Forward Modeling Of Controlled Source Electromagnetic Method In Two Dimensional Anisotropic Strata

Controlled source audio-frequency magnetotellurics (CSAMT) is traditionally based on the electrical isotropic theory. However, it has been well recognized that the electrical anisotropic is widely present in the earth interior. If the problem of anisotropic stratum is treated according to the assumption of isotropic theory, the results of the inversion interpretation are often unreliable and sometimes even erroneous. Therefore, it has important theoretical significance and application value to study the electromagnetic response of the CSAMT method under the condition of two dimensional anisotropic strata.Although scholars domestic and abroad have been trying to study the electromagnetic field response and numerical calculation of various electromagnetic exploration methods under the condition of anisotropy, the controlled source electromagnetic method based on the electrical anisotropy is still far from practical utilizition. Starting from the Maxwell equations with sources, the earth electromagnetic response under the condition of two dimensional symmetric anisotropy is derived. In this case, the TE and TM mode are decoupled and the TM mode is the same as that of the isotropic condition, so only the results of the TE model is shown. The effect of anisotropy on MT method is serious and can not be ignored from the forward modeling calculation. In this paper, the electromagnetic field response at frequency domain of infinite line source under the condition of two dimensional anisotropic strata is derived. The partial differential equations of the electric field component and the magnetic field component parallel to the line source are obtained and the finite element method is used to solve the problem. The calculation of a series of models show that TE mode is less reliable compare with TM mode for situation of infinite line source. The value of TE mode is much larger than TM mode to at least two decades. By calculating the 2D anisotropic anomalous body in either homogeneous half-space or one-dimensional layered media, the isotropic background and anisotropic anomalous body can be clearly figured out. By changing the anisotropic coefficient and rotation angle from main electrical axis of anisotropic model, it is obvious different from anisotropic case both for apparent resistivity and impedance phase curves. The results indicate that error will be very large if we still use electrical isotropic theory when dealing with CSAMT data at anisotropic media. In such situation, the calculation should base on anisotropic theory instead of electrical anisotropic one. Through the study of CSAMT in anisotropic formation, it is helpful to deepen the understanding of the CSAMT method and improve the exploration results and application level under the condition of electrical anisotropy.