A transient electromagnetic method low signal-to-noise ratio observation data standard deviation estimation method and system

Abstract

The application provides a transient electromagnetic method low signal-to-noise ratio observation data standard deviation estimation method and system, and belongs to the electromagnetic method detection field.The method comprises the following steps: drawing a decay curve of transient electromagnetic method observation data with time in a double logarithmic coordinate system, determining low signal-to-noise ratio observation data, a fitting segment number and a to-be-fitted observation data number; converting the to-be-fitted observation data to a logarithmic domain; constructing a deviation square sum equation between a logarithmic domain linear fitting function and to-be-fitted observation data in the logarithmic domain; solving a least square fitting function of the deviation square sum equation; calculating a least square fitting function linear domain value of an observation time in a certain fitting segment, and taking the deviation absolute value between the least square fitting function linear domain value and the to-be-fitted observation data at the corresponding observation time as the standard deviation of the to-be-fitted observation data; and until the standard deviations of the observation data of all fitting segments are estimated.The application is favorable for improving the subsequent processing and inversion interpretation precision of transient electromagnetic method data.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic detection, and more specifically, relates to a method and system for estimating the standard deviation of low signal-to-noise ratio observation data using transient electromagnetic methods. Background Technology

[0002] The standard deviation of observational data plays a crucial role in geophysical inversion; specifically, data with smaller standard deviations contribute more to the inversion results. Transient electromagnetic methods (TEM) are a geophysical exploration method widely used in metal ore exploration, hydrogeological surveys, and urban underground space exploration. However, most TEM instruments do not provide the standard deviation of observational data, requiring manual estimation. Currently, the industry typically uses a certain percentage of observations as the standard deviation. TEM observational data exhibits a high signal-to-noise ratio (SNR) in the early stages and a low SNR in later stages. Therefore, the observational data curve is smooth in the early stages, but the smoothness decreases significantly in later stages, even exhibiting jumps. Based on this characteristic, existing methods set a small standard deviation at the initial time, increasing with the increase of observation time. However, this standard deviation setting method has low accuracy and requires a high level of experience from data processing personnel, especially for data with low SNR in later stages, where reasonable estimation of the standard deviation is particularly difficult. Summary of the Invention

[0003] To address the shortcomings of existing technologies, the present invention aims to provide a method and system for estimating the standard deviation of low signal-to-noise ratio observation data using transient electromagnetic methods. This invention addresses the problem that most existing transient electromagnetic method instruments do not provide the standard deviation of observation data, requiring manual estimation of the standard deviation, which is particularly difficult for late-stage data with low signal-to-noise ratios.

[0004] To achieve the above objectives, this invention provides a method for estimating the standard deviation of low signal-to-noise ratio observation data using transient electromagnetic methods, comprising the following steps:

[0005] Step 1: Based on the transient electromagnetic method observation data of a single measuring point and its corresponding observation time, plot the decay curve of the transient electromagnetic method observation data over time in a double logarithmic coordinate system;

[0006] Step 2: Determine the data corresponding to the attenuation curve with smoothness below the preset smoothness threshold as low signal-to-noise ratio observation data, and determine the number of fitting segments and the number of observation data to be fitted based on the slope change of the attenuation curve; wherein, the transient electromagnetic method observation data is magnetic field step response or induced electromotive force.

[0007] Step 3: For the current fitting segment, transform the observed data to be fitted to the logarithmic domain;

[0008] Step 4: Construct the equation for the sum of squared deviations between the logarithmic domain linear fitting function and the logarithmic domain observation data to be fitted;

[0009] Step 5: Solve for the least squares fitting function of the equation for the sum of squared deviations;

[0010] Step 6: Calculate the linear domain value of the least squares fitting function at the observation time within the current fitting segment, and use the absolute value of the deviation between the linear domain value of the least squares fitting function at the observation time and the observation data to be fitted as the standard deviation of the observation data to be fitted.

[0011] Step 7: Move on to the next fitted segment and repeat steps 3 through 6 until the standard deviation of the observed data for all fitted segments has been estimated.

