Forward modeling of 3D DC resistivity based on high-order adaptive finite element and its application in Qinshui Basin

Considering the fact that the accuracy of an adaptive finite element solution is mainly affected by the cell size (h) and the order of a shape function (p), we should adaptively refine the meshes to be dense enough or apply a higher-order shape function in the meshes to acquire a high-accuracy finite element solution. However, this will greatly increase the time burden and require sufficient me-mory space of the computer. In light of these problems, in this paper, we combine an h-adaptive refinement algorithm with a higher-order shape function for the forward modeling of a 3D DC resistivity model. In the program, we use the tensor pro-duct of 1D polynomials to generate a shape function of any order in the 3D space and apply Kelly posteriori error estimation to guide the adaptive refinement of meshes. Numerical examples show that in the case of p=3, our program has high accuracy, and the convergence of the finite element solutions is faster than that in the case of p=1 or 2. This means that the most accurate finite element solution with the fewest degrees of freedom can be obtained when the order of the shape function is 3. Finally, the simulation of 3D DC resistivity is performed on the 3D modeling of a coalbed fracturing monitoring region in the southern Qinshui Basin, verifying the effectiveness of our program. © 2021, Editorial Department OIL GEOPHYSICAL PROSPECTING. All right reserved.