Maxwell II: StaticΒΆ

Purpose

Provide background and physical understanding for steady state Maxwell equations as they apply to geoscience problems.

When electromagnetic fields no longer change with time then Maxwell’s equations are in a “steady state”. Here we examine these equations and present analytic and numerical results for the resultant fields for some common sources in simple earth structures. Sources can be galvanic, where current is injected into the earth, or magnetic, where the source field arises from steady state currents flowing in circuit. The practical applications are wide ranging. The most common is the DCR (DC resistivity) survey which is used exploration, environmental and geotechnical studies. Examples of the use of DCR for mineral exploration can be found in the Mt. Isa Case History. That case history also illustrates how IP (Induced Polarization) can be analysed using steady state equations. Any current flowing in the earth will generate magnetic fields which can be measured. This is referred to as an MMR (MagnetoMetric Resistivity). Finally, earth materials can have a magnetic permeability that is different from that of free space. In the presence of an external field such material will become magnetized and the fields can be measured and interpreted. This constitutes the foundation of all magnetic field surveys which use the earth’s magnetic field (caused by “steady state” currents in the core). {example} It is also observed in exploration studies using low frequency airborne EM surveys. In such cases, eventhough the sources fieldis time-varying, the EM induction effects are negligible and the process can be considered as DC.

To illucidate the fundamental physics we focus on some simple models (whole spaces, half spaces with and without topography) and examine fields, fluxes, currents, build up of electric charges. A conductive and magnetic sphere, buried in the wholespace or halfspace provides much insight that is useful for steady state problems and also for later problems when induction is important. Interactive notebooks and good visualization tools help consolidate this insight.

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