| This dissertation models some aspects of the physics of earthquakes and obtains estimates of the thickness and density of the Martian crust and elastic lithosphere. Specifically, we treat earthquakes utilizing the dynamics of a highly nonlinear system which we associate with the upper brittle layer of the Earth. We consider two models of self-organized criticality (SOC) (height-arrow model and Eulerian walker model) which exhibit a scaling behavior similar to the Gutenberg-Richter frequency-magnitude law for earthquakes. The models are studied by numerical simulations and analytical methods. Another aspect of earthquake physics, the irreversible processes which produce seismic events and cause deformations of the crust, is considered from the damage mechanics point of view. The solutions of the fiber-bundle model and several models of continuum damage mechanics allow us to quantify the seismic activation prior to large earthquakes (increases in Benioff strain) and to study relaxation processes (aftershocks) following large events.; We further report on the study of the thickness and density of the Martian crust and elastic lithosphere. Using recent data, obtained from the Mars Global Surveyor mission, we are able to constrain the thicknesses of both the Martian crust and elastic lithosphere to 90 ± 10 km. To accomplish this we use the assumption of Airy type compensation for the Hellas basin and wavelet transform analyses of the global circle tracks of gravity and topography. We also find that the mean crustal density is 2, 960 ± 50 kg m −3. |
