We are going to solve the differential equation with the boundary conditions $latex \psi_{xx} +[100 - \beta ]\psi = 0$ $latex \implies \psi_{xx} = [\beta - 100] \psi$ Let's take the simpler boundary condition $latex \psi(x=\pm 1) =0$. Now, the first... Continue Reading →

Signals can be any time-varying or space-varying quantity. Examples: speech, temperature readings, seismic data, stock price fluctuations. A signal has one or more frequency components in it and can be viewed from two different standpoints: time-domain and frequency domain. In... Continue Reading →

MATLAB Codes: clear; close all; clc t = linspace(0,10*pi,1000); x = t.*cos(t); y = t.*sin(t); z=linspace(0,2*pi,1000); plot3(x,y,z,'LineWidth',8) axis tight, grid on, view(35,30) c = 1:numel(t); surface([x(:), x(:)], [y(:), y(:)], [z(:), z(:)], ... [c(:), c(:)],... Continue Reading →

The curvature of the curve is the amount by which it deviates from being a straight line. It is defined as the reciprocal of the radius of the best fitting circle. So, the curvature of a straight line is zero.... Continue Reading →

To find a basic introduction of GA, the first part can be found here. III. Examples using Genetics Algorithm In these examples, we will use Matlab and its function ga to apply GA for the optimization problem. For the manual... Continue Reading →

I. Introduction In daily life as well as in doing research, we might come to problems that require a lowest/highest value of variables, e.g.: find the shortest way from home to work, buying household items with a fixed amount of money,... Continue Reading →

In Earth Science research, sometimes we need to construct 3D surfaces from given points, for example: creating the fault surface, locating a subducting slab from earthquake hypocenters, etc. in a region of interest in X-Y plane. In this example, we... Continue Reading →

Earthquake location problem is old, however, it is still quite relevant. The problem can be stated as to determine the hypocenter (x0,y0,z0) and origin time (t0) of the rupture of fault on the basis of arrival time data of P... Continue Reading →

Refer to Chapter 5, Introduction to Seismology, Shearer 2009. Problem: From the P-wave travel time data below (note that the reduction velocity of 8km/s), inverse for the 1D velocity model using T(X) curve fitting (fit the T(X) curve with lines,... Continue Reading →