Dynamic earthquake sequence simulation with a SBIEM without periodic boundaries

Dynamic earthquake sequence simulation is an important tool for investigating the behavior of a fault that hosts a series of earthquakes because it solves all interrelated stages in the earthquake cycle consistently, including nucleation, propagation and arrest of dynamic rupture, afterslip, locking, and interseismic stress accumulation. Numerically simulating and resolving these phenomena, which have different time and length scales, in a single framework is challenging. A spectral boundary integral equation method (SBIEM) that makes use of a fast Fourier transform is widely used because it reduces required computational costs, even though it can only be used for a planar fault. The conventional SBIEM has a periodic boundary condition as a result of the discretization of the wavenumber domain with a regular mesh; thus, to obtain an approximate solution for a fault in an infinite medium, it has been necessary to simulate a region much longer than the source distribution. Here, I propose a new SBIEM that is free from this artificial periodic boundary condition. In the proposed method, the periodic boundaries are removed by using a previously proposed method for the simulation of dynamic rupture. The integration kernel for the elastostatic effect, which reaches infinitely far from the source, is expressed analytically and replaces the one in the conventional SBIEM. The new method requires simulation of a region only twice as long as the source distribution, so the computational costs are significantly less than those required by the conventional SBIEM to simulate a fault in an infinite medium. The effect of the distance λ between the artificial periodic boundaries was investigated by comparing solutions for a typical problem setting between the conventional and proposed SBIEM. The result showed that the artificial periodic boundaries cause overestimation of the recurrence interval that is proportional to λ−2. If λ is four times the fault length, the interval is overestimated by less than 1%. Thus, the artificial periodic boundaries have only a modest effect on the conclusions of previous studies.

Formation of Neutral Points in the Polarization Characteristics of Secondary Radiation in the Semi-Infinite Medium Model

This article studies the polarization characteristics of diffusely reflected backward radiation when illuminating a semiinfinite, light-scattering medium with unpolarized radiation. The formation of neutral Babine, Brewster and Arago polarization points in the angular polarization characteristics of the secondary radiation is shown. Comparison between the results of exact numerical calculations and approximate analytical formulas has been carried out and physical conditions for the appearance of neutral points depending on the angles of illumination and the multiplicity of scattering have been analyzed.

Strain Field Development of a Rectangular Dislocation Loop in a Semi-Infinite Medium with Verification

This paper considers a rectangular Volterra dislocation loop lying beneath and parallel to a free surface in a semi-infinite material. The paper utilizes the displacement field of an infinitesimal dislocation loop to obtain the strain field and then integrate over a finite rectangular area. For the loop, it can have three non-zero Burgers vector components. The stress field is also obtained from Hooke’s law for isotropic materials. Analytical and numerical verifications of the strain and stress fields are performed. In addition, the effect of the free surface on stresses is displayed versus depth from the surface. Verification includes satisfaction of the zero-traction boundary condition, the stress equilibrium equations and the strain compatibility equations.

Semi-derivative integral method (SDIM) to transient heat conduction: Time-dependent (power-law) temperature boundary conditions

Transient heat conduction in semi-infinite medium with a power-law time-dependent boundary conditions has been solved by an integral-balance integral method applying to a semi-derivative approach. Two versions of the integral-balance method have been applied: Goodman?s method with a generalized parabolic profile and Zien?s method with exponential (original and modified) profile.

Semi-derivative integral method to transient heat conduction time-dependent heat flux boundary conditions

Transient heat conduction in semi-infinite medium with a time dependent heat flux as boundary condition has been solved by a semi-derivative integral-balance method. Two versions boundary fluxes have been considered: power-law and exponential.