A frequency division compensation method for improving the detection depth of geological radar

Abstract

The present invention discloses a frequency division compensation method for improving the detection depth of geological radar. The method first obtains radar records collected by two groups of antennas with different frequencies; performs spectrum analysis on the two groups of data to obtain the dominant frequency bands of signals with different frequencies and determine the dominant dividing point; keeps the high-frequency dominant segment of the radar data collected at high frequency unchanged, and only uses the low-frequency signal as the desired output at the low-frequency end to calculate the frequency division matching filter; then applies it to the radar data collected by all high-frequency antennas to perform frequency division compensation. The frequency division compensation technology used in the present invention fully utilizes the advantages of geological radar signals collected by low-frequency antennas and high-frequency antennas in different frequency bands and combines them, broadening the frequency band of the geological radar data, effectively improving the detection depth while maintaining the high resolution of the geological radar data.

Description

Technical Field

[0001] The present invention relates to the field of engineering geophysical exploration, and in particular to a frequency division compensation method for improving the detection depth of a geological radar. Background Art

[0002] Population growth and urban land scarcity are posing unprecedented challenges to sustainable human development. Countries around the world are implementing strategies to "reclaim underground space and resources," and the development and utilization of urban underground space has become a cutting-edge strategic scientific issue. To efficiently, safely, and fully utilize underground space, it is essential to thoroughly understand the geology of the shallow subsurface. Geological radar technology, due to its high efficiency, continuous, non-destructive, economical, and easy-to-use characteristics, has become a primary method for underground space investigation.

[0003] Radar data collected by antennas of different frequencies have their own advantages and disadvantages. Radar data collected by high-frequency antennas have higher resolution, but the detection depth is not as good as that collected by low-frequency antennas. In other words, radar data collected by a single-frequency antenna is difficult to obtain records with a wider frequency band. In addition, based on the exploration experience of 3D geological radar (200MHz) in high-water level areas (such as Hangzhou), its effective detection depth is generally less than 2m, which is difficult to meet the needs of related exploration work. Summary of the Invention

[0004] In view of the shortcomings of the prior art, the object of the present invention is to provide a frequency division compensation method for improving the detection depth of geological radar.

[0005] The object of the present invention is achieved through the following technical solution: a frequency division compensation method for improving the detection depth of geological radar, comprising the following steps:

[0006] 1. Obtain two sets of radar records collected at different antenna frequencies. Collect two sets of low-frequency and high-frequency geological radar signals, x1(t) and x2(t). High-frequency geological radar signals provide high-resolution information, while low-frequency geological radar signals have deeper penetration depth.

[0007] 2. Perform spectrum analysis on the collected radar data to obtain the dominant cutoff points at different frequencies. The dominant cutoff point refers to the critical point used to distinguish the signal dominance in different frequency ranges in spectrum analysis. Assume that f1 is the dominant cutoff point between low-frequency and high-frequency signals. That is, when |f| < |f1|, x1(t) corresponds to low-frequency dominance, and when |f| ≥ |f1|, x2(t) corresponds to high-frequency dominance.

[0008] 3. Frequency division matching filter p r (t) is obtained by keeping the high-frequency advantage segment of the high-frequency radar data unchanged and taking the low-frequency signal as the desired output at the low-frequency end to calculate the frequency-band matched filter;

[0009] 4. Frequency division compensation of geological radar signal. Using the obtained frequency division matching filter p r (t) matches the high-frequency geological radar signal x(t), and the compensated signal y0(t) is expressed as

[0010] y0(t)=x(t)*p r (t) (1)

[0011] After Fourier transform, it is expressed in the frequency domain as

[0012] Y0(f)=X(f)P r (f) (2)

[0013] Among them, x(t) is the high-frequency geological radar signal actually collected, y0(t) is the actual output filtered and compensated signal, Y0(f) and X(f) are the Fourier transforms of y0(t) and x(t), respectively.

[0014] Furthermore, step 3 is implemented by the following sub-steps:

[0015] (3.1) In order to increase the detection depth while retaining the high resolution of the desired output y(t), a matched filter p(t) is set, and the radar data x2(t) collected by the high-frequency antenna is used as the input signal to increase the detection depth while retaining the high resolution of the desired output y(t). The actual output y0(t) is expressed as:

[0016] y0(t)=x2(t)*p(t) (3)

[0017] (3.2) Considering the solution of Wiener filter based on the least squares method, the objective function is

[0018]

[0019] Among them, e t is the output error, Q is the sum of squares of the errors;

[0020] Solving the objective function, we get the Wienerhof equation,

[0021] r xx p j =r xy (5)

