Method for calculating relative permittivity of each stratum in ground radar exploration method by waveform inversion and method for estimating volumetric water content using relative permittivity calculated by the method

Abstract

To enable a relative dielectric constant of each stratum to be calculated without performing a wide-angle measurement in an underground radar serving, and thus, enable a moisture content underground to be calculated easily.SOLUTION: In an underground radar surveying method of causing an electromagnetic wave to enter underground, measuring and analyzing a returning measurement wave for of the electromagnetic wave, and surveying an underground structure, the surveying method is the method that calculates a relative dielectric constant of each stratum in a measurement point from the collected waveform by the surveying, and is the method that estimates a volume moisture content of each stratum, using the calculated relative dielectric constant. The method is configured to: obtain a reflection coefficient (R), using an incident waveform (W) and measurement waveform (X) collected by the surveying; presume that a relative dielectric constant (ε1) of the stratum of a first layer as a known value; obtain the reflection coefficient, using a general expression of estimating the electromagnetic waveform underground; calculate the relative dielectric constant (εr) of each stratum from a second layer to an i-th layer; and estimate a volume moisture content (θ), using an examination expression of TOPP (1980) from the calculated relative dielectric constant.SELECTED DRAWING: None

Description

Technical Field

[0001] The present invention relates to a method for calculating the relative permittivity of each stratum in a ground penetrating radar exploration method and a method for estimating the volumetric water content using the relative permittivity calculated by the method. More specifically, the present invention relates to a method for calculating the relative permittivity of each stratum by inversion of a waveform record recorded in a ground penetrating radar exploration and a method for estimating the volumetric water content using the relative permittivity calculated by the method.

Background Art

[0002] Conventionally, the ground penetrating radar exploration method is known as a method for detecting the buried positions of buried pipes, rocks, concrete, and other construction facilities existing in the ground and the positions of underground cavities. In this ground penetrating radar exploration method, electromagnetic waves are irradiated underground by a transmitting antenna, and the electromagnetic waves reflected by buried pipes, cavities, or soil layer boundaries underground are detected by a receiving antenna and recorded data is analyzed to determine the buried positions of buried pipes and the like. This method is widely used.

[0003] However, depth data is required to determine the buried positions of buried pipes and the like and the positions of underground cavities. In ground penetrating radar exploration, since the data of the reflected electromagnetic waves is time data, it is necessary to obtain the depth data of the buried positions of buried pipes and the like using the time data obtained in ground penetrating radar exploration. For this purpose, it is first necessary to obtain the speed of the electromagnetic waves.

[0004] Here, Equation (1) is a principle formula for obtaining the speed. In Equation (1), C is the speed of light (30 cm / ns), and ε r is the relative permittivity. That is, in order to obtain the speed of the electromagnetic waves using Equation (1), it is necessary to obtain the relative permittivity of the stratum. If the relative permittivity can be known, it is possible to calculate the speed of the electromagnetic waves using Equation (1). However, it is not easy to obtain the relative permittivity of each stratum in ground penetrating radar exploration. Therefore, conventionally, a method that can easily obtain the relative permittivity has been desired.

Equation

[0005] By the way, when the water content of river levees, road embankments, or the ballast beds and roadbeds of railway tracks increases, there is a risk of leading to liquefaction, settlement, or collapse due to strength reduction. Therefore, it is important to grasp the water content state of these structures for maintenance management. For this purpose, conventionally, the water content state in structures has been grasped using measuring instruments such as soil moisture meters and pore water pressure gauges. However, since these measurements are point measurements, at present, the measurement points are limited for long levees and railway ballast beds.

[0006] Here, electromagnetic waves depend on the relative dielectric constant (ε r ) which is one of the electrical characteristics of the ground, and its propagation speed and reflection coefficient (intensity of the reflected wave) change. Therefore, conversely, by analyzing the electromagnetic wave records collected in ground penetrating radar exploration, the relative dielectric constant of the ground and the target structure can be estimated. And when the relative dielectric constant is obtained, the volumetric water content (θ) of the ground can be estimated using the experimental formula of Topp (1980) shown in Equation (2).

[0007]

Equation

[0008] And since the ground penetrating radar exploration method is characterized by being able to explore a wide range non-destructively and efficiently, if the relative dielectric constant of the ground and the structure can be obtained by analyzing the recorded data of ground penetrating radar exploration, unlike the case of grasping the water content state in the structure using measuring instruments such as soil moisture meters and pore water pressure gauges, it becomes possible to grasp the water content distribution of long levees and railway ballast beds with high precision and economically.

[0009] Therefore, conventionally, a measurement method called the wide-angle method has been used in ground penetrating radar exploration to estimate the electromagnetic wave velocity (V) of the target ground and structure, and a method of obtaining the relative dielectric constant (ε r ) using the principle formula shown in Equation (1) has been utilized.

