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Seismology

Solving nth order differential equation for a given boundary condition

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 →

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... 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... 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,... Continue Reading →

Travel-time curve calculation for the Spherical Earth (PREM Model)

I have used the Preliminary Reference Earth Model of Dziewonski and Anderson (1981) to calculate the travel time curve. This model is very robust in the sense that it is designed to fit a wide variety of data including free-oscillation,... 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... Continue Reading →

Normal Mode Summation for calculating the synthetic seismogram for a string

When we pluck a string fixed at both ends, then this will creating a standing wave. We can get some insights on the behavior of the propagating wave by considering normal modes or free oscillations of the string. A wave... Continue Reading →

Modeling a wave on a string using finite differences

Based on problem 3.7 chapter 3 of Introduction to Seismology (Shearer) (COMPUTER) In the case of plane-wave propagation in the x direction within a uniform medium, the homogeneous momentum equation (3.9) for shear waves can be expressed as ,where u... Continue Reading →

Calculating Pressure and Tension axis given the fault plane (strike, dip and rake): Analytical solution

The fault plane is characterized by its normal vector and the direction of its motion is given by the slip vector. Here, we calculate the normal vector and the slip vector for a given fault geometry. The orientation of the... Continue Reading →

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