A method for detecting sea ice thickness based on a Cole-Cole model

Abstract

The application belongs to the technical field of geophysical exploration, and particularly relates to a method for detecting sea ice thickness based on a Cole-Cole model, which comprises the following steps: a central loop transient electromagnetic method exploration device is used; the device is placed on the sea water and the sea ice surface to observe magnetic field data; a Cole-Cole model is introduced on the basis of a pure resistivity model transient electromagnetic method theory to obtain a time-domain transient electromagnetic response of complex resistivity; a theoretical transient electromagnetic response is calculated according to a time-domain transient electromagnetic response of complex resistivity; a measured transient electromagnetic response is obtained; a nonlinear inversion method is used to perform a transient electromagnetic response inversion containing a polarization effect; Cole-Cole model parameters m 水 、τ 水 、c 水 、ρ 水 of sea water are extracted; and the ice layer thickness and the Cole-Cole model parameters of the ice layer are obtained, so that the method is suitable for the exploration of polar sea ice thickness, and the ice thickness is detected by the dielectric difference between ice and water to distinguish the sea ice medium and the sea water medium with similar resistivities, and the method solves the problem of the existing polar ice thickness detection method.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of geophysical exploration, and particularly relates to a method for detecting sea ice thickness based on a Cole-Cole model. BACKGROUND

[0002] In the extremely cold zone of the polar region, the surface of the sea will freeze and be called sea ice. Different from the conventional field exploration environment, most of the polar water area and the coast around the Antarctic are covered with sea ice, forming a unique geological environment. In recent years, among various geophysical exploration methods applied to the geological exploration in the polar environment, there is a related research on the use of transient electromagnetic method to explore the ice thickness and the shape of the glacier. It is of great significance to the cold region and polar exploration to study and distinguish the electromagnetic field propagation characteristics in the ice-water medium in the sea.

[0003] The electrical parameters of water are quite different under different states. The polar geological exploration research is mostly to distinguish the ice and snow water medium through the resistivity difference. However, in addition to the resistivity difference, the relative permittivity of water is also different for different states and types. The resistivity of seawater ranges from 0.1 to 10 Ω·m, and the relative permittivity is 81. The resistivity of sea ice ranges from 10 to 100 Ω·m, and the relative permittivity is 2.5 to 8. Therefore, in some cases, the resistivity of seawater and sea ice may be similar, but compared with the ice in the sea, water is a high polarization medium. If only the pure resistivity is considered to interpret the TEM data, it is sometimes difficult to distinguish the two media, and the interpretation result is quite different from the actual geological environment. Therefore, it is necessary to explore the ice layer through the dielectric property. SUMMARY

[0004] The technical problem to be solved by the application is to provide a method for detecting sea ice thickness based on a Cole-Cole model, which is suitable for the exploration of polar sea ice thickness and can distinguish the sea ice and seawater medium with similar resistivity by detecting the ice thickness through the dielectric difference of ice and water.

[0005] The application is implemented in the following way,

[0006] A method for detecting sea ice thickness based on a Cole-Cole model, which comprises the following steps:

[0007] Step 1: A central loop transient electromagnetic method exploration device is used, the device is placed on the surface of seawater to observe the magnetic field data, and the measured time-domain induced electromotive force data containing noise is sampled, stacked and filtered to remove the noise in the obtained induced electromotive force, so as to prepare for the subsequent inversion operation;

[0008] Step 2: Based on the transient electromagnetic method theory, obtain the expression for the transient electromagnetic response of the one-dimensional layered medium with the center loop, and obtain the transient electromagnetic response in the time domain based on the expression for the transient electromagnetic response of the one-dimensional layered medium with the center loop.

[0009] Step 3: Based on the transient electromagnetic method theory of pure resistivity model, the Cole-Cole model is introduced to obtain the transient electromagnetic response of complex resistivity in the time domain.

