Graduate Student Seminar

Speaker 1: Randy Price

Title

Stochastic Finite Element Methods and Numerical Results for the Time Dependent Heat Equation

Abstract

I will briefly go over three methods to solve a partial differential equation that has randomness involved. I will talk about Monte Carlo,Collocation, and Stochastic Galerkin methods. I will conclude with numerical results achieved after applying these methods to the time dependent heat equation with random heat diffusivity constant.

Speaker 2: Yewon Kim

Title

An Alternative to Cross-Convolution for Estimation of Splitting Parameters

Abstract

Seismic time series from a distant earthquake change their statistical properties due to "shear wave splitting" as the seismic wave encounter changes in the mineralogy of the Earth's crust. Specifically, the shear wave splitting method can be used to detect seismic anisotropy. There are two main parameters in order to quantify seismic anisotropy which are the split time and the fast axis. For estimating maximum likelihood estimators (MLE) of the parameters, We used Fourier transform and empirical spectral density to provide a fast alternative to existing grid search method. We found local MLE of one specific set of seismic data and tested these methods with multiple data sets from the Pasadena, California seismic station (PAS).