CN106556876B - A kind of three-dimensional NMR prestack inversion method based on the excitation of multifrequency off resonance - Google Patents

Abstract

The invention discloses a three-dimensional nuclear magnetic resonance pre-stack inversion method based on multi-frequency offset resonance excitation, which includes: dividing the survey area into the three-dimensional distribution characteristics of the electrical structure and conductivity of the underground medium; determining the excitation of a resonance response signal channel frequency and its Larmor frequency, and determine the frequency deviation between the excitation frequency of the FID signal in other multiple channels and the determined Larmor frequency; extract the real component and quadrature component of the FID signal in each channel and calculate Corresponding phase; establish a forward modeling model in each channel under the condition of off-resonance excitation, and obtain the response kernel function of the corresponding FID signal; construct the inversion objective function and inversion equation in each channel, and analyze the The three-dimensional complex signal inversion is carried out on the FID signal respectively; the inversion results obtained in each channel are correlated and superimposed. The invention simultaneously utilizes the advantages of complex FID signals and off-resonance excitation conditions in inversion resolution.

Description

A 3D NMR Prestack Inversion Method Based on Multi-frequency Off-Resonance Excitation

technical field

The invention relates to the field of applied geophysics, in particular to a three-dimensional nuclear magnetic resonance pre-stack inversion method based on multi-frequency offset resonance excitation.

Background technique

NMR detection is a non-invasive electromagnetic detection method that directly and quantitatively identifies the water content, permeability characteristics and pore structure of underground media by observing the free attenuation signal generated by the macroscopic magnetic moment of hydrogen protons in water after being excited by an artificial radio frequency magnetic field. . At present, nuclear magnetic resonance detection has been widely used in many exploration, engineering and scientific experiment fields such as groundwater exploration, oil well logging, landslide detection and rock sample detection. The condition for NMR to generate resonance is that the excitation frequency of the artificial radio frequency magnetic field is equal to the Larmor frequency. When there is a deviation between the excitation frequency and the Larmor frequency, the resulting signal is called an off-resonance response signal, and the excitation conditions at this time are called off-resonance excitation.

For the observed nuclear magnetic resonance free decay signal (referred to as FID signal), the current interpretation methods mainly include geophysical inversion and imaging. At present, the geophysical inversion interpretation of nuclear magnetic resonance mostly adopts the traditional amplitude inversion method based on resonance excitation conditions, and only the amplitude value of the FID signal is used in the inversion data. However, the FID signal is a complex signal in most practical cases, and more hydraulic characteristic information of the subsurface medium is contained in the real component, quadrature (imaginary) component and phase of the FID signal. Therefore, the use of complex FID signals for nuclear magnetic resonance inversion (complex signal inversion) can obtain more comprehensive information about the hydraulic characteristics of subsurface media. In addition, under off-resonance excitation conditions, the resolution matrix of NMR inversion has higher resolving power, especially the shallow resolving power.

However, in practical applications, there is no mature technical solution for the technical problem of how to simultaneously utilize the advantages of complex FID signals and off-resonance excitation conditions in inversion resolution

Contents of the invention

In order to solve the deficiencies in the prior art, the present invention discloses a three-dimensional nuclear magnetic resonance prestack inversion method based on multi-frequency off-resonance excitation. After the resonance inversion, the inversion results of each channel are correlated and superimposed inversion.

To achieve the above object, the specific scheme of the present invention is as follows:

A three-dimensional nuclear magnetic resonance prestack inversion method based on multi-frequency offset resonance excitation, comprising the following steps:

Step 1: According to the electrical prospecting method and the geological characteristics in the survey area, the survey area is divided into the electrical structure of the underground medium and the three-dimensional distribution characteristics of the conductivity;

Step 2: determining the excitation frequency and its Larmor frequency of a resonance response signal channel, and accordingly determining the frequency deviation between the excitation frequency of the FID signal in other multiple channels and the determined Larmor frequency;

Step 3: Extract the real component Re(e _i ) and the orthogonal (imaginary) component Im(e _i ) of the FID signal in each channel and calculate the corresponding phase Ph(e _i );

Step 4: Establish a forward modeling model in each channel under off-resonance excitation conditions, and obtain the response kernel function corresponding to the FID signal;

Step 5: Construct the inversion objective function and inversion equation in each channel, and perform three-dimensional complex signal inversion on the FID signal in each channel;

Step 6: Carry out correlation and superposition processing on the inversion results obtained in each channel to obtain the three-dimensional shape distribution of underground water body and the local water content parameter m(r, T ₂ ^* ) reflecting the underground water content and permeability coefficient.

