The last stepping stone along the path of Fig.
12.14 links the output of a modeling investigation
to field observations through rules of correspondence (Margenau, 1977). These come in various
forms and levels of mathematical and statistical
rigor. In the simplest form a concept, such as the
linear relationship between depth and diameter
of laccoliths as conceived by Gilbert (Fig. 1.18), is
tested by estimating the stratigraphic position of
laccoliths in the Henry Mountains (Table 1.1). In a
more quantitative evaluation the calculated slip
directions for intersecting normal faults in an
elastic model are compared to field measurements of slickenline orientations from the
Chimney Rock area (Fig. 2.31). In another example,
linear inverse theory is used to calculate the slip
distribution on a fault model for the 1999 Hector
Mine earthquake (Fig. 8.15) as constrained by
surface displacement data from satellite radar
images. The calculated slip distribution is then
used as a boundary condition in a forward elastic
model and the resulting surface displacements
compared to those from the radar image. In all of
these examples the correspondence proved
sufficiently compelling to convince the structural
geologist that the investigation was on the right
track. Discrepancies, on the other hand, motivate
further field work and modeling.
12.4 Concluding remarks
In summary, we advocate a methodology that
applies the extensive machinery of the physics and
chemistry of the processes involved, most centrally
rock deformation, both to suggest observations
and to analyze, visualize, and interpret them. In
this way, a coherent and self-consistent, if idealized, and non-unique, re-construction of the development of a geological structure may be achieved.
We concede that tectonic processes and their products will not be completely described by mechanical models, but advocate the position that the
mechanics must be complete. Thus, for prescribed
initial and boundary conditions a forward model is
generated that may produce likenesses of some of
the observed geological structures and fabrics, to
some satisfactory degree of approximation. If the
forward model fails to produce satisfactory likenesses we learn that one or more of the postulates
is inappropriate and must be excluded or modified.
One cannot, however, exclude or modify the fundamental laws upon which the mechanical model
is based. The general method we advocate is the
construction of a sequence of quantitative models,
graduated in their degree of detail, and successively providing an improved understanding.
12.4 CONCLUDING REMARKS
477
12.14 links the output of a modeling investigation
to field observations through rules of correspondence (Margenau, 1977). These come in various
forms and levels of mathematical and statistical
rigor. In the simplest form a concept, such as the
linear relationship between depth and diameter
of laccoliths as conceived by Gilbert (Fig. 1.18), is
tested by estimating the stratigraphic position of
laccoliths in the Henry Mountains (Table 1.1). In a
more quantitative evaluation the calculated slip
directions for intersecting normal faults in an
elastic model are compared to field measurements of slickenline orientations from the
Chimney Rock area (Fig. 2.31). In another example,
linear inverse theory is used to calculate the slip
distribution on a fault model for the 1999 Hector
Mine earthquake (Fig. 8.15) as constrained by
surface displacement data from satellite radar
images. The calculated slip distribution is then
used as a boundary condition in a forward elastic
model and the resulting surface displacements
compared to those from the radar image. In all of
these examples the correspondence proved
sufficiently compelling to convince the structural
geologist that the investigation was on the right
track. Discrepancies, on the other hand, motivate
further field work and modeling.
12.4 Concluding remarks
In summary, we advocate a methodology that
applies the extensive machinery of the physics and
chemistry of the processes involved, most centrally
rock deformation, both to suggest observations
and to analyze, visualize, and interpret them. In
this way, a coherent and self-consistent, if idealized, and non-unique, re-construction of the development of a geological structure may be achieved.
We concede that tectonic processes and their products will not be completely described by mechanical models, but advocate the position that the
mechanics must be complete. Thus, for prescribed
initial and boundary conditions a forward model is
generated that may produce likenesses of some of
the observed geological structures and fabrics, to
some satisfactory degree of approximation. If the
forward model fails to produce satisfactory likenesses we learn that one or more of the postulates
is inappropriate and must be excluded or modified.
One cannot, however, exclude or modify the fundamental laws upon which the mechanical model
is based. The general method we advocate is the
construction of a sequence of quantitative models,
graduated in their degree of detail, and successively providing an improved understanding.
12.4 CONCLUDING REMARKS
477