CN118210066A - Ground nuclear magnetic resonance small coil signal enhancement method based on wave field transformation - Google Patents
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Abstract
The invention relates to the field of geophysical exploration, in particular to a ground nuclear magnetic resonance small coil signal enhancement method based on wave field transformation, which solves the problems that a large coil measurement technology is difficult to apply in environments with complex terrains such as cities, plateaus and the like, and the signal is weak and the detection depth is limited in the traditional small coil measurement technology. Obtaining nuclear magnetic resonance signals and a quasi-seismic wave field transformation equation; solving nuclear magnetic resonance signals and a quasi-seismic wave field transformation equation by a Tikhonov regularization method to realize wave field inverse transformation and obtain quasi-seismic wave field values of all receiving coils; according to the correlation of the water content information reflected by the adjacent receiving coils, taking each receiving coil as a center, synthesizing aperture based on a green function, and obtaining a quasi-seismic wave field value synthesized by each receiving coil; based on wave field transformation theory, the synthesized quasi-seismic wave field value is transformed back to nuclear magnetic resonance signal value, and the invention improves the accuracy of the subsequent forward and backward analysis result.
Description
Technical Field
The invention relates to the field of geophysical exploration, in particular to a ground nuclear magnetic resonance small coil signal enhancement method based on wave field transformation.
Background
Ground nuclear magnetic resonance detection (Surface Nuclear Magnetic Resonance, SNMR) is a widely used geophysical technique based on the principle of nuclear magnetic resonance and applied directly to the earth's surface. The ground nuclear magnetic resonance detection technology can directly acquire the information of the position, the content, the occurrence state and the like of the underground water through the detection of hydrogen protons, has the advantages of strong pertinence, nature, direct and the like, and provides important technical support for the positioning and dynamic monitoring of the underground water. However, the ground nuclear magnetic resonance detection signal is very weak and is only in the nano-volt level, and in environments with complex terrains such as cities, plateaus and the like, the traditional large coil measurement method is often greatly limited, and the small coil measurement method shows unique advantages in the background, but the small coil is accompanied with the remarkable problems of weak signal, limited detection depth and the like. Therefore, in order to cope with the challenges of complex terrain conditions, it is particularly critical to develop a signal enhancement technology based on small coils, which is beneficial to improving the signal strength and expanding the coverage area, so that more accurate and wide measurement is realized.
In the nuclear magnetic resonance underground water detection device based on the adiabatic pulse excitation source and the method thereof disclosed in CN109597134A, the main control unit controls the high-power voltage modulation circuit and the frequency modulation circuit to work by configuring the transmission parameters through the upper computer, and the adiabatic pulse excitation current is transmitted through the high-power serial transmission circuit, so that the initial amplitude of nuclear magnetic resonance signals is improved, and the signal to noise ratio of the received nuclear magnetic resonance signals is further improved. However, this approach has a relatively limited range of applicability, especially for shallow layers where the signal enhancement effect is not significant.
In the 'magnetic resonance oil gas detection device and detection method of a helicopter pre-polarization field' disclosed in CN107102367A, a direct current electric field is generated by introducing current into a pre-polarization coil, so that hydrogen nuclei in oil are pre-polarized, and the magnetization intensity of the hydrogen nuclei is increased. The method adopts a small coil of 6-8 meters to generate a pre-polarization field to improve the magnetization intensity, but the pre-polarization field has limited application range and is difficult to be applied to large-scale groundwater exploration.
The ground nuclear magnetic resonance detection method has limited exploration precision and low efficiency, and is difficult to obtain effective nuclear magnetic resonance signals in environments with complex terrains such as cities, plateaus and the like.
Disclosure of Invention
The invention aims to solve the difficult problem that the ground nuclear magnetic resonance measurement is difficult to be carried out by applying a large coil in the environment with complex terrains such as cities, plateaus and the like, and the small coil signal is too weak, and provides a ground nuclear magnetic resonance small coil signal enhancement method based on wave field transformation.
The present invention has been achieved in such a way that,
A method for enhancing a ground nuclear magnetic resonance small coil signal based on wave field transformation, the method comprising:
a. According to the differential relation between the nuclear magnetic resonance signal and the nuclear magnetic resonance response field, a classical transformation formula of the nuclear magnetic resonance response field and the quasi-seismic wave field is utilized to obtain a transformation formula of the nuclear magnetic resonance signal and the quasi-seismic wave field;
b. Solving nuclear magnetic resonance signals and a quasi-seismic wave field transformation equation by a Tikhonov regularization method to realize wave field inverse transformation and obtain quasi-seismic wave field values of all receiving coils;
c. according to the correlation of the water content information reflected by the adjacent receiving coils, respectively taking each receiving coil as a center, and synthesizing aperture based on a green function to obtain a quasi-seismic wave field value synthesized by each receiving coil;
d. based on the wave field transformation theory, the synthesized quasi-seismic wave field value is transformed back to the nuclear magnetic resonance signal value.