[0010] Step four: Based on the theoretical transient electromagnetic response calculated from the time-domain transient electromagnetic response of complex resistivity, and the measured transient electromagnetic response from Step one, a nonlinear inversion method is used to invert the transient electromagnetic response including polarization effects, and the Cole-Cole model parameters m of seawater are extracted. 水 τ 水 c 水 ρ 水 ;

[0011] Step 5: Based on the Cole-Cole model parameters m of seawater obtained in Step 4. 水 τ 水 c 水 ρ 水 A mathematical model of the two-layer structure of sea ice and seawater was established;

[0012] Step 6: Use a transient electromagnetic exploration device to observe magnetic field data on the sea ice surface, and sample, overlay, and filter the measured data;

[0013] Step 7: Based on the theoretical transient electromagnetic response of the time-domain transient electromagnetic response calculation theory of complex resistivity, and the measured transient electromagnetic response of Step 6, a nonlinear inversion method is used to perform transient electromagnetic response inversion with polarization effect, and extract the ice thickness and Cole-Cole model parameters of the ice layer.

[0014] Furthermore, step two specifically includes the following steps:

[0015] 2Ⅰ. A step current is provided by the transmitter, and the induced electromotive force is received by the receiver. The corresponding geological information, the thickness and resistivity of each layer of medium are deduced from the received induced electromotive force.

[0016] Under the condition that the transmitted current is an ideal step signal, the transient electromagnetic response in the frequency domain perpendicular to the receiving point of the center loop in a classical one-dimensional layered medium is expressed as follows:

[0017]

[0018]

[0019]

[0020] Z n =Z n (4)

[0021]

[0022] In the above formula, n is the number of media layers; j = 1, 2, 3, ..., n; r is the distance from the receiving loop to the transmitting loop; h is the height of the center loop above the ground; h j Z represents the thickness of each dielectric layer; a represents the radius of the emission loop; Z represents the thickness of each dielectric layer. j To find the intermediate value of the wave impedance; Z j Let Z be the wave impedance of the j-th layer. 1 It is the wave impedance of the first layer; J k (x) is the k-th order Bézier function; n is the number of layers in the medium; σ is the conductivity; I0 is the amplitude of the emitter loop current; i is the imaginary unit; λ is the Hankel transform parameter; d is the differential sign; ω is the frequency; u is an intermediate quantity; μ0 is the permeability of free space.

[0023] Equation (3) is the recursive expression for the wave impedance from the nth layer to the first layer of the medium. The numerical calculation order is as follows: Z is calculated using equation (2). n The wave impedance Z of the nth layer is calculated using equation (4). n Then calculate Z using equation (2). n-1 Finally, Z is calculated using equation (3). n-1 ,

[0024] Since the upper half-space and the 0th layer are air layers in a uniform half-space environment, σ0 = 0, therefore u0 = λ. With r = 0 and J0(0) = 1 for the center loop device, equation (1) H can be derived based on the above conditions. z (ω) simplifies to:

[0025]

[0026] 2Ⅱ. The Hankel transform of the expression is performed using the Guptasarma-Singh linear numerical 140-point filtering algorithm. The calculation formula is as follows:

[0027]

[0028]

[0029]

[0030] In the above formula, i = 1, 2, 3, ..., l; λ i The location of the sampling point is l; the length of the integration interval is l; W iJ represents the coefficients of a linear filter; k (x) is a k-th order Bézier function; d is the differential symbol; K(λ) is an arbitrary expression, and b is an arbitrary variable. Equation (7) is the format of the Hankel transform. As long as the arbitrary expression is transformed into the format of equation (7) and then the Hankel transform is performed, it is transformed into equation (8). The coefficients of the 140-point Hankel J1 transform linear filter with l = 140 are used for calculation, where a0 = -7.91001919, S0 = 0.087967143957, and the 140-point Hankel weighting coefficients are known. The expression is simplified to:

[0031]

[0032] 2Ⅲ. The frequency domain transient electromagnetic response expression is transformed to the time domain using the piecewise linear approximation cosine transform algorithm to obtain the time domain transient electromagnetic response.

