Computation Of Magnetic Fields Of Isomerism Direct Current Point Source In Layered Earths

Magnetometric is a conductive electric prospecting method which measures magnetic field. This paper gives a modeling simulation method of magnetometric in layered medium. This method does not use complicated body integral but takes a easier method named additive virtual current which separate magnetic field of point source into two parts, one is generated from a given round plant, the other is generated from lead. Based on this theory, first derive potential of each layer through Laplace equation, then get vertical current density expression by potential, at last derive magnetic field expression of direct current point source and isomerism point source in layered medium using rotating theorem of current magnetic field. Two expression both have double integral of Bessel function, which is difficult to calculate directly. Using property of Bessel function, the expression is simplied to single integral, and the calculation quantity is reduced.When programming to compute, there are two problems need to be solved. One is how to calculate undefined coefficient in potential expression, the other is how to calculate Bessel function. For undefined coefficient, the relationship of undefined coefficient of each layer can be derived through boundary condition, then the undefined coefficient could be calculated by program; For high surging Bessel function, this paper uses direct integral, and the result shows that this method has high precision.The modeling result of several kinds of layered medium shows that the magnetic field of magnetometric is mainly influenced by the transmitting direction of current line in medium. When the medium is uniform whole space, the direction of current line does not influenced by the medium, and the magnetic field all counteract, so the magnetic is zero everywhere. For layered medium, because the resistivity changes at the surface between two layers, the direction of current line changes at the same time. The larger the ratio of two resistivity is, the larger the swing of curve changes. The closer the source is to the surface, the larger the swing of curve change. For point source, if the upper resistivity is larger than the nether one, the peak value is positive; if the upper resistivity is smaller than the nether one, the peak value is negative. When observe point is close to point source, the magnetic field is close to zero. This is because a quite small space nearby point source can be approximate to be a uniform whole space. For isomerism point source, the magnetic field is mainly influenced by the line, but the magnetic field of line does not reflect distributing of medium underground, so when analyse results the magnetic field of line should be subtracted. Magnetic response curve of isomerism point source is lightly influenced by the obliquity. Changing obliquity only results changing swing of curve but not affect the shape. Changing the relative position of observe point to the source will make the swing of curve changes. The closer to the surface, the larger the swing is. The result of gas hydrate model shows that point source is better at surveying gas hydrate than isomerism point source. This is because current line of isomerism point source mostly centralize between the two point source, less transmit down. The result of borehole model shows that isomerism point source has larger magnetic response than point source because of the same reason.Several modeling result in this paper shows that the expression of point source and isomerism point source is correct. And the compute method is quick and precise.The analysis of result shows that magnetometric is fit for layered medium survey. It can reflect depth and resistivity of medium well, and can plot out stratum in borehole survey. But after all magnetometric is conductive electric prospecting method, when the thickness or the depth of medium is too large or the resistivity of overlay layer is too large, magnetometric can not get good result.