Download Presentation
Advanced Mathematics in Seismology

Loading in 2 Seconds...

1 / 17

# Advanced Mathematics in Seismology - PowerPoint PPT Presentation

Advanced Mathematics in Seismology. Dr. Quakelove. or: How I Learned To Stop Worrying And Love The Wave Equation. When Am I Ever Going To Use This Stuff?. Wave Equation. Diffusion Equation. Complex Analysis. Linear Algebra. The 1-D Wave Equation. F = k[u(x,t) - u(x-h,t)].

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

## PowerPoint Slideshow about ' Advanced Mathematics in Seismology' - eve-howell

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Dr. Quakelove

or:

How I Learned To Stop Worrying

And Love The Wave Equation

When Am I Ever Going To Use This Stuff?

Wave Equation

Diffusion Equation

Complex Analysis

Linear Algebra

The 1-D Wave Equation

F = k[u(x,t) - u(x-h,t)]

F = k[u(x+h,t) – u(x,t)]

k

k

m

m

m

u(x-h,t)

u(x,t)

u(x+h,t)

F = m ü(x,t)

The 1-D Wave Equation

M = N m

L = N h

K = k / N

Solution to the Wave Equation
• Use separation of variables:
Solution to the Wave Equation
• Now we have two coupled ODEs:
• These ODEs have simple solutions:
Solution to the Wave Equation
• The general solution is:
• Considering only the harmonic component:
• The imaginary part goes to zero as a result of boundary conditions
And in case you don’t believe the math

Harmonic and exponential

solutions

Pure harmonic solutions

The 3-D Vector Wave Equation
• We can decompose this into vector and scalar potentials using Helmholtz’s theorem:

where