[0033] Furthermore, in step 2Ⅲ, the cosine transform is obtained using the piecewise linear approximation method, and the cosine transform converts the inverse Fourier transform... Simplified to:

[0034]

[0035] The cosine transform and the Fourier transform have similar frequency domain differentiation properties, that is, the cosine transform of tf(t) is jK′(ω), t 2 The cosine transform of f(t) is -K″(ω), which gives:

[0036]

[0037] By using the piecewise linear approximation method, the integration interval [0, ∞) of K(ω) is divided into several segments. The graph of K′(ω) is approximated as several horizontal lines parallel to the x-axis, while the graph of K″(ω) is approximated as several impulse functions. The expression for K″(ω) is:

[0038]

[0039] Substitute the expression for K″(ω) into get:

[0040]

[0041] In the formula, the value of N can be set by the user, and it is the number of sampling points for the frequency. The larger the value of N, the higher the calculation accuracy.

[0042] The frequency-domain transient electromagnetic response expression is transformed to the time domain using the piecewise linear approximation cosine transform algorithm, resulting in the time-domain transient electromagnetic response expression:

[0043]

[0044]

[0045] In the formula, t represents time; Im represents the imaginary part; Re represents the real part; ω represents the frequency.

[0046] Furthermore, replacing the conductivity σ with the complex resistivity in the Cole-Cole model, the mathematical expression of the Cole-Cole model is:

[0047]

[0048] In the formula, ρ(ω) is the complex resistivity, m is the polarizability, a physical quantity describing the charging and discharging speed of the medium, 0 < m < 1; τ is the time constant, a physical quantity describing the sluggishness of the excitation polarization process, with a value range of 0.001 < τ < 100; c is the frequency correlation coefficient, with a value range of 0.1 < c < 0.6; ρ0 is the zero-frequency resistivity, and the three parameters m, τ, and c are the spectral parameters replaced by the Cole-Cole model.

[0049] Furthermore:

[0050] In step four, the square of the absolute value of the difference between the measured transient electromagnetic response and the theoretical transient electromagnetic response is set as the fitness function f(t), that is:

[0051] f(t)=(H L -H S ) 2

[0052] H L H is the theoretical value. S For actual values, constraints are set: 0 < m < 1, 0 < h < 100 (m), 0.1 ≤ c ≤ 0.6, 0.01 ≤ τ ≤ 1 (s). To find the optimal solution, the logarithm of the transient electromagnetic response data is first taken, followed by nonlinear inversion. The minimum value of f(t) is calculated iteratively to obtain the optimal parameters, and the Cole-Cole model parameters m of seawater are extracted. 水 τ 水 c 水 ρ 水 .

[0053] Compared with the prior art, the beneficial effects of this invention are as follows:

[0054] This invention studies and distinguishes the propagation characteristics of electromagnetic fields in water-ice media in the ocean. Compared with traditional polar geological exploration methods that distinguish water-ice media based on resistivity differences, this invention explores ice layers by examining dielectric properties, which can differentiate between seawater and sea ice with similar resistivity. Furthermore, the introduction of polarization effects prevents significant discrepancies between the interpretation results and the actual environment. This is the first time the Cole-Cole model has been applied to the differentiation of water-ice media, facilitating its practical application. This method provides new technical support for polar exploration methods, effectively improving the reliability of ice thickness detection and also promoting the practical application of polarization effects in transient electromagnetic methods. Attached Figure Description

[0055] Figure 1 This is a flowchart of a method for detecting sea ice thickness based on the Cole-Cole model provided in an embodiment of the present invention;

[0056] Figure 2 This is a schematic diagram of a bipolar emission current with a duty cycle of 1:1 provided in an embodiment of the present invention;

[0057] Figure 3 This is the equivalent circuit diagram of the Cole-Cole model provided in the embodiments of the present invention;

[0058] Figure 4 This is a schematic diagram of the transient electromagnetic response of a one-dimensional layered medium with a central loop considering polarization effects, provided in an embodiment of the present invention.