[0012] More preferably, the logarithmic domain linear fitting function is Where a and c are the slope and intercept of the linear fitting function; It is a linear fitting function in the logarithmic domain; For the logarithmic field observation time.

[0013] More preferably, the equation for the sum of squares of the deviations between the logarithmic domain linear fitting function and the logarithmic domain observation data to be fitted is:

[0014]

[0015] Among them, (log 10 (t i ),log 10 (v i () represents the logarithmic domain observation data to be fitted; The logarithmic domain fitting function and the logarithmic domain observation data to be fitted (log 10 (t i ),log 10 (v i The deviation between )); n1 and n2 are the start and end numbers of the observed data of the segment to be fitted; the range of i is [n1, n2].

[0016] On the other hand, the present invention provides a system for estimating the standard deviation of low signal-to-noise ratio observation data using transient electromagnetic methods, comprising:

[0017] The low signal-to-noise ratio observation data determination module is used to plot the decay curve of the transient electromagnetic method observation data over time in a double logarithmic coordinate system based on the transient electromagnetic method observation data of a single measurement point and its corresponding observation time, and to determine the data corresponding to the decay curve with smoothness lower than a preset smoothness threshold as low signal-to-noise ratio observation data; wherein, the transient electromagnetic method observation data is a magnetic field step response or induced electromotive force.

[0018] The fitting segment determination module is used to determine the number of fitting segments and the number of observation data to be fitted based on the slope change of the attenuation curve corresponding to the low signal-to-noise ratio observation data.

[0019] The data transformation module is used to transform the observed data to be fitted to the logarithmic domain for the current fitting segment;

[0020] The least squares fitting function solution module is used to construct the equation of the sum of squares of the deviation between the logarithmic domain linear fitting function and the logarithmic domain observation data to be fitted, and to solve the least squares fitting function of the equation of the sum of squares of the deviation.

[0021] The standard deviation construction module for the observation data to be fitted is used to calculate the value of the least squares fitting function in the linear domain of the observation time within the current fitting segment, and to use the absolute value of the deviation between the value of the least squares fitting function in the linear domain and the observation data to be fitted as the standard deviation of the observation data to be fitted.

[0022] The determination module is used to determine whether the current fitting segment is the last fitting segment. If not, it will switch to the next fitting segment and drive the data transformation module to execute.

[0023] More preferably, the logarithmic domain linear fitting function is Where a and c are the slope and intercept of the linear fitting function; It is a linear fitting function in the logarithmic domain; For the logarithmic field observation time.

[0024] More preferably, the equation for the sum of squares of the deviations between the logarithmic domain linear fitting function and the logarithmic domain observation data to be fitted is:

[0025]

[0026] Among them, (log 10 (t i ),log 10 (v i () represents the logarithmic domain observation data to be fitted; The logarithmic domain fitting function and the logarithmic domain observation data to be fitted (log 10 (t i ),log 10 (v i The deviation between )); n1 and n2 are the start and end numbers of the observed data of the segment to be fitted; the range of i is [n1, n2].

[0027] In summary, compared with the prior art, the above-described technical solutions conceived by this invention have the following advantages:

[0028] Beneficial effects:

[0029] This invention provides a method and system for estimating the standard deviation of low signal-to-noise ratio observation data using transient electromagnetic methods. Based on the fact that the late-stage transient electromagnetic pulse response and step response are both linear functions in the logarithmic domain, and their slopes are independent of parameters such as the source magnetic moment, measurement point location, and half-space medium, a linear function can be constructed in the logarithmic domain to fit the late-stage transient electromagnetic data. The absolute value of the deviation between the measured data and the linear fitting function value is used to approximate the standard deviation of the observation data, conforming to the diffusion law of the transient electromagnetic field. This method can effectively recover the standard deviation of the observation data, which is beneficial for improving the accuracy of subsequent processing and inversion interpretation of transient electromagnetic method data. Attached Figure Description

[0030] Figure 1 This is a flowchart of the method for estimating the standard deviation of low signal-to-noise ratio observation data using transient electromagnetic methods provided in this embodiment of the invention;

[0031] Figure 2(a) is a schematic diagram of 30 observation data of a single measuring point provided in Embodiment 1 of the present invention;

