Geoscience Reference
In-Depth Information
y = h
y = h
x = h
x = h
Air
z
z
Earth surface
Air
Earth surface
Subsurface
(b) One-dimensional layered model
(a) Halfspace model
y
y = h
x
x
Air
Air
z
z
Earth surface
Earth surface
Object
(c) Two-dimensional pipe
model
(d) Three-dimensional finite
length cylinder model
fIGURe 6.15
Dimensionality of models: (a) a homogenous half-space that extends to infinity in the
x
and
y
directions, (b) a layered-earth model that extends to infinity in the
x
and
y
directions, (c) a two-dimensional
pipe model that extends to infinity in the
y
direction, and (d) a three-dimensional object that has finite dimen-
sions in all three directions.
approximation to the boundary between two half-spaces. This brings us to a very important point
about models:
models are idealized approximations to the distribution of objects in the subsurface
.
Models make it possible to simulate geophysical measurements mathematically, and they are never
an exact replication of conditions in the subsurface.
The layered earth (Figure 6.15b) is an example of a one-dimensional model. It is one dimen-
sional because the physical properties change in only one dimension. A pipe that is infinitely long
(Figure 6.15c) is an example of a two-dimensional object, and a spheriod (Figure 6.15d) is an exam-
ple of a three-dimensional object.
Forward models like that shown in Figure 6.15 are used by geophysicists in a variety of ways,
including the following:
•
Presurvey prediction of the response expected from targets in the surface. Calculating
models prior to a survey prevents using a particular technique when the theory predicts
that the resulting field measurements will not detect a target.
Design of field surveys to optimize line and station spacing.
•
•
Inversion of field data.
Nearly all geophysical measurements that follow the basic laws of Newtonian and Maxwellian
physics can be approximated by mathematical models. These mathematical models describe the
spatial and temporal (time-dependent) “state” of the EM field. In other words, the models describe
