Amplitude of seismic signal is related to changes in acoustic impedance Z, which is equal to the product of bulk density ρ and P-wave velocity V, itself related to lithology, fluid, and porosity.
The basic physics behind AVO analysis is that the strength of a reflection does not only depend on the acoustic impedance—it also depends on the angle of incidence. Only when this angle is 0 (a vertical, or zero-offset, ray) does the simple relationship above hold.
Boundary Conditions
The nature of the two media fixes the densities and elastic constants and thus the velocities. The angles of reflection and refraction are fixed in terms of the velocities, as will be shown below. The only variables remaining to satisfy the boundary conditions are the amplitudes of the waves generated. When both media are solids, there are four equations resulting from the boundary conditions, so that we must have four variables.
A P-wave (or an S-wave) incident on an interface separating two solids must in general generate reflected and refracted S-waves as well as reflected and refracted P- waves. Thus for an incident P-wave, we have reflected and refracted P-waves at the angles \(\theta_1\) and \(\theta_2\) and reflected and refracted S-waves at the angles \(\delta_1\) and \(\delta_2\) , The waves whose mode changes at an interface (the reflected and refracted S-waves in the foregoing example) are called converted waves.
S-waves have two degrees of freedom, and motion perpendicular to the plane containing the incident wave and the normal to the interface is not involved in conversion from P- to S-waves nor vice versa. Where the interface is horizontal, this is equivalent to saying that incident P-waves can generate reflected and refracted P- and SV-waves but not SH-waves, that incident SV -waves can generate P- and SV -waves, but that incident SH-waves generate only reflected and refracted SH-waves.