Further, the step a specifically includes:
introducing an alternating current with Larmor frequency into the transmitting coil, and generating an excitation field in an underground space to enable hydrogen protons in underground water to enter an excited state; after the current is cut off, the hydrogen protons in transition release energy and gradually return to the low-energy-level balance state, and in the process, the receiving coil on the ground generates induction signals, namely nuclear magnetic resonance signals; constructing a differential relation between nuclear magnetic resonance signals and nuclear magnetic resonance response fields:
（1），
Wherein, Is a diffusion field time variable,/>Is a space variable,/>For nuclear magnetic resonance signals,/>Is a nuclear magnetic resonance response field;
The classical transformation formula of nuclear magnetic resonance response field and quasi-seismic wave field is:
（2），
Wherein, Is a quasi-seismic wave field time variable,/>As pseudo-seismic wave field, the space variable/>, is omittedThen formula (2) is rewritten as:
（3）
Substituting equation (3) into equation (1), To omit the pseudo-seismic wavefield after spatial variation,/>To omit the nuclear magnetic resonance response field after the space variable, a transformation relation between nuclear magnetic resonance signals and quasi-seismic wave fields is obtained:
（4），
discretizing the integration area to integrate Domain division into/>And (3) integrating each segment respectively, and summing to obtain:
（5），
Wherein, For sampling points,/>For/>Nuclear magnetic resonance signal value at time,/>For/>Moment in/>The segmentation interval in the domain is/>Integral kernel function value of/>For/>The segmentation interval in the domain is/>Is a quasi-seismic wave field value; direct calculation/>, using uncertain integration：
（6）。
Further, the step b specifically includes:
The formula (5) is rewritten into a linear equation set form:
（7），
Wherein, Is nuclear magnetic resonance signal value,/>For the integral kernel function value,For the quasi-seismic wave field value, equation (7) represents the quasi-seismic wave field value/>And nuclear magnetic resonance signal value/>A conversion relationship between the two;
Solving the nuclear magnetic resonance signal and the quasi-seismic wave field transformation equation of the formula (7) by applying a Tikhonov regularization method to obtain quasi-seismic wave field values of each receiving coil 。
Further, the step c specifically includes:
the total number of the receiving coils on one measuring line is set as ，/>Marking the 1 st receiving coil position as/> according to the positions of the receiving coils as any positive integerFirst/>Receiving coil position is/>Determining the range of synthetic aperture/>Is that；
In the first placeThe receiving coils are centered, wherein/>Calculating phase and amplitude coefficients:
（8），
Wherein, Is a phase coefficient,/>For the amplitude coefficient,/>Is a phase weighting coefficient,/>Is the amplitude weighting coefficient,/>For/>Receive coil and center coil/>Linear distance of/>Is magnetic permeability,/>Is the relative permeability of the medium,/>Is vacuum permeability,/>Is the conductivity of the medium;
Synthesizing pore diameters based on a Grignard function by using the formula (9):
（9），
Wherein, To divide the central coil/>, within the synthetic aperture rangeQuasi-seismic wavefield values for other receive coils,/>Is the central coil/>And (5) synthesizing a simulated seismic wave field value.
Further, the step d specifically includes:
Based on a wave field transformation theory, the quasi-seismic wave field value synthesized by each receiving coil is transformed back to a nuclear magnetic resonance signal value:
（10），
Wherein, ，/>，/>For each of the receiver coils, synthesized nuclear magnetic resonance signal values,/>And synthesizing a simulated seismic wave field value for each receiving coil.
The invention has the beneficial effects that: the invention provides a ground nuclear magnetic resonance small coil signal enhancement method based on wave field transformation, which solves the problems that in environments with complex terrains such as cities, plateaus and the like, the measurement is difficult to be carried out by applying a large coil technology, and the measurement of the traditional small coil has weak signals, limited detection depth and the like. Compared with the prior art, the invention converts nuclear magnetic resonance signal data into quasi-seismic wave field data based on the correlation of echo signals of the same geologic body on adjacent receiving coils, and then synthesizes the aperture, and the intensity of the signals is obviously enhanced after inverse transformation, thereby improving the accuracy of the subsequent forward analysis result, and compensating the problems of weak signals, low detection efficiency and the like in the traditional small coil measurement, and having important significance for the application and popularization of the ground nuclear magnetic resonance technology.