[0059] Figure 5 This is a schematic diagram of a one-dimensional mathematical model of layered media of sea ice and seawater provided in an embodiment of the present invention. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0061] See Figure 1 As shown, a method for detecting sea ice thickness based on the Cole-Cole model is described, the method comprising:

[0062] Step 1: Using a central loop transient electromagnetic method exploration device, the device is placed on the sea surface to observe magnetic field data. The measured time-domain induced electromotive force data containing noise is sampled, superimposed, and filtered to remove noise from the obtained induced electromotive force, in preparation for subsequent inversion operations.

[0063] Step 2: Based on the transient electromagnetic method theory, obtain the expression for the transient electromagnetic response of the one-dimensional layered medium with the center loop, and obtain the transient electromagnetic response in the time domain based on the expression for the transient electromagnetic response of the one-dimensional layered medium with the center loop.

[0064] Step 3: Based on the transient electromagnetic method theory of pure resistivity model, the Cole-Cole model is introduced to obtain the transient electromagnetic response of complex resistivity in the time domain.

[0065] Step four: Based on the theoretical transient electromagnetic response calculated from the time-domain transient electromagnetic response of complex resistivity, and the measured transient electromagnetic response from Step one, a nonlinear inversion method is used to invert the transient electromagnetic response including polarization effects, and the Cole-Cole model parameters m of seawater are extracted. 水 τ 水 c 水 ρ 水 ;

[0066] Step 5: Based on the Cole-Cole model parameters m of seawater obtained in Step 4. 水 τ 水 c 水 ρ 水 A mathematical model of the two-layer structure of sea ice and seawater was established;

[0067] Step 6: Use a transient electromagnetic exploration device to observe magnetic field data on the sea ice surface, and sample, overlay, and filter the measured data;

[0068] Step 7: Based on the theoretical transient electromagnetic response of the time-domain transient electromagnetic response calculation theory of complex resistivity, and the measured transient electromagnetic response of Step 6, a nonlinear inversion method is used to perform transient electromagnetic response inversion with polarization effect, and extract the ice thickness and Cole-Cole model parameters of the ice layer.

[0069] In step one, a center-loop transient electromagnetic method exploration device is used. A 1.0mm diameter conductor is wound with 12 turns of a 2m square loop as the transmitting coil. The receiving coil uses a magnetic probe with an effective area of ​​1750m². The transmitter frequency is 50Hz, the transmitting current is 4.54A, and the off-time is 217μs. The device is placed on the sea surface to observe magnetic field data. The measured time-domain induced electromotive force data, which contains noise, is sampled, superimposed, and filtered to remove noise from the obtained induced electromotive force, preparing for subsequent inversion operations. Compared with other electromagnetic methods, the transient electromagnetic method has advantages such as portability, high precision, high resolution, speed, efficiency, and low cost. The transient electromagnetic method exploration device is used to observe magnetic field data on the sea surface, employing methods such as... Figure 2Using a square wave with a duty cycle of 1:1 and a short turn-off time as the transmission current, a center loop device with high lateral resolution, good coupling, simplicity, light weight, and strong polarization effect is adopted to obtain the transient electromagnetic response of the seawater medium in a one-dimensional uniform half-space of the center loop. The measured data are sampled, power frequency noise is suppressed, random noise is suppressed by superposition and averaging, the fall edge of the turn-off time is corrected, and the data channels are extracted.

[0070] In step two, a center loop device is used, with 1.0mm diameter wire wound into a square loop of 12 turns with a side length of 2m as the transmitting coil. The receiving coil uses a magnetic probe with an effective area of ​​1750m2. The transmitter frequency is selected as 50Hz, the transmitting current is 4.54A, and the turn-off time is 217μs. The following environmental assumptions are made:

[0071] (1) Assume that the polar environment medium is linear and homogeneous and isotropic;

[0072] (2) Assume that the magnetic permeability μ of the polar environment medium is equal to the vacuum magnetic permeability μ0, that is, μ=μ0;

[0073] (3) Assume that the underground medium in the polar environment is a conductive medium, and the volume charge cannot accumulate, i.e., q = 0.

[0074] By providing a step current through a transmitter and receiving the induced electromotive force through a receiver, the corresponding geological information, the thickness and resistivity of each layer of the medium can be deduced from the received induced electromotive force due to the different electrical parameters of the underground medium.