[0010] That is, in wide-angle measurement in ground penetrating radar exploration, a plurality of measurement data with different isolation distances between the transmitting and receiving antennas are acquired, and the formula shown in Equation (3) is applied to obtain the propagation speed of electromagnetic waves.

[0011] Here, FIG. 2 is a diagram for explaining wide-angle measurement. In FIG. 2, the separation between the transmitting antenna T and the receiving antenna R is L when it is close 1 and L when it is far 2 , and the propagation times at that time are t 1 , t 2 respectively, and this is the case where the depth to the boundary is d. The electromagnetic wave propagation speed v of medium A can be obtained by solving the simultaneous equations of Equation (3).

[0012]

Equation

Prior Art Documents

Patent Documents

[0013]

Patent Document 1

Patent Document 2

Patent Document 3

Patent Document 4

Patent Document 5

Patent Document 6

Patent Document 7

Summary of the Invention

Problems to be Solved by the Invention

[0014] However, in the currently most widely used device with an integrated transceiver antenna, there is a problem that wide-angle measurement with different antenna isolation distances cannot be performed, and the propagation speed cannot be obtained.

[0015] In this regard, in the three-dimensional ground penetrating radar device that has been rapidly spreading recently, it is possible to automatically perform measurements with different antenna isolation distances by using a plurality of built-in transceiver antennas. Therefore, although the isolation distance is limited, wide-angle measurement can be easily performed.

[0016] However, in wide-angle measurement, since it is necessary to acquire and analyze a plurality of data (usually about 10 data) with different antenna isolation distances of the transceiver antenna, if there is data containing noise even in a part of the acquired data, there is a problem that the estimation accuracy of the propagation speed obtained by the analysis decreases. For example, in the measurement on a railway track, when performing wide-angle measurement, it has been found that the data with a large antenna isolation distance inevitably contains noise from the rails and reinforcing bars around the antenna and the clutter containing them, and the propagation speed cannot be accurately estimated.

[0017] Therefore, in the present invention, instead of wide-angle measurement, waveform inversion analysis is applied to the waveform record recorded by a set of transceiver antennas with the smallest isolation distance to directly calculate the relative dielectric constant from the waveform record, and further, the problem is to estimate the volumetric water content using the calculated relative dielectric constant.

Means for Solving the Problems

[0018] The method for calculating the relative dielectric constant of each stratum in the ground penetrating radar exploration method of the present invention by waveform inversion is a method for calculating the relative dielectric constant of each stratum at the measurement point by inverting the waveform record recorded in the ground penetrating radar exploration, Using the incident waveform (W) and the measured waveform (X) obtained by the ground penetrating radar exploration, the reflection coefficient (R) is obtained by Equation 4 obtained by rewriting the general formula for obtaining the measured waveform from the incident waveform and the reflection coefficient, Assume that the relative permittivity (ε1) of the first layer is a known value, Using the obtained reflection coefficient (R) and the assumed relative permittivity of the first layer, the relative permittivity (ε i ) of each layer from the second layer to the i-th layer is calculated by Equation 5, which is characterized by this. However, R(ω), X(ω), and W(ω) are the representations in the frequency domain of the reflection coefficient, the measured waveform, and the incident waveform time series, respectively. , rn is Of the reflection coefficient time series Expression in the time domain, ω is the angular frequency.

[0019]

Equation

[0020]

Equation

[0021] And the volume water content estimation method of the present invention that estimates the volume water content using the relative permittivity calculated by the above method is Using Equation 4, the reflection coefficient (R) is obtained using the incident waveform (W) and the measured waveform (X) recorded in the exploration, Assume that the relative permittivity (ε 1 ) of the first layer is a known value, Using Equation 5, the relative permittivity (ε i ) of each layer from the second layer to the i-th layer is calculated, Using the calculated relative permittivity, the volume water content (θ) of each layer at the measurement point is estimated by Equation 2, which is characterized by this.

Effect of the Invention

[0022] In the relative permittivity calculation method of the present invention, first, the reflection coefficient (R) is obtained using Equation 4 obtained from Equation 6, which represents the measured waveform (X). And then, the equation of Equation 7, which is a principle equation representing the relationship between the reflection coefficient of electromagnetic waves and the relative permittivity, is used. That is, the following inversion analysis is applied to the waveform recording to obtain the reflection coefficient (r i ), and the relative permittivity (ε i ) is estimated using Equation 8 obtained by rewriting Equation 7.

[0023] In addition, the water content estimation method of the present invention is a method of estimating the volumetric water content (θ) of each stratum at the measurement point by using the relative permittivity calculated by the above method according to Equation 2.

