Stalnaker, Jack Lee (2004-08). A finite element approach to the 3D CSEM modeling problem and applications to the study of the effect of target interaction andtopography. Doctoral Dissertation.
The solution of the secondary coupled-vector potential formulation of Maxwell??s equations governing the controlled-source electromagnetic (CSEM) response of an arbitrary, threedimensionalconductivitymodelmust be calculatednumerically.The ﬁnite elementmethod is attractive, because it allows the model to be discretized into an unstructured mesh, permitting the speciﬁcation of realistic irregular conductor geometries, and permitting the mesh to be reﬁned locally, where ﬁner resolution is needed. The calculated results for a series ofsimple test problems, ranging from one-dimensionalscalar diﬀerentialequations to three-dimensional coupled vector equations match the known analytic solutions well, with error values several orders of magnitude smaller than the calculated values. The electromagnetic ﬁelds of a fully three-dimensional CSEM model, recovered from the potentials using the moving least squares interpolation numerical diﬀerentiation algorithm, compares well with published numerical modeling results, particularly when local reﬁnement is applied. Multiple buried conductors in a conductive host interact via mutual induction and current ﬂow through the host due to the dissipation of charge accumulated on the conductor boundary. The eﬀect of this interaction varies with host conductivity, transmitter frequency, and conductor geometry, orientation, and conductivity. For three test models containingtwo highly conductive plate-like targets, oriented in various geometries (parallel, perpendicular, and horizontal), mutual coupling ranges as high as twenty times the total magnetic ﬁeld. The eﬀect of varying host conductivity is signiﬁcant, especially at high frequencies. Numerical modeling also shows that the vorticity of the currents density induced in a vertically oriented plate-like conductor rotates from vertical at high frequencies, to horizontal at low frequencies, a phenomenon conﬁrmed by comparison with time domain ﬁeld data collected in Brazos County, Texas. Furthermore, the eﬀect of the presence of a simple horst on the CSEM response of a homogeneous conductive earth is signiﬁcant, even when the height of the horst is only a fraction of the skin depth of the model. When the transmitter is placedon topofthe horst, the currents inducedtherein account for nearly all of the total magnetic ﬁeld of the model, indicating that topography, like mutual coupling must be accounted for when interpreting CSEM data.