CN104360404A - Magnetotelluric regularization inversion method based on different constraint conditions - Google Patents

Abstract

The invention provides a magnetotelluric regularization inversion method based on different constraint conditions. On the basis of traditional regularization inversion, by means of introducing various stable functionals with different properties, the regularization inversion with different constraint conditions is achieved, and the requirement for the magnetotelluric data inversion under various geological conditions is met.

Description

Based on the mt regularization inversion of various boundary conditions

Technical field

The present invention relates to the geophysical probing technique field in geoscience, particularly relate to a kind of mt regularization inversion based on various boundary conditions.

Background technology

Magnetotelluric method is a kind of geophysical exploration method utilizing natural alternating electromagnetic field research earth electrical structure.The method depth of exploration is only relevant with the frequency of electromagnetic field, and cost is low, work is convenient, investigation depth is greatly and not by the shielding of resistive formation.It is very wide that these advantages make the method apply in the research of MAFIC ROCKS IN DEEP CRUST earth mantle electrical structure, hydrocarbon resources generaI investigation, geothermal resource prospecting, the monitoring of earthquake activity omen etc., is a kind of important non-seismic methods method.

Regularization inverting has been proved to be a kind of reliable and stable magnetotelluric method, but in traditional inversion interpretation, the constraint condition of model all adopts Occam constraint condition.Because Occam constraint condition is minimum based on the norm value of model first order derivative or second derivative, the inverse model unusual light of generation, for the geological condition containing clumpy structure (as hydrocarbon-bearing pool etc.), generally can not provide rational inversion result.Therefore need the regularization inversion with various boundary conditions is discussed, to meet the magnetotelluric data inverting under multiple geologic condition.

Summary of the invention

(1) technical matters that will solve

In view of above-mentioned technical matters, the invention provides a kind of mt regularization inversion based on various boundary conditions, with the degree of accuracy of the scope of application and data that improve mt regularization inversion.

(2) technical scheme

The mt regularization inversion that the present invention is based on various boundary conditions comprises: steps A: measured the electricalresistivityρ obtaining search coverage by magnetotelluric method _obsand phase place ; Step B: by the electricalresistivityρ of search coverage _obsand phase place build the initial model m of mt inverting ₀with reference model m _ref, wherein, initial model m ₀with reference model m _refmodel parameter comprise: electricalresistivityρ and degree of depth h; Step C: build relative to reference model m _refstable functional Φ _m; Step D: build Magnetotelluric data d based on stratified model _obsjust drilling the cost functional Φ of data _d, wherein, Magnetotelluric data d _obsfor electricalresistivityρ _obsand phase place the matrix of composition; Step e: based on stable functional Φ _m, cost functional Φ _dwith regularization factors α, build the general objective functional of the regularization inverting of following form: Φ=Φ _d+ α Φ _m, wherein, regularization factors α is arithmetic number; And step F: with initial model m ₀for starting condition, adopt the minimum value of optimization algorithm to general objective function phi to solve, obtain, to should minimum value, being in the value of a series of electricalresistivityρs of different depth h.

(3) beneficial effect

The present invention is based on the mt regularization inversion of various boundary conditions on the basis of traditional regularization inverting, by introducing, there is multiple stable functional of different nature, achieve the regularization inverting with various boundary conditions, meet the magnetotelluric data inverting under multiple geologic condition, the accuracy obtaining data is high.

Accompanying drawing explanation

Fig. 1 is the mt regularization inversion basic flow sheet based on various boundary conditions;

Fig. 2 A is the comparison diagram using the regularization inverse model of least model constraint condition in the present embodiment, Bostic direct inversion model and true model;

Fig. 2 B uses least model in the present embodiment to retrain the MAGNETOTELLURIC RESPONSE ON comparison diagram of regularization inverse model, Bostic direct inversion model and the true model obtained;

Fig. 3 A is the comparison diagram of regularization inverse model, Bostic direct inversion model and the true model that in use the present embodiment, minimal gradient supports constraint condition;

Fig. 3 B uses minimal gradient in the present embodiment to support the MAGNETOTELLURIC RESPONSE ON comparison diagram retraining the regularization inverse model, Bostic direct inversion model and the true model that obtain.

