# Fatti equation

An approximate solution to the Zoeppritz equation, used in seismic analysis.

Fatti et al^{[1]} gave a formulation derived from the Aki-Richards equation, which does not account for the critical angle since it only computes with the incident angle (that is, it does not contain Snell's law):

where *R*_{PP} is the P-wave reflectivity, θ is the incidence angle, *I* is the acoustic impedance for P and S waves (denoted by subscript), *V* is acoustic velocity, and ρ is bulk density. The deltas indicate that the difference at each interface is to be used, and given as a proportion of the average of the quantity across the interface (so that these coefficients are positive).

Many people read the equation as three terms: the first driven principally by acoustic P-wave impedance, the second by shear wave impedance, and the third by density.

## Implementation in Modelr

## Implementation in Python

Fatti's formula is implemented in **bruges** as `bruges.reflection.fatti`

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## References

- ↑ Fatti et al (1994), Geophysics 59(9), p 1362