[0024] Therefore, in the present invention, instead of wide-angle measurement, waveform inversion analysis is applied to the waveform record recorded by the set of transmitting and receiving antennas with the smallest isolation distance, and it becomes possible to directly calculate the relative permittivity from the waveform record. Furthermore, it becomes possible to estimate the volumetric water content by using the calculated relative permittivity.

[0025] By using this method, it is possible to obtain the change in relative permittivity of each stratum from the shallow part to the deep part directly below the position of the transmitting and receiving antennas. Then, by converting the obtained relative permittivity into volumetric water content using Equation 2, it is possible to grasp the fine changes in the volumetric water content in dikes, embankments, railway beds, and roadbeds. Therefore, it is possible to efficiently grasp the relative permittivity and water content over a wide range.

[0026]

Equation

[0027]

Equation

[0028]

Equation

Brief Description of the Drawings

[0029]

Figure 1

Figure 2

Embodiments for Carrying Out the Invention

[0030] In the method for calculating the relative permittivity of each stratum in the ground penetrating radar exploration method of the present invention by waveform inversion, it is a method for calculating the relative permittivity of each stratum at the measurement point by inverting the waveform record recorded in the ground penetrating radar exploration. First, Obtained by ground penetrating radar exploration Using the incident waveform (W) and the measured waveform (X), Rewrote the general formula for obtaining the measured waveform from the incident waveform and the reflection coefficient The reflection coefficient (R) is obtained by Equation (4).

[0031] Then, assuming that the relative permittivity (ε 1 ) of the first layer is a known value, Using the obtained reflection coefficient (R) and the relative permittivity of the first layer assumed to be known Equation (5) By , the relative permittivity (ε i ) of each stratum from the second layer to the i-th layer is calculated.

[0032] And in the method for estimating the volumetric water content of the present invention using the relative permittivity calculated by the relative permittivity calculation method of the present invention, the volumetric water content is estimated by Equation (2) using the relative permittivity obtained by the above method.

Example

[0033] An example of the method for calculating the relative permittivity of each stratum in the ground penetrating radar exploration method of the present invention by waveform inversion (hereinafter simply referred to as the "relative permittivity calculation method") will be described. The relative permittivity calculation method of this example is a method for calculating the relative permittivity of each stratum at the measurement point by inverting the waveform record recorded in the ground penetrating radar exploration in the ground penetrating radar exploration method.

[0034] Here, FIG. 1 is a diagram for explaining the principle of the relative permittivity calculation method of this example. In the figure, from the right end, it shows the measured waveform with the vertical axis as time, the incident waveform, the reflection coefficient, and the reflection coefficient, relative permittivity, and stratum cross-section with the vertical axis as depth.

[0035] And in this example, first, Obtained by ground penetrating radar exploration The incident waveform (W) And Using the measured waveform (X), Rewrote the general formula for obtaining the measured waveform from the incident waveform and the reflection coefficient The reflection coefficient (R) is obtained by the foregoing Equation 4. Here, Equation 6 Is is a general formula for obtaining a measured waveform from an incident waveform and a reflection coefficient, and Equation 4 is an equation obtained by rewriting Equation 6. In the ground penetrating radar exploration method, since an incident waveform (W) and a measured waveform (X) are obtained, in the relative permittivity calculation method of this embodiment, first, the reflection coefficient (R) is obtained by Equation 4 obtained by transforming Equation 6.

[0036] Next, in the relative permittivity calculation method of this embodiment, the relative permittivity of the first layer is assumed to be a known value. That is, since the first layer is the ground surface and it is possible to easily know what the medium is, a known value that is already known as the relative permittivity of the medium of the first layer is assumed to be the relative permittivity of the first layer.

[0037] Then, next, using the reflection coefficient obtained by Equation 4 and Assumed to be known the relative permittivity of the first layer, the relative permittivity of the target layer is calculated by Equation 5.

[0038] Here, Equation 7 is a principle formula for obtaining the reflection coefficient at the boundary between the i-th and (i + 1)-th strata. In this embodiment, the reflection coefficient at the boundary between the first and second strata is defined as r 1 .

[0039] Next, Equation 8 is an equation obtained by rewriting Equation 7. If the reflection coefficient at the boundary between the i-th and (i + 1)-th strata is obtained by Equation 4, then the relative permittivity ε i of the i-th stratum can be used to obtain the relative permittivity of the (i + 1)-th stratum by Equation 8. For example, when the relative permittivity of the first layer is ε 1 , since the reflection coefficient (r 1 ) at the boundary between the first and second strata is obtained by Equation 4, the relative permittivity of the second layer is obtained by Equation 8.

[0040] Therefore, in this embodiment, as described above, in order to assume that the relative permittivity ε 1 of the first layer is a known value, if the reflection coefficient is obtained by Equation 4, r n in Equation 5 can be obtained. Therefore, it is possible to obtain the relative permittivity of each stratum in order from the second stratum using Equation 5.