Embodiment

For making the object, technical solutions and advantages of the present invention clearly understand, below in conjunction with specific embodiment, and with reference to accompanying drawing, the present invention is described in more detail.It should be noted that, in accompanying drawing or instructions describe, similar or identical part all uses identical figure number.The implementation not illustrating in accompanying drawing or describe is form known to a person of ordinary skill in the art in art.In addition, although herein can providing package containing the demonstration of the parameter of particular value, should be appreciated that, parameter without the need to definitely equaling corresponding value, but can be similar to corresponding value in acceptable error margin or design constraint.

The present invention is on the basis of traditional regularization inverting.By introducing, there is multiple stable functional of different nature, thus achieve the regularization inverting with various boundary conditions.

In one exemplary embodiment of the present invention, provide a kind of mt regularization inversion based on various boundary conditions.Fig. 1 is according to the process flow diagram of the embodiment of the present invention based on the mt regularization inversion of various boundary conditions.As shown in Figure 1, the present embodiment comprises based on the mt regularization inversion of various boundary conditions:

Steps A: measured the electricalresistivityρ obtaining search coverage by magnetotelluric method _obsand phase place ;

Wherein, electricalresistivityρ _obsand phase place be vector form, the value in vector is a series of measurement data.

Step B: by the electricalresistivityρ of search coverage _obsand phase place build the initial model m of mt inverting ₀with reference model m _ref;

Wherein, initial model m ₀with reference model m _refmodel parameter comprise: electricalresistivityρ and degree of depth h.The stratified model of types of models for obtaining based on Bostic (Bostick) direct inversion method.

It should be noted that, if do not have enough information or condition to provide reference model, reference model m _refalso 0 can be set as.

The stratified model obtained based on Bostic (Bostick) direct inversion method has following form:

$h=\sqrt{{\mathrm{\ρ}}_{\mathrm{obs}}/\mathrm{\ω\μ}}---\left(2\right)$

Wherein, ρ _obswith be respectively and measure by magnetotelluric method the resistivity of search coverage and the observation data of phase place that obtain, ω is angular frequency, and μ is the magnetic permeability in vacuum.

Step C: according to exploration object, build relative to reference model m _refstable functional Φ _m;

Wherein, functional Φ is stablized _mcan be the wherein a kind of of following functional:

(1) least model constraint functional Φ _m1:

${\mathrm{\Φ}}_{m1}={\left|\right|m-m_{\mathrm{ref}}\left|\right|}_{L_2}^2---\left(3\right)$

(2) functional Φ is retrained the most gently _m2:

${\mathrm{\Φ}}_{m2}={\left|\right|\▿(m-m_{\mathrm{ref}})\left|\right|}_{L_2}^2---\left(4\right)$

(3) most Smoothing Constraint functional Φ _m3:

${\mathrm{\Φ}}_{m3}={\left|\right|{\▿}^2\left(m-m_{\mathrm{ref}}\right)\left|\right|}_{L_2}^2---\left(5\right)$

(4) total variation (Total variation, TV) retrains functional Φ _m4:

${\mathrm{\Φ}}_{m4}={\left|\right|\▿(m-m_{\mathrm{ref}})\left|\right|}_{L_1}---\left(6\right)$

(5) the total variation constraint functional Φ revised _m5:

${\mathrm{\Φ}}_{m5}=\sqrt{{\left|\right|\▿(m-m_{\mathrm{ref}})\left|\right|}_{L_1}^2+{\mathrm{\β}}^2}---\left(7\right)$

(6) minimum support (minimum support, MS) retrains functional Φ _m6:

${\mathrm{\Φ}}_{m6}=\frac{{\left|\right|m-m_{\mathrm{ref}}\left|\right|}_{L_2}^2}{{\left|\right|m-m_{\mathrm{ref}}\left|\right|}_{L_2}^2+{\mathrm{\β}}^2}---\left(8\right)$

(7) minimal gradient supports (minimum gradient support, MGS) and retrains functional Φ _m7:

${\mathrm{\Φ}}_{m7}=\frac{{\left|\right|\▿(m-m_{\mathrm{ref}})\left|\right|}_{L_2}^2}{{\left|\right|\▿(m-m_{\mathrm{ref}})\left|\right|}_{L_2}^2+{\mathrm{\β}}^2}---\left(9\right)$

Wherein, m is the model needing to carry out retraining, for L ₂the quadratic sum of norm, for L ₁norm, for gradient operator, β is model roughness regulatory factor, is one to be far smaller than the positive number of 1 (as 10 ^-15).Adopt the first five to plant stablize the inversion result that functional tries to achieve is smooth model solution, and it is rough model solution that employing latter two stablizes the inversion result that functional tries to achieve.

