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Implementation of thermal pressurization [Noda and Lapusta, 2010]

Implementation of thermal pressurization [Noda and Lapusta, 2010]. Diffusion of temperature normal to the fault. T α th ω ρ c. : Temperature : Thermal diffusivity : Heat generation per unit volume : Density : Heat capacity per unit mass. Diffusion of fluid pressure normal to the fault.

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Implementation of thermal pressurization [Noda and Lapusta, 2010]

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  1. Implementation of thermal pressurization [Noda and Lapusta, 2010] Diffusion of temperature normal to the fault T αth ω ρ c : Temperature : Thermal diffusivity : Heat generation per unit volume : Density : Heat capacity per unit mass Diffusion of fluid pressure normal to the fault αhy Λ : Hydraulic diffusivity : Fluid pressure change / temperature change Heat source distribution w : Half width of the shear zone

  2. Fourier domain Diffusion of temperature normal to the fault Θ Ω l : F. T. (in y direction) of temperature : F. T. (in y direction) of heat generation : Wavenumber corresponding to y Diffusion of fluid pressure normal to the fault Π : . T. (in y direction) of pore pressure Heat source distribution

  3. They are in a form Analytic integration Assuming constant B(t) (heat source) during a timestep, This is first order accurate, and unconditionally stable in a sense that numerical error decays exponentially. This process is iterated to make the scheme second order accurate in time.

  4. After descretization, FFT is not needed. lj is set evenly in logarithmic scale, and Finv is calculated based on trapezoidal rule for log(l). Pros : Thermal pressurization is not a rate-limiting process in computations. No history storage is needed. Unconditionally stable. TP can be implemented into earthquake sequence simulation without significant extra computational cost. Cons : It is difficult to account for change in the material properties. Comparison with analytic solution for boxcar (in time) heat source. [Noda and Lapusta, 2010 Fig. 2]

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