Depth of Point Scatterer = 2 m

Depth of Point Scatterer = 0.1 m Depth of Point Scatterer = 1 m

Depth of Point Scatterer = 2 m

(c) Hyperbolic time-distance curves for velocities of 0.05, 0.1, 0.15, 0.20, 0.25, and 0.30 m/ns

FIGURE 7.9 Backscattered reflection from a point in the subsurface, as a function of surface position: (a) point model and hypothetical time-distance cross section, (b) change in hyperbola shape as a function of velocity and depth, and (c) time-distance plots of different velocities of the host material and depths of a point scatterer.

Spatial effects on GPR data are directly related to the velocity of the material. These effects are summarized in Figure 7.9. A signal reflected from a point in the subsurface (Figure 7.9a) appears as a hyperbola on the GPR record, because a backscattered reflection occurs when transmit-receive antennas approach the center of the buried object and when the antennas are moving away from the object. The shape of the hyperbola is directly related to the velocity, with a flattening of the hyperbola corresponding to an increase in velocity. The effect of changing the velocity on the shape of the hyperbola is shown in Figure 7.9b, and the simple equation that determines the shape of the hyperbola on the time-distance cross section is t(x) = 2r/v, where t is the two-way travel time of the backscattered GPR pulse at a distance x away from the center of the point, for a velocity v of the material.

Figure 7.9c suggests that the velocity of a material can be determined directly from GPR data, when the data contain an anomaly from a point scatterer (e.g., as approximated by a buried pipe, or the sharp edge of an object that is crossed by a GPR line of measurement traces). The velocity can be calculated from time-distance relationships by taking the two-way travel time values at the maximum point over the reflection hyperbola (corresponding to x = 0, with the corresponding two-way time t0) and another point (e.g., any distance from the center of the hyperbola, call it Xj, and the corresponding two-way time tj) along the reflection hyperbola, and applying the following relationship:

An analogous field computation of velocity can be obtained over a layer.

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