Further, in step one, when considering the geological characteristics in the survey area, the possible underground water storage and water-conducting structures and their three-dimensional distribution characteristics are analyzed according to the existing geological data in the survey area.

Further, in step 1, the method for dividing the survey area into the three-dimensional distribution characteristics of the electrical structure and conductivity of the underground medium is the electrical prospecting method, including: carrying out high-density electrical or transient electromagnetic methods in the survey area Electrical prospecting methods.

Further, in step 2, specifically: it is necessary to use multiple excitation frequencies in the measurement area for NMR excitation and observation, and the observed signals are respectively recorded in multiple signal channels, and the multiple excitation frequencies One should be equal to the Larmor frequency in the survey area, denoted as f _L , and the other excitation frequencies f _i (i=1～N-1) have a certain degree of deviation from the Larmor frequency Δf _i =|f _i - f _L |.

Further, in step three, the signal extraction method of the real component and the quadrature component of the FID signal adopts a quadrature lock-in amplification method, and the phase of the FID signal is obtained from its corresponding real component and quadrature component.

Further, in Step 4, establish a forward modeling model in each channel under off-resonance excitation conditions: establish an initial model reflecting underground water content and permeability coefficient based on the geological data obtained in the survey area and the three-dimensional electrical structure of the underground medium.

Further, in step 4, the process of obtaining the response kernel function corresponding to the FID signal is:

Establish an electrical model based on the determined three-dimensional distribution of the resistivity of the underground medium, and use the vector finite element method to dissect and disperse;

Using the three-dimensional vector finite element method to calculate the three-dimensional distribution of the artificial radio frequency excitation magnetic field in each channel corresponding to the excitation frequency; where the excitation frequency is the Larmor frequency channel corresponding to Δf _i = 0;

The response kernel function of the FID signal in each channel is calculated by using the three-dimensional distribution.

Further, in step five, specifically: on the basis of considering the excitation frequency deviation in each channel, the real component and orthogonal component of the FID signal correspond to the real part and imaginary part of the response kernel function in the inversion equation of the respective channel respectively ;

The objective function and inversion equation are constructed by using the three-dimensional complex signal inversion method, and the response signals in each channel are respectively inverted, so as to obtain the local water content parameter m _i (r, T _{2 (i)} ^* ) and m _L (r, T ₂ ^* );

m _i (r,T _2(i) ^* ) and m _L (r,T ₂ ^* ) represent the inversion results of the response signal under off-resonance excitation and Larmor frequency excitation in the i-th channel, respectively.

Further, in Step 6, the method of correlating and superimposing the inversion results obtained in each channel is: selecting the inversion results m _i (r,T _{2(i )} ^* ) are respectively correlated with the inversion result m _L (r, T ₂ ^* ) of the response signal under Moiré frequency excitation, and their normalized cross-correlation coefficient c _i (r) is obtained;

Afterwards, correlation and superposition are used to correlate and superpose the inversion results of the response signals in all channels, so as to obtain the local water content parameter m(r, T ₂ ^* ) that finally reflects the underground water content and permeability coefficient.

The invention proposes a three-dimensional NMR pre-stack inversion method based on multi-frequency offset resonance excitation. At the same time, the advantages of complex FID signals and off-resonance excitation conditions in inversion resolution are utilized.

Beneficial effects of the present invention:

The technical solution proposed by the present invention improves the resolution of the inversion results from the following four levels:

(1) Taking advantage of the advantages of multi-channel observation, the amount of observation data is significantly increased compared with traditional single-frequency (channel) observation, and the inversion resolution is improved from the level of observation data;

(2) The complex signal inversion method is adopted. After the received FID signal is orthogonally decomposed, the complex signal inversion (complex signal inversion) has better vertical resolution and anti-noise characteristics; especially in When the ground conduction property is good, since the orthogonal component of the FID signal is added to the inversion process, the complex signal inversion method has a higher degree of depth resolution;

(3) Due to the use of multi-channel FID signals in the inversion; the data involved in the inversion not only include response signals under Larmor frequency excitation, but also response signals under multiple off-resonance excitations; off-resonance excitations of different frequencies The inversion resolution ability has been improved to varying degrees, especially the shallow resolution;

(4) The correlation superposition method of multi-channel inversion results, "strengthening the strengths and avoiding weaknesses" of the inversion results in each channel, suppressing the inversion plus anomalies in each channel, so as to obtain a clearer and more accurate inversion result.

