A numerical technique is developed to solve the three‐dimensional potential distribution about a point source of current located in or on the surface of a half‐space containing arbitrary two‐dimensional conductivity distribution. Finite difference equations are obtained for Poisson's equations by using point‐ as well as area‐discretization of the subsurface. Potential distributions at all points in the set defining the half‐space are simultaneously obtained for multiple point sources of current injection. The solution is obtained with direct explicit matrix inversion techniques. An empirical mixed boundary condition is used at the “infinitely distant” edges of the lower half‐space. Accurate solutions using area‐discretization method are obtained with significantly less attendant computational costs than with the relaxation, finite‐element, or network solution techniques for models of comparable dimensions.
A numerical technique has been developed to solve the three‐dimensional (3-D) potential distribution about a point source of current located in or on the surface of a half‐space containing an arbitrary 3-D conductivity distribution. Self‐adjoint difference equations are obtained for Poisson’s equation using finite‐difference approximations in conjunction with an elemental volume discretization of the lower half‐space. Potential distribution at all points in the set defining the subsurface are simultaneously solved for multiple point sources of current. Accurate and stable solutions are obtained using full, banded, Cholesky decomposition of the capacitance matrix as well as the recently developed incomplete Cholesky‐conjugate gradient iterative method. A comparison of the 2-D and 3-D simple block‐shaped models, for the collinear dipole‐dipole array, indicates substantially lower anomaly indices for inhomogeneities of finite strike‐extent. In general, the strike‐extents of inhomogeneities have to be approximately 10 times the dipole lengths before the response becomes 2-D. The saturation effect with increasing conductivity contrasts appears sooner for the 3-D conductive inhomogeneities than for corresponding models with infinite strike‐lengths. A downhole‐to‐surface configuration of electrodes produces diagnostic total field apparent resistivity maps for 3-D buried inhomogeneities. Experiments with various lateral and depth locations of the current pole indicate that mise‐à‐la‐masse surveys give the largest anomaly if a current pole is located asymmetrically and, preferably, near the top surface of the burried conductor.
Despite over 2 decades of international and national monitoring of electrical signals with the hope of detecting precursors to earthquakes, the scientific community is no closer to understanding why precursors are observed only in some cases. Laboratory measurements have demonstrated conclusively that self potentials develop owing to fluid flow and that both resistivity and magnetization change when rocks are stressed. However, field experiments have had much less success. Many purported observations of low‐frequency electrical precursors are much larger than expectations based on laboratory results. In some cases, no precursors occurred prior to earthquakes, or precursory signals were reported with no corresponding coseismic signals. Nonetheless, the field experiments are in approximate agreement with laboratory measurements. Maximum resistivity changes of a few percent have been observed prior to some earthquakes in China, but the mechanism causing those changes is still unknown. Anomalous electric and magnetic fields associated with fluid flow prior to earthquakes may have been observed. Finally, piezomagnetic signals associated with stress release in earthquakes have been documented in measurements of magnetic fields.
Induction in electrically conductive seawater attenuates the magnetotelluric (MT) fields and, coupled with a minimum around 1 Hz in the natural magnetic field spectrum, leads to a dramatic loss of electric and magnetic field power on the sea floor at periods shorter than 1000 s. For this reason the marine MT method traditionally has been used only at periods of 103 to 105 s to probe deep mantle structure; rarely does a sea‐floor MT response extend to a 100-s period. To be useful for mapping continental shelf structure at depths relevant to petroleum exploration, however, MT measurements need to be made at periods between 1 and 1000 s. This can be accomplished using ac-coupled sensors, induction coils for the magnetic field, and an electric field amplifier developed for marine controlled‐source applications. The electrically quiet sea floor allows the attenuated electric field to be amplified greatly before recording; in deep (1-km) water, motional noise in magnetic field sensors appears not to be a problem. In shallower water, motional noise does degrade the magnetic measurement, but sea‐floor magnetic records can be replaced by land recordings, producing an effective sea‐surface MT response. Field trials of such equipment in 1-km-deep water produced good‐quality MT responses at periods of 3 to 1000 s; in shallower water, responses to a few hertz can be obtained. Using an autonomous sea‐floor data logger developed at Scripps Institution of Oceanography, marine surveys of 50 to 100 sites are feasible.
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