes too wide, asperities do not interact anymore and rupture independently. However, an interesting mode of interaction was observed in the model with an intermediate width of the aseismic gap: In this model the asperities began to stably rupture in anti-phase following multiple seismic cycles. These 3D modeling results, while insightful, must be considered preliminary because of the limitations in resolution. The technique developed in this thesis for cross-scale modeling of seismic cycles can be used to study the effects of multiple seismic cycles on the long-term deformation of the upper plate. The technique can be also extended to the case of continental transform faults and for the advanced 3D modeling of specific subduction zones. This will require further development of numerical techniques and adaptation of the existing advanced highly scalable parallel codes like LAMEM and ASPECT.},
  language  = {en}
}
@misc{Metz2019,
  type      = {Master Thesis},
  author    = {Metz, Malte},
  title     = {A quasi-dynamic and self-consistent rupture model to simulate earthquake ruptures},
  doi       = {10.25932/publishup-47310},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-473100},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xi, 113},
  year      = {2019},
  abstract  = {Dynamic earthquake rupture modeling provides information on the rupture physics as the rupture velocity, frictions or tractions acting during the rupture process. Nevertheless, as often based on spatial gridded preset geometries, dynamic modeling is depending on many free parameters leading to both a high non-uniqueness of the results and large computation times. That decreases the possibilities of full Bayesian error analysis. To assess the named problems we developed the quasi-dynamic rupture model which is presented in this work. It combines the kinematic Eikonal rupture model with a boundary element method for quasi-static slip calculation. The orientation of the modeled rupture plane is defined by a previously performed moment tensor inversion. The simultanously inverted scalar seismic moment allows an estimation of the extension of the rupture. The modeled rupture plane is discretized by a set of rectangular boundary elements. For each boundary element an applied traction vector is defined as the boundary value. For insights in the dynamic rupture behaviour the rupture front propagation is calculated for incremental time steps based on the 2D Eikonal equation. The needed location-dependent rupture velocity field is assumed to scale linearly with a layered shear wave velocity field. At each time all boundary elements enclosed within the rupture front are used to calculate the quasi-static slip distribution. Neither friction nor stress propagation are considered. Therefore the algorithm is assumed to be "quasi-static". A series of the resulting quasi-static slip snapshots can be used as a quasi-dynamic model of the rupture process. As many a priori information is used from the earth model (shear wave velocity and elastic parameters) and the moment tensor inversion (rupture extension and orientation) our model is depending on few free parameters as the traction field, the linear factor between rupture and shear wave velocity and the nucleation point and time. Hence stable and fast modeling results are obtained as proven from the comparison to different infinite and finite static crack solutions. First dynamic applications show promissing results. The location-dependent rise time is automatically derived by the model. Different simple kinematic models as the slip-pulse or the penny-shaped crack model can be reproduced as well as their corresponding slip rate functions. A source time function (STF) approximation calculated from the cumulative sum of moment rates of each boundary element gives results similar to theoretical and empirical known STFs. The model was also applied to the 2015 Illapel earthquake. Using a simple rectangular rupture geometry and a 2-layered traction regime yields good estimates of both the rupture front propagation and the slip patterns which are comparable to literature results. The STF approximation shows a good fit with previously published STFs. The quasi-dynamic rupture model is hence able to fastly calculate reproducable slip results. That allows to test full Bayesian error analysis in the future. Further work on a full seismic source inversion or even a traction field inversion can also extend the scope of our model.},
  language  = {en}
}
@article{MuldashevSobolev2020,
  author    = {Muldashev, Iskander A. and Sobolev, Stephan},
  title     = {What controls maximum magnitudes of giant subduction earthquakes?},
  series = {Geochemistry, geophysics, geosystems},
  volume    = {21},
  journal   = {Geochemistry, geophysics, geosystems},
  number    = {9},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {1525-2027},
  doi       = {10.1029/2020GC009145},
  pages     = {15},
  year      = {2020},
  abstract  = {Giant earthquakes with magnitudes above 8.5 occur only in subduction zones. Despite the developments made in observing large subduction zone earthquakes with geophysical instruments, the factors controlling the maximum size of these earthquakes are still poorly understood. Previous studies have suggested the importance of slab shape, roughness of the plate interface contact, state of the strain in the upper plate, thickness of sediments filling the trenches, and subduction rate. Here, we present 2-D cross-scale numerical models of seismic cycles for subduction zones with various geometries, subduction channel friction configurations, and subduction rates. We found that low-angle subduction and thick sediments in the subduction channel are the necessary conditions for generating giant earthquakes, while the subduction rate has a negligible effect. We suggest that these key parameters determine the maximum magnitude of a subduction earthquake by controlling the seismogenic zone width and smoothness of the subduction interface. This interpretation supports previous studies that are based upon observations and scaling laws. Our modeling results also suggest that low static friction in the sediment-filled subduction channel results in neutral or moderate compressive deformation in the overriding plate for low-angle subduction zones hosting giant earthquakes. These modeling results agree well with observations for the largest earthquakes. Based on our models we predict maximum magnitudes of subduction earthquakes worldwide, demonstrating the fit to magnitudes of all giant earthquakes of the 20th and 21st centuries and good agreement with the predictions based on statistical analyses of observations.},
  language  = {en}
}