Description of drawings

Fig. 1 is the implementation process of the present invention.

Detailed ways:

The present invention is described in detail below in conjunction with accompanying drawing:

The invention discloses a three-dimensional nuclear magnetic resonance prestack inversion method based on multi-frequency off-resonance excitation. The method is based on multi-channel nuclear magnetic resonance response signals under resonance excitation and multi-frequency off-resonance excitation. Three-dimensional complex signal inversion is carried out on the response signal; after the inversion, the results in each channel are correlated and superimposed to finally obtain the local water content parameter m(r, T ₂ ^* ) that reflects the underground water content and permeability coefficient. As shown in Figure 1, the specific steps are:

(1) Electrical analysis first, combined with existing geological data and electrical exploration methods, to divide the electrical structure of the underground medium and the three-dimensional distribution of conductivity (resistivity);

(2) Determine a resonant response signal channel and its Larmor frequency, and accordingly determine the frequency deviation between the excitation frequency of the FID signal in other multiple channels and the Larmor frequency;

(3) Extract the real component Re(e _i ) and the quadrature (imaginary) component Im(e _i ) of the FID signal in each channel and calculate the corresponding phase Ph(e _i );

(4) Establish a forward modeling model in each channel under off-resonance excitation conditions, and obtain the kernel function corresponding to the FID signal;

(5) Construct the inversion objective function and inversion equation in each channel, and perform three-dimensional complex signal inversion on the FID signal in each channel;

(6) Correlation and superposition processing is carried out on the inversion results obtained in each channel to obtain the three-dimensional shape distribution of the underground water body and the local water content parameter m(r, T ₂ ^* ) reflecting the underground water content and permeability coefficient.

Among them, step (1) includes the following process: first, analyze the possible underground water storage and water-conducting structures and their three-dimensional distribution characteristics according to the existing geological data in the survey area; secondly, use the existing electrical prospecting data, or Carry out electrical exploration methods such as high-density electrical method or transient electromagnetic method to divide the electrical structure of underground media and the three-dimensional distribution of conductivity (resistivity).

The parameter determination in step (2) requires the excitation and observation of nuclear magnetic resonance with multiple excitation frequencies in the measurement area, and the observed signals are recorded in multiple signal channels, and the number of channels is denoted as N. One of the multiple excitation frequencies should be equal to the Larmor frequency in the survey area, which is recorded as f ₀ , and the other excitation frequencies are recorded as f _i (i=1～N-1). Deviation Δf _i =|f _i -f ₀ |.

The signal extraction method of the real component and the quadrature (imaginary) component of the FID signal in step (3) can adopt the quadrature lock-in amplification method, and the phase of the FID signal is obtained by its corresponding real component and quadrature component. Since the quadrature lock-in amplification method is a mature technology, it will not be repeated here.

In step (4), the method of establishing the forward modeling model in each channel under off-resonance excitation conditions and obtaining the corresponding FID signal response kernel function is as follows:

1) Establish a preliminary model m ₀ (r, T ₂ ^* ) that reflects the underground water content and permeability coefficient according to the geological data analysis obtained in step (1) and the three-dimensional electrical structure of the underground medium;

2) Establish an electrical model according to the three-dimensional distribution of the resistivity of the underground medium determined in step (1), and use the vector finite element method to dissect and separate it; use the three-dimensional vector finite element method to calculate the artificial Three-dimensional Distribution of Radio Frequency Excited Magnetic Field Underground Wherein, Δf _i =0 corresponding to the channel whose excitation frequency is the Larmor frequency. Regarding the separation and calculation method of vector finite element, it is not repeated here because it is a mature technology;

3) For the FID signals in all N receiving channels (including N-1 channels under off-resonance excitation and 1 channel under Larmor frequency excitation), use Calculate the response kernel function K _3D [q, ρ(r), r, Δf _i ] of the FID signal in each channel, and its expression is:

The kernel function K _3D [q, ρ(r), r, Δf _i ] itself is a complex variable function, where q is the NMR excitation pulse moment, ρ(r) is the three-dimensional resistivity distribution function of the underground medium, and r is The three-dimensional coordinates of the underground medium, Δf _i is the deviation between the excitation frequency of the FID signal in the i-th receiving channel and the Larmor frequency, f _i is the excitation frequency of the i-th channel, M ₀ is the static magnetization of water in a unit volume constant, I ₀ is the excitation current intensity, and ζ _TR is the phase difference between the excitation current and the FID signal due to the conductivity of the underground medium. θ _eff(i) is the effective chamfering angle corresponding to the FID signal in the i-th channel, and its expression is:

where γ is the gyromagnetic ratio constant of hydrogen protons in water.

