pylops.avo.avo.ps¶

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

PS reflection coefficient

Computes the coefficients for the PS 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 scalar) G1 : np.ndarray first coefficient for VP $$[n_{theta} \times n_{vsvp}]$$ G2 : np.ndarray second coefficient for VS $$[n_{theta} \times n_{vsvp}]$$ G3 : np.ndarray third coefficient for density $$[n_{theta} \times n_{vsvp}]$$

Notes

The approximation in [1] is used to compute the PS reflection coefficient as linear combination of contrasts in $$V_P$$, $$V_S$$, and $$\rho$$. More specifically:

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

where $$G_2(\theta) = tan \theta / 2 [4 (V_S/V_P)^2 sin^2 \theta - 4(V_S/V_P) cos \theta cos \phi]$$, $$G_3(\theta) = -tan \theta / 2 [1 - 2 (V_S/V_P)^2 sin^2 \theta + 2(V_S/V_P) cos \theta cos \phi]$$, $$\frac{\Delta V_S}{\bar{V_S}} = 2 \frac{V_{S,2}-V_{S,1}}{V_{S,2}+V_{S,1}}$$, and $$\frac{\Delta \rho}{\bar{\rho}} = 2 \frac{\rho_2-\rho_1}{\rho_2+\rho_1}$$. Note that $$\theta$$ is the P-incidence angle whilst $$\phi$$ is the S-reflected angle which is computed using Snell’s law and the average $$VS/VP$$ ratio.

 [1] Xu, Y., and Bancroft, J.C., “Joint AVO analysis of PP and PS seismic data”, CREWES Report, vol. 9. 1997.