Sensitivity analysis of viscoelastic models of the earth crustal deformation to input parameters based on outcome surface deformation field



The scope of this research is to investigate the effect of geometrical and physical input parameters in crustal viscoelastic deformation models. To do this analysis viscoelastic model of Wang et al., 2006 is used. The increasing quality of data on time-dependent deformation of the Earth's surface can be used to extract more details on the spatial and temporal development of earthquake-related crustal deformation. Different variables are involved in these processes; some of them perform more accurately than others. In this research, surface deformation is modeled in two dip-slip and strike slip faults, in a medium composed of an elastic layer over an inelastic half-space, sensitivity analysis is performed on all geometrical and physical parameters. Among physical and geometrical parameters, performing of this analysis on less accurately determined parameters from displacement field data is recommended. These parameters are viscosity of the half-space, thickness of the elastic layer and dip angle of the fault plane. According to obtained results of this research, sensitivity of the viscoelastic model to input parameters is independent of type of faulting. From the variability analysis, the location of most appropriate displacement data to obtain values for the studied parameters is determined. For example according to obtained results, coseismic and postseismic displacement analysis show high dependency on fault slip above rupture surface of the fault, however it shows less sensitivity to fault length.
When analyzing the co-seismic displacement, a strong dependency on the dip angle of the fault plane is found. Points with large displacements also show a large variability when the dip angle varies. The area over the rupture plane is the one where the largest displacements take place. Therefore, surface measurements in this area are the most suitable for ascertaining the most likely value for the dip angle.
By contrast, varying the thickness of the elastic layer leads to small differences in general, especially small in the area immediately beyond the surface projection of the lower end of the rupture plane. This indicates that co-seismic displacement measurements, especially around the mentioned area, are not recommendable for trying to ascertain an accurate value for this parameter.
In the analysis of the post-seismic deformation it is found that, on average, deviations from a reference model are large above the rupture plane when varying the viscosity and the thickness of the elastic layer. In this area, the dip angle does not influence the results as much as the other two parameters. Further away from the rupture surface along dip direction, in the area immediately beyond the surface projection of the lower end of the rupture plane, the dip angle becomes the most influential parameter. Further away, where the magnitude of the horizontal displacement reaches another maximum, the viscosity and the thickness of the elastic layer have again a greater effect than the dip angle of the rupture surface.
Accordingly, measurements in areas of large post-seismic displacements are more suitable for deriving a value for the viscosity. In particular, above the rupture area, values depend heavily on this parameter. The same region can also provide data that is useful for ascertaining the thickness of the elastic layer, although for this parameter the area where the minimum displacement occurs is not as appropriate as for the viscosity.
The dip angle, in general, cannot be accurately derived using post-seismic deformation data. The magnitude of the variability associated with this parameter is very small. The best place to find a value for this parameter is the area where the post-seismic displacement changes direction.
So the best data to derive the value of the viscosity is the post-seismic deformation over the area where the rupture takes place, although any area with large magnitude post-seismic displacements can provide more useful data. For the thickness of the elastic layer it is also advisable to use postseismic data from the area above the fault plane, whereas the dip is better determined by means of coseismic data.
Both of coseismic and postseismic displacement analysis show high dependency to locking depth of the fault especially above the rupture surface of the fault. The amount of sensitivity is especially high for coseismic displacements.
Coseismic and postseismic displacement analysis show small sensitivity to Lame coefficients of elastic layer above rupture surface of the fault and it is reduced for Lame coefficients of visco-elastic layer.
Coseismic displacement analysis does not show sensitivity to elastic or visco-elastic layer density, however postseismic displacement analysis shows small sensitivity, so modeling is not an appropriate tool for elastic layer or visco-elastic half space density determination.