[0022] The optimal parameters are

[0023] p j =r xx -1 r xy (6)

[0024] Among them, r xx is the autocorrelation matrix of x2(t), P j is the frequency-division matched filter, r xy is the cross-correlation vector of x2(t) and y(t);

[0025] (3.3) Constructing a frequency-division matched filter in the frequency domain: f1 is the dominant dividing point between the low-frequency band and the high-frequency band, that is, the x1(t) signal is mainly concentrated at the low-frequency end, and the x2(t) signal is concentrated at the high-frequency end; taking the x2(t) signal as input, the desired output y(t) after Fourier transform is Y(f), which should retain its high-frequency advantage while compensating for the low-frequency band, that is:

[0026]

[0027] where X1(f) and X2(f) are the Fourier transforms of x1(t) and x2(t), respectively.

[0028] At the same time, transform (3) into the frequency domain for solution, and after Fourier transform, we get:

[0029] Y0(f)=X2(f)P(f) (8)

[0030] Where Y0(f) and X2(f) are the Fourier transforms of the actual output y0(t) and input x2(t), respectively.

[0031] The matched filter can be expressed as

[0032] P(f)=Y0(f) / X2(f) (9)

[0033] Substituting the expression of the expected output Y(f) in formula (7) into the above formula, we get:

[0034]

[0035] In the interval |f|<|f1|, P(f) can be further expressed as:

[0036]

[0037] Where α is the pre-whitening percentage to avoid numerical instability in Equation (11) when solving the filtering operator.

[0038] (3.4) The P(f) obtained at this time is a complex number, which can not only compensate for the lack of amplitude, but also produce a time shift on the waveform's phase axis. However, in the actual processing process, there is no need to change the phase. Therefore, the frequency division matched filtering method adopts zero-phase filtering, that is, only the amplitude compensation of the high-frequency end of the conventional data is performed without modifying the phase spectrum. The operator P actually used in the matched filter is r(f) shall meet the following requirements:

[0039]

[0040] The beneficial effect of the present invention is that it fully utilizes the advantages of the geological radar signals collected by the low-frequency antenna and the high-frequency antenna in different frequency bands, realizes the frequency division compensation of the high-frequency radar signal by constructing a frequency division matching filter, and broadens the bandwidth, thereby providing an effective implementation plan for improving the exploration depth of the geological radar and improving the detection capability of the ground penetrating radar in the field of urban underground space investigation. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is a flow chart of the frequency division compensation technology for improving the detection depth of geological radar;

[0042] Figure 2 It is the profile of geological radar signal collected by low-frequency antenna (70MHz);

[0043] Figure 3 It is the profile of geological radar signal collected by high frequency antenna (170MHz);

[0044] Figure 4 This is a comparison chart of single-channel spectra of two groups of geological radar signals, high frequency and low frequency;

[0045] Figure 5 is the average frequency-divided matched filter p r (t) Spectrum diagram;

[0046] Figure 6 These are cross-sectional comparison diagrams on a test line. (a) is the cross-sectional diagram of a 170 MHz high-frequency signal, (b) is the cross-sectional diagram of a 70 MHz low-frequency signal, and (c) is the cross-sectional diagram of the radar signal after the high-frequency signal undergoes frequency division and matching filtering.

[0047] Figure 7 Figure 2 is a comparison of single-channel spectra. (a) is the high-frequency (170 MHz) single-channel spectrum diagram, (b) is the low-frequency (70 MHz) single-channel spectrum diagram, and (c) is the single-channel spectrum diagram of the actual output y0(t) after the high-frequency signal is matched filtered. DETAILED DESCRIPTION

[0048] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0049] like Figure 1 As shown, this embodiment provides a frequency division compensation method for improving the detection depth of geological radar, which includes the following steps:

[0050] 1. Obtain two sets of radar records collected at different antenna frequencies. Collect two sets of geological radar signals at 70MHz and 170MHz, respectively x1(t) and x2(t). The profiles are as follows: Figure 2 、 Figure 3 As shown, Figure 2 The 70MHz radar signal has a deeper penetration depth due to its lower frequency and can provide deeper information. Figure 3 The 170MHz radar signal uses its higher frequency to provide high-resolution shallow geological information;

[0051] 2. Perform spectrum analysis on the collected radar data to obtain the dominant dividing points of different frequencies. Figure 4 For the spectrum analysis of single channels x1(t) and x2(t), f1 is the dominant dividing point between low-frequency and high-frequency signals. That is, when |f| < |f1|, x1(t) corresponds to a low-frequency advantage, and when |f| ≥ |f1|, x2(t) corresponds to a high-frequency advantage.