Drawings
FIG. 1 is a flow chart of a method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a quasi-seismic wavefield time domain discretization provided by an embodiment of the invention;
Fig. 3 is a schematic diagram of a synthetic aperture of a ground nmr receiving coil according to an embodiment of the present invention;
1. The first receiving coil, the second receiving coil, the third receiving coil, the fourth receiving coil, the fifth receiving coil, the sixth receiving coil, the seventh receiving coil and the 8 measuring lines are arranged.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Referring to fig. 1 in combination with fig. 2 and fig. 3, a ground nuclear magnetic resonance small coil signal enhancement method based on wave field transformation comprises the following steps:
a. Constructing a nuclear magnetic resonance signal and a quasi-seismic wave field transformation equation: according to the differential relation between the nuclear magnetic resonance signal and the nuclear magnetic resonance response field, a classical transformation formula of the nuclear magnetic resonance response field and the quasi-seismic wave field is utilized to obtain a transformation formula of the nuclear magnetic resonance signal and the quasi-seismic wave field;
b. Solving nuclear magnetic resonance signals and a quasi-seismic wave field transformation equation by a Tikhonov regularization method to realize wave field inverse transformation and obtain quasi-seismic wave field values of all receiving coils;
c. according to the correlation of the water content information reflected by the adjacent receiving coils, respectively taking each receiving coil as a center, and synthesizing aperture based on a green function to obtain a quasi-seismic wave field value synthesized by each receiving coil;
d. Based on wave field transformation theory, the synthesized quasi-seismic wave field value is transformed back to nuclear magnetic resonance signal value, so that nuclear magnetic resonance signal enhancement is realized, and subsequent forward and backward analysis is facilitated.
Wherein step a specifically comprises:
introducing an alternating current with Larmor frequency into the transmitting coil, and generating an excitation field in an underground space to enable hydrogen protons in underground water to enter an excited state; after the current is cut off, the hydrogen protons in transition release energy and gradually return to the low-energy-level balance state, in the process, the receiving coil on the ground generates induction signals, namely nuclear magnetic resonance signals, the nuclear magnetic resonance signals and nuclear magnetic resonance response fields are diffusion fields, and the differential relation between the nuclear magnetic resonance signals and the response fields is shown in formula (1):
（1），
Wherein, Is a diffusion field time variable,/>Is a space variable,/>For nuclear magnetic resonance signals,/>Is a nuclear magnetic resonance response field;
The classical transformation formula of nuclear magnetic resonance response field and quasi-seismic wave field is formula (2):
（2），
Wherein, Is a quasi-seismic wave field time variable,/>Is a pseudo-seismic wave field. Since this transformation involves only time/>And quasi-seismic wavefield time/>And spatial position/>Independent, omit space variable/>Then formula (2) is rewritten as:
（3），
Substituting the formula (3) into the formula (1) to obtain a transformation relation between nuclear magnetic resonance signals and a quasi-seismic wave field as formula (4):
（4），
Referring to fig. 2, the integration area is discretized to integrate into Domain division into/>In this embodiment, 30 segments are taken, each segment is integrated, and then summed to obtain formula (5):
（5），
wherein the number of sampling points 30,/>For/>Nuclear magnetic resonance signal value at time,/>For/>Moment in/>The segmentation interval in the domain is/>Integral kernel function value of/>For/>The segmentation interval in the domain is/>Is a quasi-seismic wavefield value. Direct calculation/>, using uncertain integration：
（6），
The step b specifically comprises the following steps:
The formula (5) is rewritten into a linear equation set form:
（7），
Wherein, Is nuclear magnetic resonance signal value,/>For the integral kernel function value,For the pseudo-seismic wavefield value, equation (7) gives the pseudo-seismic wavefield value/>And nuclear magnetic resonance signal value/>Conversion relation between the two.
Solving the quasi-seismic wavefield value in equation (7)：
As a further optimization, since the formula (7) is a system of pathological equations, the constraint on the transformation results is poor, and the nuclear magnetic resonance signal valueSmaller fluctuations may cause quasi-seismic wavefield values/>And because of large variation, the solution cannot be carried out by adopting a direct inversion method. An additional constraint is introduced to reduce the pseudo-seismic wave field value/>, by adopting a Tikhonov regularization methodTo improve stability, objective function/>The design is as follows:
Wherein/> Representing the two norms of the vector,/>Is regularization factor,/>For/>A step difference matrix.