[0041] The relative permittivity calculation method of this embodiment will be specifically described by taking the case where there are three layers of strata as an example. When there are three layers of strata, the reflection coefficient r at the boundary between the first and second layers obtained by inversion 1 and the reflection coefficient r at the boundary between the second and third layers of strata 2 are used. Substitute the known relative permittivity of the first layer into Equation 5 above to obtain the relative permittivity of the second layer and the relative permittivity of the third layer. Equation 9 is the equation for obtaining the relative permittivity of the second layer, and Equation 10 is the equation for obtaining the relative permittivity of the third layer.

[0042]

Equation

[0043]

Equation

[0044] Thus, according to the relative permittivity calculation method of this embodiment, by applying waveform inversion analysis to the waveform record recorded by the set of transmitting and receiving antennas with the smallest isolation distance without performing wide-angle measurement, the change in the relative permittivity of each stratum from the shallow part to the deep part directly below the position of the transmitting and receiving antennas, which is the measurement point, can be easily obtained from the incident waveform and the measurement waveform. Therefore, in ground penetrating radar exploration, it is possible to obtain a wide range of relative permittivities. And by calculating the relative permittivity by the method of this embodiment, in addition to estimating the water content described later, it becomes possible to easily obtain various data obtained using the relative permittivity.

[0045] Next, an embodiment of the method for estimating the volumetric water content of the present invention will be described. In the volumetric water content estimation method of this embodiment, the volumetric water content (θ) is estimated using the relative permittivity of each stratum calculated by the above method according to the empirical formula of TOPP (1980), Equation 2.

[0046] That is, using the number 4, the reflection coefficient (R) is obtained using the incident waveform (W) and the measurement waveform (X) recorded in the exploration, and the relative permittivity (ε 1 ) of the first layer is assumed to be a known value, and using the number 5, the relative permittivity (ε i ) of each layer from the second layer to the i-th layer is calculated. Then, thereafter, using the calculated relative permittivity, from the number 2, the volumetric water content (θ) of each layer at the measurement point is estimated.

[0047] Thus, in the volumetric water content estimation method of this embodiment, since the volumetric water content is obtained using the relative permittivity obtained by the above-described relative permittivity calculation method of the present invention, without performing wide-angle measurement, as described above, it is possible to grasp minute changes in the volumetric water content in levees, embankments, railway beds, and roadbeds.

[0048] In the above description, a method of estimating the volumetric water content using the relative permittivity calculated by the relative permittivity calculation method of the present invention has been described. However, the use of the relative permittivity calculated by the relative permittivity calculation method of the present invention is not necessarily limited to estimating the volumetric water content, and it is used for obtaining various other data.

Industrial Applicability

[0049] According to the relative permittivity calculation method and the water content estimation method of the present invention, by using the incident waveform and the measurement waveform, the relative permittivity of each layer can be calculated, and further, the water content can be estimated using the calculated relative permittivity. Therefore, it is applicable to the general method of calculating the relative permittivity using the waveform record recorded in the radar exploration, and the general method of estimating the volumetric water content using the relative permittivity calculated using the waveform record recorded in the radar exploration.

Claims

**Claim 1** In a ground penetrating radar exploration method, a method for calculating the relative permittivity of each stratum at a measurement point by inverting a waveform record recorded in the ground penetrating radar exploration, comprising: using the incident waveform (W) and the measurement waveform (X) obtained by the ground penetrating radar exploration, obtaining the reflection coefficient (R) by Equation 1 obtained by rewriting the general formula for obtaining the measurement waveform from the incident waveform and the reflection coefficient, Assume that the relative permittivity (ε １ ) of the first layer is a known value, and Using the obtained reflection coefficient (R) and the relative permittivity of the first layer assumed to be known, the relative permittivity (ε ｉ ) of each layer from the second layer to the i-th layer is calculated according to Equation 2. wherein R(ω), X(ω), and W(ω) are the expressions in the frequency domain of the reflection coefficient, the measurement waveform, and the incident waveform time series, respectively, and ω is the angular frequency. Further, rn in Equation 2 is the expression in the time domain of the reflection coefficient time series, and εi is the relative permittivity. 【Number 1】 【Number 2】 **Claim 2** A method for estimating the volumetric water content of each stratum using the relative permittivity calculation method according to Claim 1, comprising: obtaining the reflection coefficient (R) using the incident waveform (W) and the measurement waveform (X) recorded in the exploration by Equation 1; Assume that the relative permittivity (ε １ ) of the first layer is a known value, and Using the number 2, the relative permittivity (ε ｉ ) of each layer from the second layer to the i-th layer is calculated, estimating the volumetric water content (θ) of each stratum at the measurement point by Equation 3 using the calculated relative permittivity. [Number 3]

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