[0032] Figure 2(b) is a schematic diagram of the observation data to be fitted provided in Embodiment 1 of the present invention;

[0033] Figure 2(c) is a schematic diagram of the fitting function with the minimum sum of squared deviations provided in Embodiment 1 of the present invention;

[0034] Figure 3(a) is a schematic diagram of 30 observation data of a single measuring point provided in Embodiment 2 of the present invention;

[0035] Figure 3(b) is a schematic diagram of the observation data to be fitted provided in Embodiment 2 of the present invention;

[0036] Figure 3(c) is a schematic diagram of the fitting function with the minimum sum of squared deviations provided in Embodiment 2 of the present invention. Detailed Implementation

[0037] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0038] Method principle: The late response of the transient electromagnetic method can be approximated by an asymptotic expression; when the underground medium is a homogeneous half-space, the late magnetic field impulse response excited by the magnetic dipole source... If the step response b(t) satisfies the power law, then the asymptotic expressions are Equations (1) and (2), respectively:

[0039]

[0040] b(t)≈c2t -3 / 2 (2)

[0041] in, t is the observation time; m is the magnetic moment; μ0 is the magnetic permeability in vacuum; π is pi; σ is the conductivity of the uniform half-space medium; taking the logarithm to the base 10 of formulas (1) and (2) respectively, we get formulas (3) and (4);

[0042]

[0043] log 10 (b(t))≈log 10 (c2)-1.5log 10 (t)(4)

[0044] As can be seen from formulas (3) and (4), the late transient electromagnetic pulse response and the step response are both linear functions in the logarithmic domain, and their slopes are independent of parameters such as the magnetic moment of the source, the position of the measuring point, and the half-space medium. This indicates that a linear function can be constructed in the logarithmic domain to fit the late transient electromagnetic data. Therefore, the absolute value of the deviation between the measured data and the linear fitting function value can be used to approximate the standard deviation of the observed data.

[0045] However, in practice, data acquisition may cease before the transient electromagnetic field decays to its late stage. Furthermore, the actual subsurface medium is not a homogeneous half-space, but rather primarily composed of layered media with localized electrical anomalies. Considering the actual situation, numerous numerical results indicate that the transient electromagnetic responses acquired at the latest points in the observation time series still satisfy a linear function in the logarithmic domain. Therefore, the absolute value of the deviation between the measured data and the linear fitting function value can still be used as an approximation for the standard deviation of the observed data.

[0046] Based on the principles of the above methods, such as Figure 1 As shown, this invention provides a method for estimating the standard deviation of low signal-to-noise ratio observation data using transient electromagnetic methods, comprising the following steps:

[0047] Step 1: Input the transient electromagnetic observation data v and its corresponding time t for a single measuring point; let the number of data points at this measuring point be n, and denote the j-th data point as (t). j ,v j The range of j is [1, n]; the observed data v is the magnetic field step response b or the induced electromotive force, which is determined by the impulse response. Obtained through conversion;

[0048] Step 2: Plot the decay curve of transient electromagnetic observation data over time in a double logarithmic coordinate system, and identify the data corresponding to the curve with poor smoothness as low signal-to-noise ratio observation data; further determine the number of fitting segments and the corresponding number of data to be fitted based on the change of the curve slope.

[0049] Step 3: For the current fitting segment, input the observation data to be fitted (t)i ,v i ), and transform it to the logarithmic field (log 10 (t i ),log 10 (v i The range of i is [n1, n2], where n1 and n2 are the start and end numbers of the observation data in the fitted segment;

[0050] Step 4: Let the logarithmic domain linear fitting function be... Where a and c are the slope and intercept of the linear fitting function, respectively, the logarithmic domain fitting function is constructed to fit the logarithmic domain observed data (log). 10 (t i ),log 10 (v i Deviation between )) Its sum of squares equation is formula (5):

[0051]

[0052] Step 5: Use the least squares method to find the fitting function that minimizes the sum of squared deviations. That is, the least squares fitting function;

[0053] Step 6: Calculate the log-least-square fitting function Its linear field value With a certain observation data v i The absolute value of the deviation between the two is taken as the observed data v i Standard deviation;

[0054] Step 7: Move on to the next fitting segment and repeat steps 3 through 6 until the standard deviation of the observed data for all fitting segments has been estimated.

