Reflection modeling at an interface: the concept

Forward modeling of seismic reflections at an interface between two elastic half-spaces is a traditional way of setting expectations for the character of seismic traces between the overburden shale and sand reservoir; at gas/oil, gas/water, and oil/water contacts; as well as at various unconformities present in the subsurface. To conduct such computations, the elastic properties of both half-spaces are required. If we know the site-specific transforms between the rock properties and conditions and the elastic properties, we can compute seismic reflections at an interface as a function of porosity, lithology, and fluid. In the next section of this chapter we will review the mathematical apparatus used to compute seismic reflections and then proceed with utilizing these equations for assessing the seismic signatures from the properties of the rock half-spaces forming the interface.

Normal reflectivity and reflectivity at an angle

The reflectivity at an interface between two elastic bodies is defined as the ratio of the reflected wave amplitude to the incident wave amplitude. As the wave strikes the interface, it produces the reflected and transmitted waves (Figure 4.1). Here we will analyze only the reflected P-wave. The incident P-wave can approach the interface in the direction normal to the interface or at a non-zero angle (Figure 4.1). The angle of incidence is defined as the angle between the direction of propagation of the wave front and the direction normal to the interface between the two half-spaces. While a normal-incidence P-wave does not produce S-waves, a P-wave at a non-zero incident angle produces reflected and transmitted S-waves. In the following equations for the P-to-P reflectivity, the properties of the upper interface are marked by subscript “1” while those of the lower interface are marked by subscript “2.”