Wave Propagation Modeling and Amplitude-Variation-with-Offset Response in a Fractured Coalbed

Coalbed methane can be detected employing the amplitude-variation-with-offset technique. However, there are two issues in applying this technique to a coalbed: strong azimuthal anisotropy resulting from high-density fractures, and the seismic response being composed of many or several individual reflections within the coalbed. To overcome these difficulties, we present an exact solution for reflections in extensive dilatancy anisotropy media. First, we build a three-layer model and simulate the wave propagation in this model. Then we derive an exact P-and converted S-wave reflection coefficient equation based on boundary conditions. Finally, substituting given model parameters into the exact equation, we obtain the variation in the reflection coefficient with incidence angle. The results show that the fracture factors, wavelet frequency and thickness of the coalbed have different effects on the reflection coefficient. Furthermore, we create a synthetic seismogram by forward calculation, and the result fits well with results of the exact equation.