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 thing which we wanna do is to convert this equation in the first order form.... Continue Reading →

# Introduction to Genetics Algorithm (GA) (Part 2)

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 of using this function, you can find it at https://www.mathworks.com/help/gads/ga.html or type in Matlab: help ga... Continue Reading →

# Introduction to Genetics Algorithm (GA) (Part 1)

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, etc. These problems could be called "optimization" and today we will introduce an algorithm to... Continue Reading →

# Best-fit quadratic surface from given points in 3D using Matlab

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 will show how to create a best-fit quadratic surface from given points in 3D using... Continue Reading →

# Locating Earthquake using Geiger’s Method

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 and S waves. Here, we have considered hypocenter in the cartesian coordinate system. It can... Continue Reading →

# Simple 1D velocity model inversion from P arrival time

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, then invert for the ray parameter p and delay time τ(p), then solve for the velocity... Continue Reading →

# Ray tracing through a 1-D velocity model

Refer to Chapter 4 of Shearer, Introduction to Seismology. For a ray piercing through Earth, the ray parameter (or horizontal slowness) p is defined by several expressions: where u = 1/v is the slowness, θ is the ray incidence angle, T is the travel time, X is the horizontal range and utp is the slowness at the... Continue Reading →

# Constrained Least Square Fitting

Let us try to understand the least square fitting method using an example: Example ---Utpal Kumar (IES, Academia Sinica)

# Seismic Resolution

Seismic resolution and fidelity are the two important measures of the quality of the seismic record and the seismic images. Seismic resolution quantifies the level of precision, such as the finest size of the subsurface objects detectable by the seismic data whereas the seismic fidelity quantifies the truthfulness such as the genuineness of the data... Continue Reading →