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The high- and low-frequency limits of are then connected by a simple frequency
function to obtain the final model

| |
(79) |

where the transition frequency is defined
| |
(80) |

and where . Equation (79)
has a single singularity (a branch point) at .
Causality requires that with an time dependence,
all singularities and zeroes of a transport coefficient like
must reside in the lower-half complex plane.
Equation (79) satisfies this physically important constraint.

** Next:** Patchy-Saturation Modeling Choices
** Up:** Patchy-Saturation Transport
** Previous:** High-frequency limit of
Stanford Exploration Project

10/14/2003