The fundamental theorem of applied geophysics

Abstract

In all methods of geophysical prospecting, the attempt is made to ascertain the depth and extent of deposits (ore, oil, ground‐water) by means of certain measurements made on the Earth's surface. The question as to whether and under what conditions such an analysis may be made in a unique manner constitutes the fundamental problem of applied geophysics.The problem requires a separate solution for each method. In 1927, I published a solution for the electrodynamical method. As for the other geophysical methods, in the absence of a solution, recourse is had to a rule formulated by Professor A. O. Rankine as follows: “Underground structures, agreeable to the geophysicist's experience, have to be taken as hypotheses, and tested by calculation and comparison with the data provided by surface‐observations.” It is a very laborious and uncertain procedure. Even if one, by good luck, succeeds in divining a hypothetical underground structure which is in ideal agreement as respects the calculated and observed values, yet there is no certainty that this corresponds with reality. The physical values at the surface are uniquely determined by the underground structure but the inverse theorem—namely, that the underground structure may be uniquely ascertained from physical measurements made at the surface—does not necessarily follow. Indeed, it is not upon physics nor upon mathematics (however imposing some of the displays of the latter) but upon geology that the successful interpretation of geophysical measurements usually depends. The hypothetical structure must be “agreeable to the geologist's experience.” This is, according to Rankine “the geologist's selection rule.” It signifies no guide in the terra incognita, but, on the contrary, the exclusion of it. Until the fundamental problem is solved, the geophysicist will be obliged to work only in geologically known country.