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The space-domain finite-differences solution to equation (9)
is derived based on the square-root expansion,
first introduced to Geophysics by Muir
Claerbout (1985):
| |
(10) |

where the coefficients , and take the form:
| |
(11) |

In the special case of Cartesian coordinates,
*a*=*s* and *b*=1, equation (10) takes the familiar form
| |
(12) |

where the coefficients *c*_{1} and *b* take different
values for different orders of the Muir expansion:
*c*_{15}=(*c*_{1},*b*)=(0.50,0.00) for the equation, and
*c*_{45}=(*c*_{1},*b*)=(0.50,0.25) for the equation.

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Stanford Exploration Project

10/23/2004