In the early stage in exploration, whether there are mineral reserve to explore search coverage, for avoiding omission to exploit mineral reserve, most Smoothing Constraint functional can be adopted.In later stage exploration, in order to accurately verify mineral reserve reserves, least model can be adopted to retrain functional.

Step D: build Magnetotelluric data d based on stratified model _obsjust drilling the cost functional Φ of data _d;

Datum target functional Φ _dcan be one of them of following two kinds of functionals:

${\mathrm{\Φ}}_{d1}={\left|\right|W_d[d_{\mathrm{obs}}-F\left(m\right)]-X_{*}\left|\right|}_{L_2}^2---\left(10\right)$

${\mathrm{\Φ}}_{d2}={\left|\right|\left[W_d\right[d_{\mathrm{obs}}-F\left(m\right)]-X_{*}||}_{L_1}^2---\left(11\right)$

Wherein, with be respectively L ₁and L ₂the quadratic sum of norm; for Magnetotelluric data; W _dfor the diagonal matrix of observation data standard deviation; X _*for the expectation value of data fitting, for computer simulation data, due to noiseless in data.Therefore X _*=0; For actual observation data, due to containing random noise, meet the χ of theory of probability ²distribution, X _*value be the number M of observation station.

Wherein, F is just calculation of just drilling computing, and just drilling computing F (m) can be: analytical method, method of finite difference and Finite Element.

As adopted analytical method, just drilling computing F (m) can solve in the following way:

$\mathrm{\ρ}=\frac{1}{\mathrm{\ω\μ}}{\left|{\hat{Z}}_1\right|}^2---\left(12\right)$

Wherein, for the wave impedance on ground floor ground, IM and RE represents imaginary part and real part to asking for plural number respectively.For n layer stratified model, the wave impedance on ground floor ground provided by following recursive form:

${\hat{Z}}_i=Z_i\frac{Z_i(1-e^{-2k_i{h}_i})+{\hat{Z}}_{i+1}(1+e^{-2k_i{h}_i})}{Z_i(1+e^{-2k_i{h}_i})+{\hat{Z}}_{i+1}(1+e^{-2k_i{h}_i})}---\left(14\right)$

......

${\hat{Z}}_1=Z_1\frac{Z_1(1-e^{-2k_1{h}_1})+{\hat{Z}}_2(1+e^{-2k_1{h}_1})}{Z_1(1+e^{-2k_1{h}_1})+{\hat{Z}}_2(1+e^{-2k_1{h}_1})}---\left(15\right)$

......

${\hat{Z}}_n=Z_n$

Wherein, Z _i=-i ω μ/k _ibe the intrinsic impedance of i-th layer, be the propagation coefficient of i-th layer, ω is angular frequency, and μ is the magnetic permeability in vacuum, ρ _iand h _ibe respectively resistivity and the thickness of i-th layer.

As adopted method of finite difference and Finite Element, just drilling computing F (m) should solve based on the discrete form of the following differential equation:

$\frac{\∂E_x}{\∂z}+\mathrm{i\ω\μ\σ}{E}_x=0---\left(17\right)$

$\frac{\∂E_y}{\∂z}+\mathrm{i\ω\μ\σ}{E}_y=0---\left(18\right)$

Wherein, ω is angular frequency, and μ is the magnetic permeability in vacuum, and σ is conductivity, E _xand E _ybe respectively the x of electric field intensity, y component.

Step e: based on stable functional Φ _m, cost functional Φ _dwith regularization factors α, build the general objective functional Φ of regularization inverting;

General objective functional Φ has following form

Φ＝Φ _d+αΦ _m(19)

Wherein, regularization factors α is arithmetic number.The present embodiment gets 1.

Step F: with initial model m ₀for starting condition, adopt the minimum value of optimization algorithm to general objective function phi to solve, obtain, to should minimum value, being in the value of a series of electricalresistivityρs of different depth h.

In this step, adopt optimization algorithm to solve general objective functional minimum value, obtain suitable model and inversion interpretation is carried out to magnetotelluric data, wherein just comprise the value of a series of electricalresistivityρs being in different depth h.

Wherein, optimization method can adopt the one in following methods: generalized inverse, singular value decomposition method, method of steepest descent, Newton method, quasi-Newton method, method of conjugate gradient, Trust Region, simulated annealing, genetic algorithm, particle cluster algorithm, evolution algorithmic.About various optimization method, pertinent texts is all described in detail, explains no longer in detail herein.