α _i is the inclination angle corresponding to the response signal in the i-th channel, and its expression is:

In step (5), on the basis of considering the excitation frequency deviation in each channel, the three-dimensional complex signal inversion method is used to construct the objective function and inversion equation, and the response signal in each channel is inverted; The local water cut parameters mi ( _r ,T _2(i) ^* ) and m _L (r,T ₂ ^* ) of the local water content rate and permeability coefficient information; _mi (r,T _2(i) ^* ) and m _L (r ,T ₂ ^* ) represent the inversion results of the response signals under off-resonance excitation and Larmor frequency excitation in the i-th channel, respectively.

The constructed inversion objective function is:

The corresponding inverse equation is:

Among them, T _2(i) ^* is the relaxation constant of the FID signal in the i-th channel, m _i (r,T _2(i) ^* ) is the model parameter vector of the i-th channel in all receiving channels, m ₀ ( r,T _2(i) ^* ) is the initial reference model parameter vector, m _i ⁿ (r,T _2(i) ^* ) is the iterative value of the nth step of the inversion iterative formula in the i-th channel, Δm _i ⁿ (r,T _2(i) ^* ) is the increment of the model parameter vector at the n-th inversion iteration in the i-th channel, e _i is the observed data vector in the i-th channel, f[m _i (r ,T _2(i) ^* )] is the observation data vector for forward reconstruction, C is the smooth constraint matrix, λ is the regularization parameter, and D is the observation error matrix for weighting

Among them, ε _i,j is the error of the jth element in the observed data vector e _i in the ith channel. J is the Jacobian matrix for calculating partial derivatives, and the elements J _{i and k} in the matrix are

in, is the jth element in the response vector fitted by the model parameters after the nth iteration, m _i(k) is the kth element in the model parameter vector in the ith channel. Under the condition of considering off-resonance excitation, the corresponding relationship between the observed data vector e _i and the model parameter vector m _i (r,T _2(i) ^* ) in each channel is:

In step (6), the method of correlating and superimposing the inversion results obtained in each channel is as follows: select the inversion results m _i (r, T _2(i) ^* ) corresponding to the response signal under the off-resonance excitation condition Respectively correlate with the inversion result m _L (r, T ₂ ^* ) of the response signal under Moiré frequency excitation and obtain its normalized cross-correlation coefficient c _i (r). Afterwards, correlation and superposition are used to correlate and superpose the inversion results of the response signals in all channels, so as to obtain the local water content parameter m(r, T ₂ ^* ) that finally reflects the underground water content and permeability coefficient. Select the inversion result m _i (r, T ₂ ^* ) in the corresponding channel of the non-optimal response signal, correlate with the inversion result m _L (r, T ₂ ^* ) of the best response signal respectively, and calculate their normalization The mutual (mutual) correlation coefficient c _i (r) of the transformation;

Among them, m _L(k) (r,T ₂ ^* ) is the kth element in the inversion result m _L (r,T ₂ ^* ) vector corresponding to the FID signal under Larmor frequency excitation, m _{i(k )} (r,T _2(i) ^* ) is the kth element in the vector of the inversion result mi ( _r ,T _2(i) ^* ) corresponding to the FID signal excited by the ith off-resonance frequency, M is the dimensionality of the vectors m _L (r,T ₂ ^* ) and _mi (r,T _2(i) ^* ). Finally, correlation and superposition are used to correlate and superpose the inversion results of response signals in all channels, so as to obtain the local water content parameter m(r, T ₂ ^* ) that finally reflects underground water content and permeability coefficient.

Although the specific implementation of the present invention has been described above in conjunction with the accompanying drawings, it does not limit the protection scope of the present invention. Those skilled in the art should understand that on the basis of the technical solution of the present invention, those skilled in the art do not need to pay creative work Various modifications or variations that can be made are still within the protection scope of the present invention.

