Dictionary:Helmholtz equation

From SEG Wiki
Jump to navigation Jump to search
This page contains changes which are not marked for translation.
Other languages:

{{#category_index:H|Helmholtz equation}} The space-dependent form of the wave equation for a wave that is harmonic in time:


where , =angular frequency, and V=velocity.

Derivation of the Helmholtz equation

Given the homogeneous form of the scalar wave equation


Here , is time, is the wavespeed, and is the wave field.

If we replace by its Fourier transform representation


noting that the second derivative of with respect to time

the following Fourier integral form


Because the only way for this Fourier integral representation to vanish is if its integrand vanishes, the Helmholtz equation appears


External links

find literature about
Helmholtz equation
SEG button search.png Datapages button.png GeoScienceWorld button.png OnePetro button.png Schlumberger button.png Google button.png AGI button.png