pylops.avo.avo.akirichards¶

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

Three terms Aki-Richards approximation.

Computes the coefficients of the of three terms Aki-Richards 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 Aki-Richards approximation $$[n_{theta} \times n_{vsvp}]$$ G2 : np.ndarray second coefficient of three terms Aki-Richards approximation $$[n_{theta} \times n_{vsvp}]$$ G3 : np.ndarray third coefficient of three terms Aki-Richards approximation $$[n_{theta} \times n_{vsvp}]$$

Notes

The three terms Aki-Richards approximation is used to compute the reflection coefficient as linear combination of contrasts in $$V_P$$, $$V_S$$, and $$\rho$$. More specifically:

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

where $$G_1(\theta) = \frac{1}{2 cos^2 \theta}$$, $$G_2(\theta) = -4 (V_S/V_P)^2 sin^2 \theta$$, $$G_3(\theta) = 0.5 - 2 (V_S/V_P)^2 sin^2 \theta$$, $$\frac{\Delta V_P}{\bar{V_P}} = 2 \frac{V_{P,2}-V_{P,1}}{V_{P,2}+V_{P,1}}$$, $$\frac{\Delta V_S}{\bar{V_S}} = 2 \frac{V_{S,2}-V_{S,1}}{V_{S,2}+V_{S,1}}$$, and $$\frac{\Delta \rho}{\bar{\rho}} = 2 \frac{\rho_2-\rho_1}{\rho_2+\rho_1}$$.