[0075] Based on the principles of transient electromagnetic methods, Maxwell's equations, and the matter equations of electromagnetism, and after reasonable assumptions and simplifications, the expression for the transient electromagnetic response in the frequency domain perpendicular to the receiving point of the central loop in a one-dimensional layered medium is obtained:

[0076]

[0077]

[0078]

[0079] Z n =Z n (4)

[0080]

[0081] In the above formula, j = 1, 2, 3, ..., n; r is the distance from the receiving loop to the transmitting loop; h is the height of the center loop above the ground; h j Let be the thickness of each medium layer; 'a' be the radius of the emission loop, which is a rectangular loop with side length L. Zj To find the intermediate value of the wave impedance; Z j Let Z be the wave impedance of the j-th layer. 1 It is the wave impedance of the first layer; J k (x) is the k-th order Bézier function; n is the number of layers in the medium; σ is the conductivity; I0 is the amplitude of the emitter loop current, i is the imaginary unit; λ is the Hankel transform parameter, d is the differential sign; ω is the frequency; u is an intermediate quantity; μ0 is the permeability of free space.

[0082] Equation (3) is the recursive expression for the wave impedance from the nth layer to the first layer of the medium. The numerical calculation order is as follows: Z is calculated using equation (2). n The wave impedance Z of the nth layer is calculated using equation (4). n Then calculate Z using equation (2). n-1 Finally, Z is calculated using equation (3). n-1 .

[0083] Since the upper half-space and the 0th layer are air layers in a uniform half-space environment, σ0 = 0, therefore u0 = λ. The center loop device has r = 0 and J0(0) = 1. Based on the above conditions, H can be... z (ω) simplifies to:

[0084]

[0085] The expression contains the integral of the Bézier function J1(λa). The integral of such a high-frequency oscillating function with a relatively slow decay rate is generally calculated using mathematical numerical filtering methods, because the integral containing a first-order Bézier function cannot be solved analytically.

[0086] H z (ω)integral interior It also contains λ, ω, μ0, σ j h j There are five parameters, among which λ is an important parameter of the Hankel transform.

[0087] Numerical methods for calculating Hankel integrals include the Guptasarma-Singh numerical filtering transform and the Anderson numerical filtering transform. The Guptasarma-Singh filter coefficients are significantly superior to the Anderson filter coefficients in terms of computational speed and accuracy. Therefore, the Guptasarma-Singh linear numerical 140-point filtering algorithm is used to perform a Hankel transform on the expression. The calculation formula is as follows:

[0088]

[0089]

[0090]

[0091] In the above formula, i = 1, 2, 3, ..., l; here λ i The location of the sampling point is l; the length of the integration interval is l; W i These are the coefficients of a linear filter. The coefficients of a 140-point Hankel J1 transform linear filter with l = 140 are calculated, where a0 = -7.91001919, S0 = 0.087967143957, and the 140-point Hankel weighting coefficients are known. The expression simplifies to:

[0092]

[0093] The sine and cosine transforms have relatively short computation time and meet the required accuracy. In the one-dimensional forward modeling of the transient electromagnetic method, based on the characteristic that the real part of some expressions in the quadratic field response function is an even function and the imaginary part is an odd function, the Fourier transform can be simplified to a sine and cosine transform.

[0094] The cosine transform is obtained by using the piecewise linear approximation method. The cosine transform is essentially the inverse Fourier transform.

[0095] Simplified to:

[0096]

[0097] The cosine transform and the Fourier transform have similar frequency domain differentiation properties, that is, the cosine transform of tf(t) is jK′(ω), therefore t 2 The cosine transform of f(t) is -K″(ω), therefore we get:

[0098]

[0099] The piecewise linear approximation method divides the integration interval [0, ∞) of K(ω) into several segments. As long as the interval between each segment is small enough, K(ω) can be approximated by several piecewise linear segments. Thus, the graph of K′(ω) approximates several horizontal lines parallel to the x-axis, while the graph of K″(ω) approximates several impulse functions. The expression for K″(ω) is:

[0100]

[0101] Substituting equation (13) into equation (12), we get:

[0102]

[0103] In the formula, the value of N can be set by the user, and it is the number of sampling points for the frequency. The larger the value of N, the higher the calculation accuracy.

