FIGURE 6.14 Extraction of profile lines from gridded data.

locate and define anomalies. If the orientation of an object of search is known, and the object is elongated in one direction, then profile lines may be the preferred means to find the location of the object. Profile lines may also be used to extract data from gridded data for modeling. Profiles can be extracted from the gridded data and can be stacked in their relative spatial position based on a level of the variable representing the position of the profile. The resulting stacked profile map gives a three-dimensional view of the data set focusing on the shorter wavelength components that may be lost in the normal contouring process. A simulated profile extraction from a set of gridded data is shown in Figure 6.14.

6.5.2 Interpretation

Interpretation of EM data is conducted as different levels of complexity, depending upon the objective. A simple metal detector beeps when it supposedly passes over a very shallow buried object, and EM data measured with more sophisticated geophysical instruments need to be plotted and analyzed. The simplest analysis consists of visual inspection of the data, and the most complex interpretations involve inverse modeling. 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. 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 inaccessible 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 measurements. 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 propagation 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 idealized 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 simplest 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

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