[0052] 3. Frequency division matching filter p r (t) is obtained. Keeping the high-frequency advantage segment of the high-frequency radar data unchanged, only taking the low-frequency signal as the desired output at the low-frequency end, the frequency-band matched filter p is calculated. r (t), after Fourier transformation, we get P r The spectrum of (f) is as follows Figure 5 As shown, when a high-frequency signal is input, P r (f) The value is 1 at the high frequency end, retaining the high frequency end characteristics of the high frequency signal, P r (f) The value at the low frequency end is greater than 1, which effectively compensates the low frequency end of the high frequency signal;

[0053] 4. Frequency division compensation of geological radar signal. The obtained frequency division matching filter p r (t) is applied to the high-frequency geological radar signal x(t) collected from a certain test line for matching processing, and the compensated signal y0(t) can be expressed as

[0054] y0(t)=x(t)*p r (t) (1)

[0055] After Fourier transform, it can be expressed in the frequency domain as

[0056] Y0(f)=X(f)P r (f) (2)

[0057] Among them, x(t) is the high-frequency geological radar signal actually collected, y0(t) is the actual output filtered and compensated signal, Y0(f) and X(f) are the Fourier transforms of y0(t) and x(t), respectively.

[0058] The x(t) signal is used as a high-frequency input, and the result after frequency division compensation is as follows: Figure 6 For a certain test line, two sets of geological radar profiles of high frequency (170MHZ) and low frequency (70MHZ) and the high frequency signal passing through p r (t) Comparison of profiles after frequency division compensation. The box shows an underground subway entrance. (a) is the 170 MHz high-frequency signal profile, (b) is the 70 MHz low-frequency signal profile, and (c) is the radar signal profile after the high-frequency signal is subjected to frequency division matching filtering. The comparison shows that after the 170 MHz signal is subjected to frequency division matching filtering, its shallow high-resolution characteristics are retained while also revealing the signal characteristics of the subway entrance within 5 meters, thus improving the detection depth. Figure 7 In the selected single-channel spectrum diagram, the low-frequency signal of the high-frequency (170MHz) input signal x(t) spectrum is severely missing, which is compensated after matched filtering. At the high-frequency end, its advantages are still retained after matched filtering, effectively widening the spectrum.

[0059] Step 3 is implemented by the following sub-steps:

[0060] (3.1) In order to increase the detection depth while retaining the high resolution of the desired output y(t), assuming that a matched filter p(t) is set and the radar data x2(t) collected by the high-frequency antenna is used as the input signal, the actual output y0(t) can be expressed as:

[0061] y0(t)=x2(t)*p(t) (3)

[0062] (3.2) Considering the solution of Wiener filter based on the least squares method, the objective function is

[0063]

[0064] Among them, e t is the output error, and Q is the sum of squares of the errors.

[0065] Solving the objective function, we get the Wienerhof equation,

[0066] r xx p j =r xy (5)

[0067] Due to the noise in nature, r xx is non-singular, so the optimal parameters are

[0068] p j =r xx -1 r xy (6)

[0069] Among them, r xx is the autocorrelation matrix of x2(t), P j is the frequency-division matched filter, r xy is the cross-correlation vector of x2(t) and y(t).

[0070] (3.3) For a more intuitive and computationally convenient approach, consider constructing a frequency-dividing matched filter in the frequency domain. f1 is the dominant dividing point between the low-frequency band and the high-frequency band, i.e., the x1(t) signal is mainly concentrated at the low-frequency end, while the x2(t) signal is concentrated at the high-frequency end. Taking the x2(t) signal as input, the desired output y(t) after Fourier transformation should retain its high-frequency advantage while compensating for the low-frequency band, i.e.:

[0071]

[0072] where X1(f) and X2(f) are the Fourier transforms of x1(t) and x2(t), respectively.

[0073] At the same time, transform (3) into the frequency domain for solution, and after Fourier transform, we get:

[0074] Y0(f)=X2(f)P(f) (8)

[0075] Where Y0(f) and X2(f) are the Fourier transforms of the actual output y0(t) and input x2(t), respectively.

[0076] The matched filter can be expressed as

[0077] P(f)=Y0(f) / X2(f) (9)

[0078] Substituting the expression of the expected output Y(f) in (7) into the above formula, we get:

[0079]

[0080] In the interval |f|<|f1|, P(f) can be further expressed as:

[0081]

[0082] Where α is the pre-whitening percentage, which is used to avoid numerical instability in equation (11) when solving the filtering operator.