[0104] The frequency-domain transient electromagnetic response expression is transformed to the time domain using the piecewise linear approximation cosine transform algorithm, resulting in the time-domain transient electromagnetic response expression:

[0105]

[0106]

[0107] In the formula,

[0108] Based on the transient electromagnetic method theory of the pure resistivity model mentioned above, the Cole-Cole model is introduced. The Cole-Cole model is a model that closely matches the IP phenomenon, and its simulated equivalent circuit is as follows: Figure 3 As shown, the mathematical expression of the Cole-Cole model is:

[0109]

[0110] In the formula, m is the polarizability, a physical quantity describing the speed of charging and discharging of the medium, 0 < m < 1; τ is the time constant, a physical quantity describing the sluggishness of the excitation polarization process, generally taking a value range of 0.001 < τ < 100; c is the frequency correlation coefficient, generally taking a value range of 0.1 < c < 0.6; ρ0 is the zero-frequency resistivity, and the three parameters m, τ, and c are the spectral parameters of the Cole-Cole model.

[0111] In step two, σ represents pure conductivity, which is the reciprocal of pure resistivity. The Cole-Cole model provides complex resistivity, which includes the parameter of polarizability. Replacing pure resistivity with complex resistivity introduces polarizability, which reflects the difference in dielectric properties of the medium. Therefore, the medium can be distinguished from a dielectric perspective by comparing polarizability. Substituting the spectral parameters of the Cole-Cole model into the definition of complex resistivity allows us to replace the original pure resistivity model with a complex resistivity model expressed by the Cole-Cole model. Further programming and simulation calculations yield the transient electromagnetic responses of two polar environment geological models that consider the dielectric properties of polar geological environments. Let the radius of the transmitting loop be 100m, the transmitting current be 10A, and the area of ​​the receiving loop be 1m². 2 The observation time is set to 10. -7 Reaching 10 seconds -2 For 100 time points, the transient electromagnetic response of the first layer (m=0.1, τ=0.01s, c=0.6, ρ=100Ω·m) and the second layer (m=0.7, τ=0.01s, c=0.6, ρ=10Ω·m) were calculated. A schematic diagram of the one-dimensional layered medium transient electromagnetic response of the Cole-Cole model center loop is introduced, as shown in the figure. Figure 4 As shown.

[0112] The nonlinear inversion methods used in steps four and seven above, such as genetic algorithms, are optimization methods. Using genetic algorithms for nonlinear inversion, the parameters of the Cole-Cole model, which minimize errors, can be calculated from the measured induced electromotive force. This allows for the inversion of transient electromagnetic responses with polarization effects. Genetic algorithms employ population search techniques, applying a series of genetic operations such as selection, crossover, and mutation to the current population to generate a new generation, gradually evolving the population to a state containing or approaching the optimal solution. The fitness function f(t) is set as the square of the absolute value of the difference between the measured transient electromagnetic response and the theoretical transient electromagnetic response, i.e.:

[0113] f(t)=(H L -H S ) 2 (18)

[0114] In equation (18), H L H is the theoretical value. S These are actual values. Set constraints: 0 < m < 1, 0 < h < 100 (m), 0.1 ≤ c ≤ 0.6, 0.01 ≤ τ ≤ 1 (s), and search for the optimal solution. Since the transient electromagnetic response value may be on the order of less than 10... -6 The value may be less than the fitness function deviation. Therefore, the transient electromagnetic response data is first logarithmized, and then nonlinear inversion is performed. According to formula (18), the minimum value of f(t) is calculated iteratively to obtain the optimal parameters and extract the Cole-Cole model parameters m of seawater. 水 τ 水 c 水 ρ 水 ;