Fig. 2 A is the comparison diagram using the regularization inverse model of least model constraint condition in the present embodiment, Bostic direct inversion model and true model.Fig. 2 B uses least model in the present embodiment to retrain the MAGNETOTELLURIC RESPONSE ON comparison diagram of regularization inverse model, Bostic direct inversion model and the true model obtained.Wherein, Bostick inverse model and the simple stratified model obtained based on Bostic (Bostick) direct inversion method, do not introduce and stablize functional, and directly solve successively raw data, do not carry out optimization.And Optimization inversion model (the general objective functional in step e) not only introduces the stable functional (most Smoothing Constraint functional) with binding feature, and in solution procedure, carry out successive ignition solved.As can be seen from Fig. 2 A and Fig. 2 B, Optimization inversion model is adopted more to press close to master pattern than traditional Bostick inverse model, and better with the matching of raw data.

Fig. 3 A is the comparison diagram of regularization inverse model, Bostic direct inversion model and the true model that in use the present embodiment, minimal gradient supports constraint condition.Fig. 3 B uses minimal gradient in the present embodiment to support the MAGNETOTELLURIC RESPONSE ON comparison diagram retraining the regularization inverse model, Bostic direct inversion model and the true model that obtain.The most Smoothing Constraint functional being different from that Fig. 2 A and Fig. 2 B adopt, what Fig. 3 A and Fig. 3 B adopted is total variation constraint functional.Can be seen by the contrast of Fig. 3 A and Fig. 2 A, select different stable functionals can obtain the inverse model of different characteristic., can be found by the contrast of Fig. 3 B and Fig. 2 B, new constraint functional does not affect the matching of data meanwhile.

So far, by reference to the accompanying drawings the present embodiment has been described in detail.Describe according to above, those skilled in the art should have the mt regularization inversion that the present invention is based on various boundary conditions and have clearly been familiar with.

In addition, the above-mentioned definition to each element and method is not limited in various concrete structures, shape or the mode mentioned in embodiment, those of ordinary skill in the art can change simply it or replace, such as: except the optimization algorithm provided in literary composition, other optimization algorithm can also be adopted to solve general objective functional minimum value.

In sum, the present invention is on the basis of traditional regularization inverting, by introducing, there is multiple stable functional of different nature, thus achieve the regularization inverting with various boundary conditions, be applicable to the magnetotelluric data (MT) under ground, aviation and oceanographic condition, audio-frequency magnetotelluric magnetic data (AMT), the application under the scenes such as controlled source audio-frequency magnetotelluric data (CSAMT).

Above-described specific embodiment; object of the present invention, technical scheme and beneficial effect are further described; be understood that; the foregoing is only specific embodiments of the invention; be not limited to the present invention; within the spirit and principles in the present invention all, any amendment made, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (10)

1., based on a mt regularization inversion for various boundary conditions, it is characterized in that, comprising:

Steps A: measured the electricalresistivityρ obtaining search coverage by magnetotelluric method _obsand phase place

Step B: by the electricalresistivityρ of search coverage _obsand phase place build the initial model m of mt inverting ₀with reference model m _ref, wherein, initial model m ₀with reference model m _refmodel parameter comprise: electricalresistivityρ and degree of depth h;

Step C: build relative to reference model m _refstable functional Φ _m;

Step D: build Magnetotelluric data d based on stratified model _obsjust drilling the cost functional Φ of data _d, wherein, Magnetotelluric data d _obsfor electricalresistivityρ _obsand phase place the matrix of composition;

Step e: based on stable functional Φ _m, cost functional Φ _dwith regularization factors α, build the general objective functional of the regularization inverting of following form: Φ=Φ _d+ α Φ _m, wherein, regularization factors α is arithmetic number; And

Step F: with initial model m ₀for starting condition, adopt the minimum value of optimization algorithm to general objective function phi to solve, obtain, to should minimum value, being in the value of a series of electricalresistivityρs of different depth h.

2. mt regularization inversion according to claim 1, is characterized in that, in described steps A, and electricalresistivityρ _obsand phase place be vector form, the value in vector is a series of measurement data.

