Читать книгу Electromagnetic Methods in Geophysics - Fabio Giannino - Страница 16

The GPR technique is similar, in principle, to the seismic reflection technique but, instead of mechanical waves, it uses high frequency (10–2500 MHz) electromagnetic pulses to explore the underground.

A radar wave, emitted by a transmitting antenna (a transmitter antenna, or transmitter, is generally indicated with “Tx”) placed directly above the ground surface, propagates in the ground and it is partially reflected by any change in the electrical properties of the subsoil. The reflected energy is then detected by the receiving antenna (a receiving antenna, or receiver, is generally indicated with “Rx”). This basic concept is schematized in the simple sketch of Figure 2.1.1, below.

Georadar antennas have a relatively large frequency band, whose width is approximately equal to the center‐frequency, that is the frequency around which most of the pulse energy is concentrated. For example, if the center‐frequency of emission of the transmitter dipole is 600 MHz, the frequency band is approximately between 300 MHz and 900 MHz. However, the intrinsic characteristics of emission, primarily depends upon the manufacturers technical specifications and technology.

Most GPR equipment uses dipole antennas (identified by their center‐frequency or by the pulse width, approximately corresponding to the reciprocal of the center‐frequency) arranged either in monostatic or in bistatic configurations. In the first case (monostatic mode) the same antenna is used for transmission and reception and the Tx and Rx dipole are contained in the same antenna case and a fixed distance from each other. In the second case (the bistatic mode) there is a constant, small offset between the two antennas, that can be placed either in separated cases (as for the low‐frequency antennas) or inside the same box (as for the higher‐frequency ones).

Generally, the offset is sufficiently small that it can be practically neglected, and the last arrangement could be considered nearly monostatic. For both arrangements the usual data acquisition is the reflection mode, performed either as continuous profiling (moving the antennas along the profile at a slow, near constant towing speed) or as stationary point collection (shifting them stepwise).

Figure 2.1.1 Sketch of the basic components of a GPR system and principle of operation.

GPR data, properly amplified, are then recorded and displayed as a two‐dimensional section with the antenna positions (or midpoint positions in case of bistatic systems) in the horizontal axis (Figure 2.1.2 a) and the two‐way travel time in the vertical axis (Figure 2.1.2 b and c). This section can be considered a normal‐incidence time section (corresponding to the zero‐offset section of the seismic reflection), where the two‐way time is plotted vertically below the midpoint position, between the Tx and the Rx, even if the actual ray path is slanted, as for the reflection from dipping interfaces or from small‐size targets (diffraction).

Typically, the vast majority of commercial GPR, are built according to a monostatic architecture. However, GPR data can be acquired using other modes depending on the relative geometry of transmitter(s) and receiver(s). These acquisition modes are known as: The Common Mid‐Point (CMP) or Common Depth Point (CDP), the Wide‐Angle Reflection and Refraction (WARR), and the transillumination (Figure 2.1.3) The first two are mainly used for the electromagnetic (EM) wave velocity determination whereas the last is used in tomographic studies.

In general, any GPR is built to measures EM waves reflection events at a given time. This means that, once the EM signal is emitted by the Tx, it travels in the ground and when the wave encounters a reflector it is scattered back and recorded by the receiver. The time spent by the EM wave to travel from the Tx to the reflector and back to the Rx is known as two‐way travel time. Hence, the electromagnetic wave propagation velocity plays an important role in the GPR data analysis, because it allows the conversion of the two‐way travel time window into depth. The EM wave, propagates at a different velocity in different mediums, depending on their physical (dielectric) properties.

Beside CMP and WARR methods to estimate EM waves velocity, other methods can be used. They are (i) the location of objects at known depth, and (ii) the reflection from a source point. In the first method, two‐way travel time is the time that an electromagnetic wave takes to travel through the ground, from the transmitting antenna to the object and back to the receiving antenna (Figure 2.1.4).

Denoting the depth of the known object with a z_known and the velocity of the electromagnetic wave with v, the two‐way travel time for a monostatic configuration of the antenna is given by:

(2.1.1)

Since the depth of the object is known, it can be taken the double travel time from a radar section and express the velocity of the electromagnetic wave using Eq. 2.1.1 (Figure 2.1.4 a).

Figure 2.1.2 Schematic illustration of data acquisition in the reflection profiling mode (a), corresponding radar time section (b) and the waves characterization (c).

The second method is based on the phenomenon that a small object, for example, the cross section of a pipe, reflects radar waves in almost all directions (Figure 2.1.4 b).

Denoting the depth of the object with z and the lateral distance of the monostatic antenna from the object with x, the length w of the wave path can be simply expressed by:

(2.1.2)

and therefore, the function of the two‐way travel time with:

(2.1.3)

Denoting with t₀ the two‐way travel time, on the vertical to the object, one has:

(2.1.4)

Therefore:

(2.1.5)

which is the formula for the so‐called “diffraction hyperbola” method. Many commercially available GPR data processing software, allows for the computation of the EM velocity propagation, automatically, based on this method.

Since from the radar section for each x position the corresponding two‐way travel time t (x) is known, the velocity can be calculated by inverting Eq. (2.1.5). The shape of the hyperbola is governed by the velocity of the wave through the ground and by the geometry of the buried object (Fruhwirth et al., 1996) (Figure 2.1.5).

Figure 2.1.3 Schematic illustration of data acquisition in the a) CMP, b) transillumination, and c) WARR, (Tx: transmitter, Rx: receiver).