[0115] Step 5: Based on the known m 水 τ 水 c 水 ρ 水 Establish mathematical models for sea ice and seawater media, such as Figure 5 As shown, where m 水 τ 水 c 水 ρ 水 The values ​​for m have already been obtained in the previous step. 冰 τ 冰 c 冰 ρ 冰 The values ​​for ice thickness h will be extracted in the next step;

[0116] The transient electromagnetic method exploration device was used again to observe magnetic field data on the sea ice surface. The first time, only the transient electromagnetic response of the seawater was measured. The parameters involved in the forward and inverse processes are m. 水 τ 水c 水 ρ 水 This study measures the transient electromagnetic response of a two-layer structure of sea ice and seawater. The parameters involved in the forward and inverse steps include m. 冰 τ 冰 c 冰 ρ 冰 And ice thickness h. A square wave with a duty cycle of 1:1 and a short turn-off time is used as the transmitting current. A center loop device with high lateral resolution, good coupling, simplicity, light weight, and strong polarization effect is used to obtain the one-dimensional transient electromagnetic response of the center loop between sea ice and seawater layered medium. The measured data are sampled, power frequency noise is suppressed, random noise is suppressed by superposition and averaging, the fall edge of the turn-off time is corrected, and the data channels are extracted.

[0117] Similarly, a nonlinear inversion method is used to invert the transient electromagnetic response with polarization effects. The square of the absolute value of the difference between the measured and theoretical transient electromagnetic responses is set as the fitness function f(t) to find the optimal solution. Since the value of the transient electromagnetic response may be on the order of 10... -6 The value may be smaller than the fitness function deviation. Therefore, the transient electromagnetic response data is first logarithmized, and then nonlinear inversion is performed to obtain the Cole-Cole model parameters m of sea ice. 冰 τ 冰 c 冰 ρ 冰 And the optimal solution for ice layer thickness h, since the polarizability of seawater is significantly higher than that of sea ice, thus realizing the distinction between ice and water media by dielectric properties.

[0118] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for detecting sea ice thickness based on the Cole-Cole model, characterized in that, The method includes: Step 1: Using a central loop transient electromagnetic method exploration device, the device is placed on the sea surface to observe magnetic field data. The measured time-domain induced electromotive force data containing noise is sampled, superimposed, and filtered to remove noise from the obtained induced electromotive force, in preparation for subsequent inversion operations. Step 2: Based on the transient electromagnetic method theory, obtain the expression for the transient electromagnetic response of the one-dimensional layered medium with the center loop, and obtain the transient electromagnetic response in the time domain based on the expression for the transient electromagnetic response of the one-dimensional layered medium with the center loop. Step 3: Based on the transient electromagnetic method theory of pure resistivity model, the Cole-Cole model is introduced to obtain the transient electromagnetic response of complex resistivity in the time domain. Step four: Based on the theoretical transient electromagnetic response calculated from the time-domain transient electromagnetic response of complex resistivity, and the measured transient electromagnetic response from step one, a nonlinear inversion method is used to invert the transient electromagnetic response including polarization effects, and the Cole-Cole model parameters of seawater are extracted. , , , ; Step 5: Based on the Cole-Cole model parameters of seawater obtained in Step 4. , , , A mathematical model of the two-layer structure of sea ice and seawater was established; Step 6: Use a transient electromagnetic exploration device to observe magnetic field data on the sea ice surface, and sample, overlay, and filter the measured data; Step 7: Based on the theoretical transient electromagnetic response of the transient electromagnetic response in the time domain of complex resistivity and the measured transient electromagnetic response in Step 6, the transient electromagnetic response with polarization effect is inverted using a nonlinear inversion method to extract the ice thickness and the Cole-Cole model parameters of the ice layer. Step two specifically includes the following steps: 2Ⅰ. A step current is provided by the transmitter, and the induced electromotive force is received by the receiver. The corresponding geological information, the thickness and resistivity of each layer of medium are deduced from the received induced electromotive force. Under the condition that the transmitted current is an ideal step signal, the transient electromagnetic response in the frequency domain perpendicular to the receiving point of the center loop in a classical one-dimensional layered medium is expressed as follows: （1）， （2）， （3）， （4）， （5）， In the above formula, The number of layers in the medium; ; The distance from the receiving loop to the transmitting loop; The height of the center loop above the ground; The thickness of each medium layer; The radius of the emission loop; To determine the intermediate value of wave impedance; Let J be the wave impedance of the j-th layer. It is the wave impedance of the first layer; for Bézier function of order; The number of layers in the medium; Electrical conductivity; This represents the amplitude of the transmitting loop current. The imaginary unit; These are the parameters of the Hankel transform. The differential symbol; For frequency; This is an intermediate quantity; The vacuum permeability; Equation (3) is the recursive expression for the wave impedance from the nth layer to the first layer of the medium. The numerical calculation order is as follows: calculate using equation (2). The impedance of the nth layer can be calculated using equation (4). Then calculate using equation (2) Finally, the result is calculated using equation (3). , Since the upper half-space and the 0th layer are air layers in a uniform half-space environment, therefore , and thus , ; center return line device ,and Based on the above conditions, equation (1) can be rewritten. Simplified to: （6）， 2Ⅱ. The Hankel transform of the expression is performed using the Guptasarma-Singh linear numerical 140-point filtering algorithm. The calculation formula is as follows: （7）， （8）， （9）， In the above formula, ; The location of the sampling point; The length of the integration interval; These are the coefficients of a linear filter; for Bézier function of order; The differential symbol; For any expression, and at the same time For any variable, equation (7) is the format of the Hankel transformation. By transforming any expression into the format of equation (7) and performing the Hankel transformation, we obtain equation (8). Hankel's 140 points The coefficients of the transformed linear filter are calculated, where... , Given the 140-point Hankel weighting coefficients, the expression simplifies to: （10）； 2Ⅲ. The frequency domain transient electromagnetic response expression is transformed to the time domain using the piecewise linear approximation cosine transform algorithm to obtain the time domain transient electromagnetic response.

