Modeling of Block-and-Fault System Dynamics and Seismicity: Description of the Model and Application to the Tibet-Himalayan Region

A model of block-and-fault system dynamics (or simpler "block model") considers a seismic region as a system of perfectly rigid blocks divided by infinitely thin plane faults. The blocks interact between themselves and with the underlying medium. The system of blocks moves as a consequence of prescribed motion of the boundary blocks and of the underlying medium. As the blocks are perfectly rigid, all deformation takes place in the fault zones and at the block base in contact with the underlying medium. Relative block displacements take place along the fault planes. This assumption is justified by the fact that for the lithosphere the effective elastic moduli of the fault zones are significantly smaller than those within the blocks. Block motion is defined so that the system is in a quasistatic equilibrium state. The interaction of blocks along the fault planes is viscous-elastic ("normal state") while the ratio of the stress to the pressure remains below a certain strength level. When the critical level is exceeded in some part of a fault plane, a stress-drop ("failure") occurs (in accordance with the dry friction model), possibly causing failure in other parts of the fault planes. These failures produce earthquakes. Immediately after the earthquake and for some time after, the affected parts of the fault planes are in a state of creep. This state differs from the normal state because of a faster growth of inelastic displacements, lasting until the stress falls below some other level. This modeling gives rise a synthetic earthquake catalogue. The Tibetan plateau and Himalayans have resulted from the continuous Indian and Eurasian plate convergence following their initial collision at about 55 million years ago. Earthquakes in the region occur mainly in response to the crustal motion and stress localization associated with this convergence. To understand the basic features of the motion and seismicity in the Tibet-Himalayan region, we develop the block model that is composed of twelve interacting upper crustal blocks. These blocks move as a consequence of the Indian plate push. We develop several sets of numerical experiments constrained by the regional seismic observations, geodetic and geological data. Synthetic large events in the numerical experiments are clustered mainly on the fault segments associated with the Himalayan Frontal Thrust as well as at some internal faults of the Tibetan plateau. The clustering of earthquakes at some fault is a consequence of dynamics of the regional fault system rather than that of the fault only. We show that variations in the relationship of magnitude to frequency of the events depend on changes in the motion of the upper crustal blocks and on the rheological properties of the lower crust and fault zones. We demonstrate in the model that the present crustal motion in the region is characterized by the north-northeastern movement of India toward Eurasia. Fluctuations in rheological properties of fault plane zones and/or the lower crust influence displacement rates of the crustal blocks and hence slip rates at the faults separating the blocks. This can explain the discrepancies in estimates of slip rates at major faults in the region (e.g., Altyn Tagh, Karakorum) over short and long time scales.