Regularization factorThe weight of the constraint in solving is controlled by the objective function/>Is minimized to obtain the pseudo-seismic wave field/>Approximate estimate of/>Can be achieved by solving this equation: /(I)According to the vector derivation rule, it is equivalent to: /(I)Solving to obtain the quasi-seismic wave field value/>, of each receiving coil。
Referring to fig. 3, the step c specifically includes:
the total number of the receiving coils on one measuring line is set as ，/>Marking the 1 st receiving coil position as/> according to the positions of the receiving coils as any positive integerFirst/>Receiving coil position is/>Determining the range of synthetic aperture/>Is that；
In the first placeThe receiving coils are centered, wherein/>Calculating phase and amplitude coefficients:
(8) Wherein/> Is a phase coefficient,/>For the amplitude coefficient,/>Is a phase weighting coefficient,/>Is the amplitude weighting coefficient,/>For/>Receive coil and center coil/>Linear distance of/>Is magnetic permeability,/>Is the relative permeability of the medium,/>Is vacuum permeability,/>Is the medium conductivity.
In this embodiment, the total number of receiving coils on the measuring line 8 is 7, the size of the receiving coils is 3m×3m, the number of turns is 20, the distance between the centers of every two coils is 10m, the position of the first receiving coil 1 is marked as-50, the position of the seventh receiving coil 7 is 50, and the range of the synthetic aperture is determinedFor/>。
Referring to fig. 3, first, phase and amplitude coefficients are calculated centering on the first receiving coil 1:
Wherein/> Is a phase coefficient,/>As magnitude coefficient, phase weighting coefficient/>0.9527, Amplitude weighting coefficient/>Is 0.5018,/>For/>The linear distance of the individual receiving coils from the central coil,For magnetic permeability, relative magnetic permeability of the earth/>Can be approximately 1, vacuum permeability/>For/>Earth conductivity/>For/>。
Synthetic pore size based on green's function:
(9) Wherein/> For synthesizing the quasi-seismic wave field values of other receiving coils except the central coil in the aperture range,/>And the simulated seismic wave field value after the synthesis of the central coil.
And respectively taking the second receiving coil 2, the third receiving coil 3, the fourth receiving coil 4, the fifth receiving coil 5, the sixth receiving coil 6 and the seventh receiving coil 7 as centers to perform synthetic aperture, shifting point by point and covering multiple times to obtain a quasi-seismic wave field value synthesized by each receiving coil.
Further, the step d specifically includes:
Based on a wave field transformation theory, the quasi-seismic wave field value synthesized by each receiving coil is transformed back to a nuclear magnetic resonance signal value:
(10) Wherein/> ，/>，/>For each of the receiver coils, synthesized nuclear magnetic resonance signal values,/>And synthesizing a simulated seismic wave field value for each receiving coil.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (5)
1. A method for enhancing a ground nuclear magnetic resonance small coil signal based on wave field transformation, which is characterized by comprising the following steps:
a. According to the differential relation between the nuclear magnetic resonance signal and the nuclear magnetic resonance response field, a classical transformation formula of the nuclear magnetic resonance response field and the quasi-seismic wave field is utilized to obtain a transformation formula of the nuclear magnetic resonance signal and the quasi-seismic wave field;
b. Solving nuclear magnetic resonance signals and a quasi-seismic wave field transformation equation by a Tikhonov regularization method to realize wave field inverse transformation and obtain quasi-seismic wave field values of all receiving coils;
c. according to the correlation of the water content information reflected by the adjacent receiving coils, respectively taking each receiving coil as a center, and synthesizing aperture based on a green function to obtain a quasi-seismic wave field value synthesized by each receiving coil;
d. based on the wave field transformation theory, the synthesized quasi-seismic wave field value is transformed back to the nuclear magnetic resonance signal value.
