Mathematical formulation of any physical process involves various complex equations, which can be solved using different analytical and or numerical techniques to get the desired solutions which can be analyzed in terms of the physical phenomena. These equations involve various types of operators such as differential, integral, divergence etc. The solution to these differential equations can be solved using the deterministic and stochastic approaches. Deterministic differential equations arise when the parameters are known with certainty, whereas stochastic differential equations are those, which include randomness in their parameters.
Modelling Earth systemfor seismological, thermal, groundwater and tsunamigenic processes is carried out using mathematical and stochastic tools and integrating the results with the available geological information. It is well established that geophysical properties exhibit non-linear behavior, hence the existing formulation for the geophysical and geological problems is being readdressed incorporating the non-linear/ stochastic geophysical models. In this project, an attempt will be made to study the Earth system processes and quantify the its behaviors.