[0083] (3.4) The P(f) obtained at this time is a complex number, which can not only compensate for the lack of amplitude, but also produce a time shift on the waveform's phase axis. However, in the actual processing process, there is no need to change the phase. Therefore, the frequency division matched filtering method adopts zero-phase filtering, that is, only the amplitude compensation of the high-frequency end of the conventional data is performed without modifying the phase spectrum. The operator P actually used in the matched filter is r (f) shall meet the following requirements:

[0084]

[0085] The present invention provides a frequency division compensation technology for improving the detection depth of geological radar. It fully utilizes the frequency band differences of geological radar data collected by different frequency antennas, and realizes the complementary advantages within different frequency bands by constructing frequency division matching filters, thereby effectively widening the frequency bandwidth of radar recording and improving the exploration depth of geological radar.

[0086] Those skilled in the art will understand that the foregoing descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art will still be able to modify the technical solutions described in the foregoing examples or substitute equivalents for some of the technical features. Any modifications, equivalent substitutions, etc. made within the spirit and principles of the invention shall be included within the scope of protection of the invention.

Claims

1. A frequency division compensation method for improving the detection depth of geological radar, characterized in that: The following steps are involved: (1) Obtain two sets of radar records collected at different antenna frequencies: collect two sets of geological radar signals, low frequency and high frequency, respectively, x1(t) and x2(t); (2) Perform spectrum analysis on the collected radar data to obtain the dominant dividing points of different frequencies: let f1 be the dominant dividing point between low-frequency and high-frequency signals. When |f| < |f1|, x1(t) corresponds to a low-frequency advantage, and when |f| ≥ |f1|, x2(t) corresponds to a high-frequency advantage, where f represents the frequency of the radar signal. (3) Frequency division matching filter p r (t) is obtained by keeping the high-frequency advantage segment of the high-frequency radar data unchanged and taking the low-frequency signal as the desired output at the low-frequency end to calculate the frequency-band matched filter. (4) Frequency division compensation of geological radar signal: using the obtained frequency division matching filter p r (t) matches the high-frequency geological radar signal x(t), and the compensated signal y0(t) is expressed as y0(t)=x(t)*p r (t) (1) After Fourier transform, it is expressed in the frequency domain as Y0(f)=X(f)P r (f) (2) Among them, x(t) is the high-frequency geological radar signal actually collected, y0(t) is the actual output signal after filtering compensation, and p r (t) is the frequency-division matched filter, Y0(f), X(f) and P r (f) are y0(t), x(t) and p respectively r The Fourier transform of (t).

2. The frequency division compensation method for improving the detection depth of geological radar according to claim 1, characterized in that: The step (3) is implemented by the following sub-steps: (3.1) Set the matched filter p(t) and the radar data x2(t) collected by the high-frequency antenna as the input signal so that the desired output y(t) retains high resolution while increasing its detection depth. The actual output y0(t) is expressed as: y0(t)=x2(t)*p(t) (3); (3.2) Considering the solution of Wiener filter based on the least squares method, the objective function is Among them, e t is the output error, Q is the sum of squares of the errors; Solving the objective function, we get the Wienerhof equation, r xx p j ＝r xy (5) The optimal parameters are p j ＝r xx -1 r xy (6) Among them, r xx is the autocorrelation matrix of x2(t), P j is the frequency-division matched filter, r xy is the cross-correlation vector of x2(t) and y(t); (3.3) Constructing the frequency-division matched filter in the frequency domain: f1 is the dominant dividing point between the low-frequency band and the high-frequency band, that is, the x1(t) signal is mainly concentrated at the low-frequency end, and the x2(t) signal is concentrated at the high-frequency end. Taking the x2(t) signal as input, the expected output y(t) obtained after Fourier transform is Y(f), which should retain its high-frequency advantage while compensating for the low-frequency band, that is: Where X1(f) and X2(f) are the Fourier transforms of x1(t) and x2(t), respectively; At the same time, transform (3) into the frequency domain for solution, and after Fourier transform, we get: Y0(f)=X2(f)P(f) (8) Where Y0(f) and X2(f) are the Fourier transforms of the actual output y0(t) and input x2(t), respectively; The matched filter can be expressed as P(f)=Y0(f) / X2(f) (9) Substituting the expression of the expected output Y(f) in (7) into the above formula, we get: In the interval |f|<|f1|, P(f) can be further expressed as: Where α is the pre-whitening percentage to avoid numerical instability in the equation when solving the filter operator; (3.4) The frequency division matched filtering method adopts zero phase filtering, so the operator P actually used in matched filtering is r (f) Satisfy:

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