[0055] Example 1: Single Fitting Segmentation

[0056] Step 1: Input the induced electromotive force data of a single measuring point and its corresponding time. There are a total of 30 observation times for this measuring point, as shown in Figure 2(a);

[0057] Step 2: Plot the decay curve of induced electromotive force over time in a double logarithmic coordinate system, and determine the 27th to 30th data points as low signal-to-noise ratio observation data; this measurement point has only one fitting segment, and the fitting data is the 25th to 30th data points, as shown in Figure 2(b);

[0058] Step 3: Input the observation data to be fitted and convert it to the logarithmic domain, where n1 and n2 are 25 and 30 respectively, as shown in Figure 2(b) and Table 1;

[0059] Step 4: Let the logarithmic domain linear fitting function be... Construct the fitting function and the logarithmic domain data to be fitted (log 10 (t i ),log 10 (v i Deviation between )) Its sum of squares equation is formula (5):

[0060]

[0061] Step 5: Use the least squares method to solve for the fitting function that minimizes the sum of squared deviations, and obtain... The sum of squared deviations is 0.005, as shown in Figure 2(c);

[0062] Step 6: Calculate the absolute value of the deviation between the fitted function and each observed data in the linear domain, and use it as the standard deviation, as shown in Table 1; Table 1 shows the observed data, fitted data, absolute value of deviation (standard deviation), and percentage standard deviation in a single fitting segment example; the unit of the linear domain observed data in Table 1 is V / (Am) 2 );

[0063] Table 1

[0064]

[0065] Example 2: Two fitted segments

[0066] Step 1: Input the induced electromotive force data of a single measuring point and its corresponding time. There are a total of 30 observation times for this measuring point, as shown in Figure 3(a);

[0067] Step 2: Plot the decay curve of induced electromotive force over time in a double logarithmic coordinate system, and determine the 21st to 30th data points as low signal-to-noise ratio observation data; there are 2 fitting segments for this measurement point, and the fitting data are the 20th to 24th data points and the 25th to 30th data points, as shown in Figure 3(b).

[0068] (1) Fitting segment 1

[0069] Step 3: Input the observation data to be fitted and convert it to the logarithmic domain, where n1 and n2 are 25 and 30 respectively, as shown in Figure 3(b) and Table 2; Table 2 shows the observation data, fitted data, absolute value of deviation (standard deviation), and percentage standard deviation in the fitting segment 1 embodiment; the unit of the linear domain observation data in Table 2 is V / (Am 2 );

[0070] Table 2

[0071]

[0072] Step 4: Let the logarithmic domain linear fitting function be... Construct the fitting function and the logarithmic domain data to be fitted (log10 (t i ),log 10 (v i Deviation between )) Its sum of squares equation is formula (5);

[0073]

[0074] Step 5: Use the least squares method to find the fitting function that minimizes the sum of squared deviations, and obtain... The sum of squared deviations is 0.0081, as shown in Figure 3(c);

[0075] Step 6: Calculate the absolute value of the deviation between the fitted function and each observation data to be fitted in the linear domain, and use it as the standard deviation, as shown in Table 2.

[0076] (2) For the fitted segment 2

[0077] Repeat steps 3 through 6, specifically:

[0078] Step 3: Input the data to be fitted and convert it to the logarithmic domain, where n1 and n2 are 20 and 24 respectively, as shown in Figure 3(b) and Table 3.

[0079] Step 4: Let the logarithmic domain linear fitting function be... Construct the fitting function and the logarithmic domain data to be fitted (log 10 (t i ),log 10 (v i Deviation between )) Its sum of squares is in the form of formula (5):

[0080]

[0081] Step 5: Use the least squares method to find the fitting function that minimizes the sum of squared deviations, and obtain... The sum of squared deviations is 0.0017, as shown in Figure 3(c).

[0082] Step 6: Calculate the absolute value of the deviation between the fitted function and the observed data in the linear domain at each observation time, and use it as the standard deviation, as shown in Table 3.

