Geoscience Reference
In-Depth Information
analyzed. The simplest analysis consists of visual inspection of the data, and the most complex
interpretations involve inverse modeling.
6.5.2.1
visual Interpretation
A visual interpretation consists of plotting the data and mapping the location of the anomalies from
profiles or a contour map of the data. Clearly the data in Figure 6.14 indicate the location of two
types of anomalies: the long linear feature that trends from the top to bottom of the contoured grid
is a pipeline, and the other features are buried pits filled with metallic debris. If anomalies stand
out on the data, like they do in Figure 6.14, and there is no need to know the depth and size of the
objects, then a visual interpretation may be adequate. However, if more detail is required from the
data, then it is necessary to model the data, using a numerical simulation of the EM response of a
buried object to an external EM field.
6.5.2.2
forward Modeling
In geophysics, we have the disadvantage of not being able to directly measure all of the forces and
responses for a particular phenomenon, because most of the lines of force are buried and inac-
cessible to direct measurement. Therefore, we must resort to making a few measurements on the
surface of the earth, a borehole, or air, and deduce the remaining points from the observed mea-
surements. In order to make these deductions, we must determine the distribution of objects in the
subsurface that created the distribution of EM fields that were measured on the surface, in the air, or
in the borehole. The procedure that we use to simulate the response from an idealized distribution
of objects in the subsurface is called the process of mathematical, or numerical, modeling.
In a more general sense, a
model is either a physical or a mathematical analog of the distribution
of physical properties in the subsurface that gave rise to the observed measurements. The physical
analog may consist of a test pit or water tank containing the objects that have been hypothesized
to cause the observed measurements. The objects and the geophysical measurement techniques are
scaled-down versions of the objects buried in the earth and the equipment that was used to make
the observed measurements. A mathematical model is often used rather than a physical model. The
mathematical model consists of a solution to a mathematical description of the diffusion of energy
in the case of EM induction and thermal methods.
Mathematical models are computed using the differential equations that describe wave propa-
gation as discussed earlier in this chapter. The models generated from solving these equations for
buried objects in the presence of a particular geophysical field are called theoretical, or forward
models. These models consist of spatial and physical property parameters. The spatial parameters
of a model are the size and location of the objects, and the physical property parameters depend
upon the type of geophysical measurement being modeled.
Models are usually composed of bodies (sometimes referred to as objects or targets) of an ideal-
ized shape. These idealized objects are represented by boundaries between physical properties. The
difference between the value of the physical property within the object and the value of the physical
property surrounding the object is called the contrast
in the physical property. The boundary is the
surface that separates the object from the surrounding (or host) material. Models are classified as
zero, one, two, or three dimensional, depending upon how many dimensions are used to define the
object. Examples of one-, two-, and three-dimensional objects are shown in Figure 6.15. The sim-
plest model is a whole-space, where there are no boundaries (only a host material). There are no true
whole-spaces, but outer space is a close approximation for most physical properties.
The surface of the earth can be modeled as the boundary between two half-spaces: an upper
half-space (the air), and a lower half-space (the solid earth). The earth is an imperfect example of
a lower half-space. We know that the earth's surface is not flat. It is a spheroid. However, within
the variations of shallow crustal and near-surface measurements, the surface of the earth is a good
