Inverse problem of potential theory
The inversion problem of potential theory is a theoretically based ambiguity problem in some applications of potential theory . Above all, it limits the interpretation of measurement data in a magnetic or gravity field , because it prevents a clear conclusion from the force field to the source point causing it .
The reversal problem got its name by analogy with the reversal of cause and effect. With a known or predetermined mass distribution inside a solid , its effect on the outside can be strictly calculated, while conversely the measured gravitational field can be caused by different mass arrangements.
Example: disruptive bodies with high density
For example, an underground disruptive body of high density (such as an ore deposit ) on the surface of the earth becomes noticeable through a clear gravity anomaly or a large deviation from the perpendicular . Compared to an undisturbed earth's crust with uniform rock , the body represents an excess of mass . The anomaly measured on the surface can, however, be explained by a shallow sturgeon body at a shallow depth as well as by a lower lying spherical body. The difference in density to the surrounding rock also cannot usually be clearly determined.
A combination of several geophysical methods or knowledge of geological rock data helps here . If the geologist can give the density contrast (e.g. of the ore against the surrounding slate ), an approximate depth determination is possible. The extent of the deposit, in turn, can be limited by extensive measurement profiles or by any tectonic fault lines .
Avoiding the ambiguity
The reversal problem also plays a role when the field is continued downwards or upwards and can only be avoided if, in addition to the gravity measurements , additional data is available from boreholes, rock samples or from interfaces. Occasionally, an analogy to the unknown parameters from similar areas or measurement campaigns helps .
For the geophysicist or mining engineer, the reversal problem relativizes a significant advantage of the potential methods, which can explore the interior of the earth very inexpensively - without time-consuming drilling and in principle without depth restrictions. On the other hand, exploration forces a particularly important method is prone to errors in the transit time curves because the artificial earthquake waves are influenced by both the density and the modulus of elasticity . Both parameters can generally only be estimated with insufficient accuracy; However, the gravitational field can provide plausible models for the density.