A modern scientific methodology for structural geology

Abstract

Papers on methodology by G. K. Gilbert from the late 19th century have attracted geologists' attention into the 21st century. Gilbert's memoir on the Henry Mountains includes two mechanical models based on physical theory found in W. J. M. Rankine's Manual of Applied Mechanics. Rankine's analysis of the stratification of hydrostatic fluids of different densities corresponds closely to Gilbert's Model #1 applied to magmatic intrusions. However, the sedimentary rocks of the Henry Mountains are not fluids, and though Model #1 failed Gilbert's tests, he did not reject it. Model #2 replaced the flexure over the laccolith with an encircling fault, enabling Gilbert to analyze laccolith formation using balanced parallel forces. His tests of Model #2 were successful and led to a physical relationship between the diameter and depth of laccoliths. We modernize Gilbert's methodology using the equations of motion for the material continuum provided by A. -L. Cauchy's First and Second Laws. These apply to rocks that deform and fracture as brittle solids, and those that deform plastically as ductile solids, as well as to magmas that flow as viscous fluids. This egalitarian functionality means that: 1) most geological structures are candidates for models based on Cauchy's Laws; 2) geologists must specify the constitutive properties of the deforming rocks or magmas; and 3) these models satisfy the conservation laws of mass and momentum. This modern methodology provides structural geologists with an on-going and self-correcting process of scientific investigation as new field and laboratory data accumulate and new hypotheses are tested.