3. mt regularization inversion according to claim 1, is characterized in that, in described step B, and initial model m ₀with reference model m _reftypes of models be the stratified model with following form:

$h=\sqrt{{\mathrm{\ρ}}_{\mathrm{obs}}/\mathrm{\ω\μ}}$

Wherein, ω is angular frequency, and μ is the magnetic permeability in vacuum.

4. mt regularization inversion according to claim 1, is characterized in that, in described step C, stable functional is the wherein one in following functional:

(1) least model constraint functional 1. _m1:

(2) functional Φ is retrained the most gently _m2:

(3) most Smoothing Constraint functional Φ _m3:

(4) total variation constraint functional Φ _m4:

(5) the total variation constraint functional Φ revised _m5:

(6) minimum support constraint functional Φ _m6:

(7) minimal gradient supports constraint functional Φ _m7:

Wherein, m is the model needing to carry out retraining, for L ₂the quadratic sum of norm, for L ₁norm, for gradient operator, β is model roughness regulatory factor.

5. mt regularization inversion according to claim 4, is characterized in that, described model roughness regulatory factor β be far smaller than 1 positive number.

6. mt regularization inversion according to claim 4, is characterized in that:

Whether there are mineral reserve to explore search coverage, adopting most Smoothing Constraint functional; Or

In order to accurately verify mineral reserve reserves, adopt least model constraint functional.

7. mt regularization inversion according to claim 1, is characterized in that, in described step D, and datum target functional Φ _done of them of following two kinds of functionals:

${\mathrm{\Φ}}_{d1}={\left|\right|W_d[d_{\mathrm{obs}}-F\left(m\right)]-X_{*}\left|\right|}_{L_2}^2$

${\mathrm{\Φ}}_{d2}={\left|\right|{[W}_d[d_{\mathrm{obs}}-F\left(m\right)]-X_{*}\left|\right|}_{L_1}^2$

Wherein, with be respectively L ₁and L ₂the quadratic sum of norm; for Magnetotelluric data; W _dfor the diagonal matrix of observation data standard deviation; X _*for the expectation value of data fitting; F is just calculation of just drilling computing, and F (m) is for just to drill computing.

8. mt regularization inversion according to claim 7, is characterized in that, adopts analytical method, is just drilling computing F (m) and adopting following form to solve:

$\mathrm{\ρ}=\frac{1}{\mathrm{\ω\μ}}{\left|{\hat{Z}}_1\right|}^2$

Wherein, for the wave impedance on ground floor ground, IM and RE represents imaginary part and real part to asking for plural number respectively;

For n layer stratified model, the wave impedance on ground floor ground provided by following recursive form:

${\hat{Z}}_i=Z_i\frac{Z_i(1-e^{-2k_i{h}_i})+{\hat{Z}}_{i+1}(1+e^{-2k_i{h}_i})}{Z_i(1+e^{-2k_i{h}_i})+{\hat{Z}}_{i+1}(1-e^{-2k_i{h}_i})}$

……

${\hat{Z}}_1=Z_1\frac{Z_1(1-e^{-2k_1{h}_1})+{\hat{Z}}_2(1+e^{-2k_1{h}_1})}{Z_1(1+e^{-2k_1{h}_1})+{\hat{Z}}_2(1-e^{-2k_1{h}_1})}$

……

${\hat{Z}}_n=Z_n$

Wherein, Z _i=-i ω μ/k _ibe the intrinsic impedance of i-th layer, be the propagation coefficient of i-th layer, ω is angular frequency, and μ is the magnetic permeability in vacuum, ρ _iand h _ibe respectively resistivity and the thickness of i-th layer.

9. mt regularization inversion according to claim 7, is characterized in that, adopts method of finite difference or Finite Element, is just drilling computing F (m) and adopting following form to solve:

$\frac{{\∂E}_x}{\∂z}+\mathrm{i\ω\μ\σ}{E}_x=0$

$\frac{{\∂E}_y}{\∂z}+\mathrm{i\ω\μ\σ}{E}_y=0$

Wherein, ω is angular frequency, and μ is the magnetic permeability in vacuum, and σ is conductivity, E _xand E _ybe respectively the x of electric field intensity, y component.

10. mt regularization inversion according to any one of claim 1 to 9, it is characterized in that, in described step F, optimization method is the one in following methods: generalized inverse, singular value decomposition method, method of steepest descent, Newton method, quasi-Newton method, method of conjugate gradient, Trust Region, simulated annealing, genetic algorithm, particle cluster algorithm and evolution algorithmic.