[0083] Table 3 shows the observed data, fitted data, absolute value of deviation (standard deviation), and percentage standard deviation in the two-part fitting implementation; the unit of the linear domain observed data in Table 3 is V / (Am). 2 );

[0084] Table 3

[0085]

[0086] Those skilled in the art will readily understand that the above description is merely 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 scope of protection of the present invention.

Claims

1. A method for estimating the standard deviation of low signal-to-noise ratio observation data using transient electromagnetic methods, characterized in that, Includes the following steps: Step 1: Based on the transient electromagnetic method observation data of a single measuring point and its corresponding observation time, plot the decay curve of the transient electromagnetic method observation data over time in a double logarithmic coordinate system; Step 2: Determine the data corresponding to the attenuation curve with smoothness below the preset smoothness threshold as low signal-to-noise ratio observation data, and determine the number of fitting segments and the number of observation data to be fitted based on the slope change of the attenuation curve; wherein, the transient electromagnetic method observation data is magnetic field step response or induced electromotive force. Step 3: For the current fitting segment, transform the observed data to be fitted to the logarithmic domain; Step 4: Construct the equation for the sum of squared deviations between the logarithmic domain linear fitting function and the logarithmic domain observation data to be fitted; Step 5: Solve for the least squares fitting function of the equation for the sum of squared deviations; Step 6: Calculate the linear domain value of the least squares fitting function at the observation time within the current fitting segment, and use the absolute value of the deviation between the linear domain value of the least squares fitting function and the observation data to be fitted as the standard deviation of the observation data to be fitted. Step 7: Move to the next fitted segment and repeat steps 3 to 6 until the standard deviation of the observed data for all fitted segments has been estimated; The logarithmic domain linear fitting function is: ;in, a and c The slope and intercept of the linear fitting function; It is a linear fitting function in the logarithmic domain; For the logarithmic field observation time; The equation for the sum of squares of the deviations between the logarithmic domain linear fitting function and the logarithmic domain observed data is: in, The observed data to be fitted is in the logarithmic domain; For the logarithmic domain fitting function and the logarithmic domain observation data to be fitted Deviation between; and The number of the start and end points of the observed data in the segment to be fitted; The range is .

2. A system for estimating the standard deviation of low signal-to-noise ratio observation data using transient electromagnetic methods, characterized in that, include: The low signal-to-noise ratio observation data determination module is used to plot the decay curve of the transient electromagnetic method observation data over time in a double logarithmic coordinate system based on the transient electromagnetic method observation data of a single measurement point and its corresponding observation time, and to determine the data corresponding to the decay curve with smoothness lower than a preset smoothness threshold as low signal-to-noise ratio observation data; wherein, the transient electromagnetic method observation data is a magnetic field step response or induced electromotive force. The fitting segment determination module is used to determine the number of fitting segments and the number of observation data to be fitted based on the slope change of the attenuation curve corresponding to the low signal-to-noise ratio observation data. The data transformation module is used to transform the observed data to be fitted to the logarithmic domain for the current fitting segment; The least squares fitting function solution module is used to construct the equation of the sum of squares of the deviation between the logarithmic domain linear fitting function and the logarithmic domain observation data to be fitted, and to solve the least squares fitting function of the equation of the sum of squares of the deviation. The standard deviation construction module for the observation data to be fitted is used to calculate the value of the least squares fitting function in the linear domain of the observation time within the current fitting segment, and to use the absolute value of the deviation between the value of the least squares fitting function in the linear domain and the observation data to be fitted as the standard deviation of the observation data to be fitted. The determination module is used to determine whether the current fitting segment is the last fitting segment. If not, it will switch to the next fitting segment and drive the data transformation module to execute. The logarithmic domain linear fitting function is: ;in, a and c The slope and intercept of the linear fitting function; It is a linear fitting function in the logarithmic domain; For the logarithmic field observation time; The equation for the sum of squares of the deviations between the logarithmic domain linear fitting function and the logarithmic domain observed data is: in, The observed data to be fitted is in the logarithmic domain; For the logarithmic domain fitting function and the logarithmic domain observation data to be fitted Deviation between; and The number of the start and end points of the observed data in the segment to be fitted; The range is .

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