Claims (9)

1. A three-dimensional nuclear magnetic resonance prestack inversion method based on multi-frequency offset resonance excitation, is characterized in that, comprising the following steps: Step 1: According to the electrical prospecting method and the geological characteristics in the survey area, the survey area is divided into the electrical structure of the underground medium and the three-dimensional distribution characteristics of the conductivity; Step 2: determining the excitation frequency and its Larmor frequency of a resonance response signal channel, and accordingly determining the frequency deviation between the excitation frequency of the FID signal in other multiple channels and the determined Larmor frequency; Step 3: Extract the real component and quadrature component of the FID signal in each channel and calculate the corresponding phase; Step 4: Establish a forward modeling model in each channel under off-resonance excitation conditions, and obtain the response kernel function corresponding to the FID signal; Step 5: Construct the inversion objective function and inversion equation in each channel, and perform three-dimensional complex signal inversion on the FID signal in each channel; Specifically: on the basis of considering the excitation frequency deviation in each channel, the real component and orthogonal component of the FID signal correspond to the real part and imaginary part of the response kernel function in the respective channel inversion equation; The objective function and inversion equation are constructed by using the three-dimensional complex signal inversion method, and the response signals in each channel are respectively inverted, so as to obtain the local water content parameter m _i (r, T _{2 (i)} ^* ) and m _L (r, T ₂ ^* ); m _i (r,T _2(i) ^* ) and m _L (r,T ₂ ^* ) represent the inversion results of the response signal under off-resonance excitation and Larmor frequency excitation in the i-th channel, respectively; Step 6: Carry out correlation and superposition processing on the inversion results obtained in each channel to obtain the three-dimensional shape distribution of the underground water body and the local water content parameter m(r, T ₂ ^* ) reflecting the underground water content and permeability coefficient. 2. A kind of three-dimensional nuclear magnetic resonance prestack inversion method based on multi-frequency offset resonance excitation as claimed in claim 1, it is characterized in that, in step 1, when considering the geological characteristics in the survey area, according to the The existing geological data are used to analyze the possible underground water storage and water-conducting structures and their three-dimensional distribution characteristics. 3. a kind of three-dimensional nuclear magnetic resonance prestack inversion method based on multi-frequency offset resonance excitation as claimed in claim 1, is characterized in that, in step 1, the electrical structure and conductivity of subsurface medium are divided into survey area The method for three-dimensional distribution characteristics is the electrical prospecting method, including: carrying out high-density electrical or transient electromagnetic electrical prospecting methods in the survey area. 4. A kind of three-dimensional nuclear magnetic resonance prestack inversion method based on multi-frequency offset resonance excitation as claimed in claim 1, it is characterized in that, in step 2, specifically: need to use multiple excitation frequencies in the survey area to carry out In the excitation and observation of nuclear magnetic resonance, the observed signals are recorded in multiple signal channels, one of the multiple excitation frequencies should be equal to the Larmor frequency in the measurement area, denoted as f _L , and the other excitation frequencies f _i (i=1˜N-1) has a certain degree of deviation Δf _i =|f _i −f _L | with respect to the Larmor frequency. 5. a kind of three-dimensional NMR prestack inversion method based on multi-frequency offset resonance excitation as claimed in claim 1, is characterized in that, in step 3, the signal extraction method of FID signal real component, quadrature component adopts positive In the lock-in amplification method, the phase of the FID signal is obtained from its corresponding real component and quadrature component. 6. a kind of three-dimensional NMR prestack inversion method based on multi-frequency off-resonance excitation as claimed in claim 1, is characterized in that, in step 4, set up the forward modeling model in each channel under the off-resonance excitation condition : According to the geological data obtained in the survey area and the three-dimensional electrical structure of the underground medium, the initial model reflecting the underground water content and permeability coefficient is established. 