2. The method for enhancing a ground nuclear magnetic resonance small coil signal based on wave field transformation according to claim 1, wherein the step a specifically comprises:
introducing an alternating current with Larmor frequency into the transmitting coil, and generating an excitation field in an underground space to enable hydrogen protons in underground water to enter an excited state; after the current is cut off, the hydrogen protons in transition release energy and gradually return to the low-energy-level balance state, and in the process, the receiving coil on the ground generates induction signals, namely nuclear magnetic resonance signals; constructing a differential relation between nuclear magnetic resonance signals and nuclear magnetic resonance response fields:
（1），
Wherein, Is a diffusion field time variable,/>Is a space variable,/>For nuclear magnetic resonance signals,/>Is a nuclear magnetic resonance response field;
The classical transformation formula of nuclear magnetic resonance response field and quasi-seismic wave field is:
（2），
Wherein, Is a quasi-seismic wave field time variable,/>As pseudo-seismic wave field, the space variable/>, is omittedThen formula (2) is rewritten as:
（3），
Substituting equation (3) into equation (1), To omit the pseudo-seismic wavefield after spatial variation,/>To omit the nuclear magnetic resonance response field after the space variable, a transformation relation between nuclear magnetic resonance signals and quasi-seismic wave fields is obtained:
（4）
discretizing the integration area to integrate Domain division into/>And (3) integrating each segment respectively, and summing to obtain:
（5）
Wherein, For sampling points,/>For/>Nuclear magnetic resonance signal value at time,/>For/>Moment in/>The segmentation interval in the domain is/>Integral kernel function value of/>For/>The segmentation interval in the domain is/>Is a quasi-seismic wave field value; direct calculation/>, using uncertain integration：
（6）。
3. The ground nuclear magnetic resonance small coil signal enhancement method based on wave field transformation according to claim 2, wherein step b specifically comprises:
The formula (5) is rewritten into a linear equation set form:
（7），
Wherein, Is nuclear magnetic resonance signal value,/>For integral kernel function value,/>For the quasi-seismic wave field value, equation (7) represents the quasi-seismic wave field value/>And nuclear magnetic resonance signal value/>A conversion relationship between the two;
Solving the nuclear magnetic resonance signal and the quasi-seismic wave field transformation equation of the formula (7) by applying a Tikhonov regularization method to obtain quasi-seismic wave field values of each receiving coil 。
4. A method for enhancing a ground nuclear magnetic resonance small coil signal based on wave field transformation according to claim 3, wherein step c specifically comprises:
the total number of the receiving coils on one measuring line is set as ，/>Marking the 1 st receiving coil position as/> according to the positions of the receiving coils as any positive integerFirst/>Receiving coil position is/>Determining the range of synthetic aperture/>For/>；
In the first placeThe receiving coils are centered, wherein/>Calculating phase and amplitude coefficients:
（8），
Wherein, Is a phase coefficient,/>For the amplitude coefficient,/>Is a phase weighting coefficient,/>For the magnitude weighting factor,For/>Receive coil and center coil/>Linear distance of/>Is magnetic permeability,/>Is the relative permeability of the medium,/>Is vacuum permeability,/>Is the conductivity of the medium;
Synthesizing pore diameters based on a Grignard function by using the formula (9):
（9），
Wherein, To divide the central coil/>, within the synthetic aperture rangeQuasi-seismic wavefield values for other receive coils,Is the central coil/>And (5) synthesizing a simulated seismic wave field value.
5. A method for enhancing a ground nuclear magnetic resonance small coil signal based on wave field transformation as claimed in claim 3, wherein the step d specifically comprises:
Based on a wave field transformation theory, the quasi-seismic wave field value synthesized by each receiving coil is transformed back to a nuclear magnetic resonance signal value:
（10），
Wherein, ，/>，/>For each of the receiver coils, synthesized nuclear magnetic resonance signal values,/>And synthesizing a simulated seismic wave field value for each receiving coil.
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|---|---|---|---|---|
| CN103033849A (en) * | 2012-12-15 | 2013-04-10 | 吉林大学 | Multichannel nuclear magnetic resonance underground water detecting instrument and field work method thereof |
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| US20190285767A1 (en) * | 2016-08-08 | 2019-09-19 | Halliburton Energy Services, Inc. | Dual Zone Nuclear Magnetic Resonance Sensing Device for Subterranean Characterization |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103033849A (en) * | 2012-12-15 | 2013-04-10 | 吉林大学 | Multichannel nuclear magnetic resonance underground water detecting instrument and field work method thereof |
| CN103712071A (en) * | 2013-12-27 | 2014-04-09 | 中国石油化工股份有限公司 | Nuclear magnetic resonance petroleum transmission pipeline leakage hidden danger detecting instrument and detecting method |
| CN106321086A (en) * | 2015-07-02 | 2017-01-11 | 中石化石油工程技术服务有限公司 | Transient measurement method for barefoot well formation resistivity |
| US20190285767A1 (en) * | 2016-08-08 | 2019-09-19 | Halliburton Energy Services, Inc. | Dual Zone Nuclear Magnetic Resonance Sensing Device for Subterranean Characterization |
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| Title |
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| 郭源: "地空电磁-核磁共振联测方法在地层富水性探测中的应用与研究", 山西煤炭, vol. 43, no. 2, 30 June 2023 (2023-06-30), pages 89 - 95 * |
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