# pylops.avo.avo.fatti¶

pylops.avo.avo.fatti(theta, vsvp, n=1)[source]

Three terms Fatti approximation.

Computes the coefficients of the of three terms Fatti approximation for a set of angles and a constant or variable VS/VP ratio.

Parameters: theta : np.ndarray Incident angles in degrees vsvp : np.ndarray or float VS/VP ratio n : int, optional number of samples (if vsvp is a scalare) G1 : np.ndarray first coefficient of three terms Smith-Gidlow approximation $$[n_{theta} \times n_{vsvp}]$$ G2 : np.ndarray second coefficient of three terms Smith-Gidlow approximation $$[n_{theta} \times n_{vsvp}]$$ G3 : np.ndarray third coefficient of three terms Smith-Gidlow approximation $$[n_{theta} \times n_{vsvp}]$$

Notes

The three terms Fatti approximation is used to compute the reflection coefficient as linear combination of contrasts in $$AI$$, $$SI$$, and $$\rho$$. More specifically:

$R(\theta) = G_1(\theta) \frac{\Delta AI}{\bar{AI}} + G_2(\theta) \frac{\Delta SI}{\bar{SI}} + G_3(\theta) \frac{\Delta \rho}{\bar{\rho}}$

where $$G_1(\theta) = 0.5 (1 + tan^2 \theta)$$, $$G_2(\theta) = -4 (V_S/V_P)^2 sin^2 \theta$$, $$G_3(\theta) = 0.5 (4 (V_S/V_P)^2 sin^2 \theta - tan^2 \theta)$$, $$\frac{\Delta AI}{\bar{AI}} = 2 \frac{AI_2-AI_1}{AI_2+AI_1}$$. $$\frac{\Delta SI}{\bar{SI}} = 2 \frac{SI_2-SI_1}{SI_2+SI_1}$$. $$\frac{\Delta \rho}{\bar{\rho}} = 2 \frac{\rho_2-\rho_1}{\rho_2+\rho_1}$$.