2. The method for detecting sea ice thickness based on the Cole-Cole model according to claim 1, characterized in that: In step 2Ⅲ, the cosine transform is obtained using the piecewise linear approximation method, and the cosine transform is the inverse Fourier transform. Simplified to: ， The cosine transform and the Fourier transform have similar frequency domain differentiation properties, namely The cosine transform is , The cosine transform is ,get: ， Using the broken line approximation method The integration interval [0, ∞) is divided into several segments. The image is approximated by several horizontal lines parallel to the x-axis, while The graph is approximated by several impulse functions. The expression is: ， Will Substituting the expression ,get: ， In the formula, the value of N can be set by the user, and it is the number of sampling points for the frequency. The larger the value of N, the higher the calculation accuracy. The frequency-domain transient electromagnetic response expression is transformed to the time domain using the piecewise linear approximation cosine transform algorithm, resulting in the time-domain transient electromagnetic response expression: （15）， （16）， In the formula, , For time; It is the imaginary part; For real part; For frequency.

3. The method for detecting sea ice thickness based on the Cole-Cole model according to claim 2, characterized in that, Complex resistivity replacing conductivity in the Cole-Cole model The mathematical expression for the Cole-Cole model is: ， In the formula, It is complex resistivity. Polarizability is a physical quantity that describes the rate of charging and discharging of a dielectric medium. ; The time constant is a physical quantity describing the sluggishness of the excited polarization process, and its value ranges from 1 to 2. ; This is the frequency correlation coefficient, with a value range of [value range missing]. ; Zero-frequency resistivity, , , The three parameters are the spectral parameters replaced by the Cole-Cole model.

4. The method for detecting sea ice thickness based on the Cole-Cole model according to claim 3, characterized in that: In step four, the square of the absolute value of the difference between the measured transient electromagnetic response and the theoretical transient electromagnetic response is set as the fitness function f(t), that is: ， This is the theoretical value. Set the constraint range for the actual value. , (m), , (s) To find the optimal solution, first take the logarithm of the transient electromagnetic response data, then perform nonlinear inversion, and iteratively calculate... The minimum value is obtained to get the optimal parameters, and the Cole-Cole model parameters of seawater are extracted. , , , .

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