7. a kind of three-dimensional nuclear magnetic resonance prestack inversion method based on multi-frequency offset resonance excitation as claimed in claim 6 is characterized in that, in step 4, the response kernel function process of seeking corresponding FID signal is: Establish an electrical model based on the determined three-dimensional distribution of the resistivity of the underground medium, and use the vector finite element method to dissect and disperse; Using the three-dimensional vector finite element method to calculate the three-dimensional distribution of the artificial radio frequency excitation magnetic field in each channel corresponding to the excitation frequency; where the excitation frequency is the Larmor frequency channel corresponding to Δf _i = 0; The response kernel function of the FID signal in each channel is calculated by using the three-dimensional distribution. 8. A kind of three-dimensional NMR pre-stack inversion method based on multi-frequency offset resonance excitation as claimed in claim 1, characterized in that, in step 6, the inversion results obtained in each channel are correlated and superimposed The processing method is as follows: select the inversion result m _i (r,T 2(i) * ) corresponding to the response signal under the off-resonance excitation condition and the inversion result m _L (r,T _2(i) ^* ) of the response signal under the moiré frequency excitation respectively ₂ ^* ) to correlate and obtain its normalized cross-correlation coefficient c _i (r); Afterwards, correlation and superposition are used to correlate and superpose the inversion results of the response signals in all channels, so as to obtain the local water content parameter m(r, T ₂ ^* ) that finally reflects the underground water content and permeability coefficient; <mrow><msub><mi>c</mi><mi>i</mi></msub><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><munderover><mo>&amp;Sigma;</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>M</mi></munderover><msub><mi>m</mi><mrow><mi>L</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></msub><mrow><mo>(</mo><mi>r</mi><mo>,</mo><msubsup><mi>T</mi><mn>2</mn><mo>*</mo></msubsup><mo>)</mo></mrow><msub><mi>m</mi><mrow><mi>i</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></msub><mrow><mo>(</mo><mi>r</mi><mo>,</mo><msubsup><mi>T</mi><mrow><mn>2</mn><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></mrow><mo>*</mo></msubsup><mo>)</mo></mrow></mrow><mrow><munderover><mo>&amp;Sigma;</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>M</mi></munderover><msup><mrow><mo>&amp;lsqb;</mo><msub><mi>m</mi><mrow><mi>L</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></msub><mrow><mo>(</mo><mi>r</mi><mo>,</mo><msubsup><mi>T</mi><mn>2</mn><mo>*</mo></msubsup><mo>)</mo></mrow><mo>&amp;rsqb;</mo></mrow><mn>2</mn></msup><munderover><mo>&amp;Sigma;</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>M</mi></munderover><msup><mrow><mo>&amp;lsqb;</mo><msub><mi>m</mi><mrow><mi>i</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></msub><mrow><mo>(</mo><mi>r</mi><mo>,</mo><msubsup><mi>T</mi><mrow><mn>2</mn><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></mrow><mo>*</mo></msubsup><mo>)</mo></mrow><mo>&amp;rsqb;</mo></mrow><mn>2</mn></msup></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow> Among them, m _L(k) (r,T ₂ ^* ) is the kth element in the inversion result m _L (r,T ₂ ^* ) vector corresponding to the FID signal under Larmor frequency excitation, m _{i(k )} (r,T _2(i) ^* ) is the kth element in the vector of the inversion result mi ( _r ,T _2(i) ^* ) corresponding to the FID signal excited by the ith off-resonance frequency, M is the dimension of vector m _L (r,T ₂ ^* ) and _mi (r,T _2(i) ^* ); <mrow><mi>m</mi><mrow><mo>(</mo><mi>r</mi><mo>,</mo><msubsup><mi>T</mi><mn>2</mn><mo>*</mo></msubsup><mo>)</mo></mrow><mo>=</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><msub><mi>c</mi><mi>i</mi></msub><msub><mi>m</mi><mi>i</mi></msub><mrow><mo>(</mo><mi>r</mi><mo>,</mo><msubsup><mi>T</mi><mrow><mn>2</mn><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></mrow><mo>*</mo></msubsup><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mo>.</mo></mrow> 9. A kind of three-dimensional nuclear magnetic resonance pre-stack inversion method based on multi-frequency offset resonance excitation as claimed in claim 7, is characterized in that, utilizes three-dimensional distribution Calculate the response kernel function K _3D [q,ρ(r),r,Δf _i ] of the FID signal in each channel, and its expression is: The kernel function K _3D [q,ρ(r),r,Δf _i ] itself is a complex variable function, where q is the NMR excitation pulse moment, ρ(r) is the three-dimensional resistivity distribution function of the underground medium, and r is The three-dimensional coordinates of the underground medium, Δf _i is the deviation between the excitation frequency of the FID signal in the i-th receiving channel and the Larmor frequency, f _i is the excitation frequency of the i-th channel, M ₀ is the static magnetization of water in the unit volume constant, I ₀ is the _excitation current intensity, ζ _TR is the phase difference between the excitation current and the FID signal due to the conductivity of the underground medium; chamfer, its expression is: Among them, γ is the gyromagnetic ratio constant of hydrogen proton in water; α _i is the inclination angle corresponding to the response signal in the i-th channel, and its expression is: