CN116127287A - Noise reduction method for resistivity method exploration signals - Google Patents

Abstract

The application provides a noise reduction method for resistivity method exploration signals, which comprises the following steps: s1, decomposing a resistivity method exploration signal by adopting an empirical mode decomposition method to obtain a plurality of IMF components; s2, fitting a plurality of IMF components by using a moving average and a least square method; and S3, superposing the processing result of the step S2 to obtain a recombined signal. According to the scheme, noise interference in the exploration data can be effectively reduced, the quality of the exploration data is improved, the inversion result of the abnormal body based on the exploration data is more accurate, and the safety of engineering construction is improved.

Description

Noise reduction method for resistivity method exploration signals

Technical Field

The application relates to the technical field of geological exploration, in particular to a noise reduction method for resistivity exploration signals.

Background

The resistivity method is a geophysical method for solving the geological problem by observing and researching the distribution rule of a stable current field artificially built in the ground based on the electrical difference (resistivity) of a geotechnical medium. The method is widely applied to the fields of resource exploration, engineering geological exploration, geological disaster investigation and the like, and the high signal-to-noise ratio data is a precondition for obtaining good exploration effects.

At present, signals collected by conventional resistivity equipment are composite signals carrying interference sources, including manually established direct current source signals and external random noise signals, and if the signals are not processed and directly used as abnormal body inversion, false abnormal bodies or abnormal body position identification errors can be caused.

Therefore, in order to reduce the influence of noise on the exploration result, the collected data must be subjected to denoising treatment; at present, positive and negative period power supply and arithmetic average are often adopted to eliminate interference of external scattered current and excitation on data acquisition, but the method has a certain inhibition effect only when external interference is constant or symmetric in a regular field in a short time, is complex and changeable for external interference field sources, has time-varying interference signals, and has unobvious resistivity data effects with different characteristics at different spatial positions.

Analyzing field electromagnetic signals and noise characteristics by using the kaliophlomis glabra, selecting db6 wavelet base to inhibit baseline drift, extracting noise similar to discharge triangular wave by using sym8 mother wavelet and a hard threshold value, finally obtaining the effect of inhibiting part of artificial noise, and verifying that the signal to noise ratio of electromagnetic data is improved after wavelet change denoising. Wang Yongbing and the like, the quality of data acquired by the deep exploration electric instrument based on 2n pseudo-random signals is improved by using a method combining modern digital signal processing and analog signals, and the defect of weak signals of the electric instrument is overcome. Xu Xiaojie, and the experimental results show that the 3 methods can suppress random noise in the high-density electrical method data, and the noise-resistant effect is better than the result obtained by the former two robust inversion.

Zhang Liang, tang Jingtian, etc. use a method of combining Variable Modal Decomposition (VMD) and Data Driven Tight Frame (DDTF) to process noise on Audio Magnetotelluric (AMT) exploration data, verify the V-DDTF, compare with other methods, and finally use a signal to noise ratio and a Nyquist diagram to make an evaluation, which proves that the V-DDTF method can obtain a better denoising effect and has the best performance. Zhang Liang, xicellet, etc. propose a residual network (res net) with deep structure and good fitting ability. This approach requires higher quality training data, but the latter processing can better denoise the Magnetotelluric (MT), which can be significant in severe interference with MT data.

The scholars all use a specific method to achieve the noise reduction effect, but the noise reduction effect is improved only to a limited extent; therefore, a new noise reduction method is needed to effectively remove noise interference existing in resistivity exploration data and improve exploration data quality.

Disclosure of Invention

The purpose of the application is to provide a noise reduction method for resistivity exploration signals, so that noise interference in resistivity exploration data is effectively removed, and exploration data quality and inversion accuracy based on the exploration data are improved. The specific technical scheme is as follows:

the application provides a noise reduction method for resistivity method exploration signals, which comprises the following steps:

s1, decomposing a resistivity method exploration signal by adopting an empirical mode decomposition method to obtain a plurality of IMF components;

s2, fitting a plurality of IMF components by using a moving average and a least square method;

and S3, superposing the processing result of the step S2 to obtain a recombined signal.

According to the noise reduction method for the resistivity method exploration signal, according to the time sequence characteristics of the original exploration signal, the original exploration signal is decomposed into IMF components with different frequencies by using an EMD algorithm; the exploration signals are smoother by using the moving average, the interference of discrete values and random noise is reduced, the exploration signals are more concentrated by using the least square method, and the influence of discrete data on exploration data is further reduced; therefore, by the scheme, noise interference in the exploration data can be effectively reduced, the quality of the exploration data is improved, the inversion result of the abnormal body based on the exploration data is more accurate, and the safety of engineering construction is improved.

In some embodiments of the present application, the step 1 includes:

step S11, searching to obtain the maximum value and the minimum value in the original exploration signal u (t), and obtaining an upper envelope v formed by the maximum value by using cubic spline interpolation ₁ And a lower envelope v formed by a minimum value ₂ ；

Step S12, calculating the mean value of the upper envelope curve and the lower envelope curve, and the difference h between the original exploration signal and the mean value ₁ (t)；

Step S13, judging the difference h ₁ (t) whether the IMF component condition is satisfied, if so, jumping to step S14, if not, letting u (t) =h ₁ (t) repeating the steps S11-S12 until the difference value meets the IMF condition;

step S14, let h ₁ (t) as a first IMF component, let u ₁ (t)＝u(t)-h ₁ (t) repeating steps S11-S13 to obtain a second IMF component h ₂ (t)；

Let u ₂ (t)＝u ₁ (t)-h ₂ And (t) and the like, stopping decomposing when the termination condition is met, and obtaining all IMF components and residual phases.

In some embodiments of the present application, step S1 further comprises length expanding the raw survey signal prior to step S11.

In some embodiments of the present application, the termination condition is: the rest part of signals are single-frequency signals or smaller than a threshold value SD;

wherein I represents the number variable of IMF components, I represents the total number of IMF components obtained by decomposition, i=1, 2, l, I, u _i-1 (t)、u _i (t) represents the residual data after removal of the 1 st to i-1 st IMF components and the 1 st to i th IMF components from the original survey signal u (t), respectively, ε [0.2,0.3 ]]。

In some embodiments of the present application, the following operation is performed on each IMF component in step S2:

and intercepting part of exploration signals in the IMF component according to the sampling time to form a cell interval, enabling the intermediate value between the cells to be equal to the average value of the cell interval, sliding the cell interval on the time sequence of the IMF component according to the step length=1, and processing each data of the IMF component to obtain the IMF component after the sliding average.

In some embodiments of the present application, the following operations are further performed on each IMF component after the moving average processing in step S2:

curve fitting is performed on N data points of each moving average processed IMF component, assuming a curve equation of f (x) =a ₀ +a ₁ x+L+a _n x ⁿ (N < N), substituting N data points into the curve equation to obtain a form equation:

A ^T Ax＝A ^T b

wherein a is ₀ 、a ₁ 、a _n All represent coefficients of curve fitting, x ⁿ Respectively representing the first and nth unknowns of the curve equation, a represents the relationship matrix, T represents the transpose of the matrix, x= (a) ₀ ,a ₁ ,L,a _n ) ^T ，b＝(y ₀ ,y ₁ ,L,y _n ) ^T ，y ₀ 、y ₁ 、y _n Respectively representing a first predicted value, a 2 nd predicted value and an n+1st predicted value obtained by fitting;

let coefficient determinant |C of formal equation ^T C|noteq0, C is a coefficient matrix representing the equation.

Drawings

In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

In fig. 1: (a) A model built for example 1 of the present application, (b) theoretical data obtained based on the model;

in fig. 2: (a) is simulation data with a signal to noise ratio of 5, (b) is simulation data with a signal to noise ratio of 20, (c) is simulation data with a signal to noise ratio of 30, and (d) is simulation data with a signal to noise ratio of 40;

FIG. 3 is a spectrum analysis chart of simulation data;

FIG. 4 is an IMF component obtained after EMD decomposition of simulation data;

FIG. 5 is a recombined signal superimposed by different IMF components;

FIG. 6 is a component of the IMF component of FIG. 4 after a running average and least squares fit;

FIG. 7 is a graph showing the comparison of the effect of the denoised data with the theoretical data;

FIG. 8 is a graph comparing denoising effects of different signal-to-noise ratio data;

fig. 9 is a graph of measured data.

Detailed Description

The following description of the embodiments of the present application will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are only some, but not all, of the embodiments of the present application. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are within the scope of the present disclosure.

In order to solve the problems that the exploration signal has noise interference, so that the quality of exploration data is low and the accuracy of inversion based on the exploration data is low, the embodiment of the application provides a noise reduction method for the exploration signal by a resistivity method. The following describes a method for reducing noise of resistivity prospecting signals according to an embodiment of the present application in detail with reference to the accompanying drawings.

The resistivity acquisition data denoising processing method provided by the embodiment of the application comprises the following steps:

step 1, decomposing a resistivity method exploration signal by adopting an Empirical Mode Decomposition (EMD) method to obtain a plurality of eigenmode function (IMF) components;

step 2, denoising the IMF components by using a moving average and least square fitting;

and step 3, overlapping the denoised IMF components to obtain a recombined signal, and carrying out abnormal body inversion based on the recombined signal.

The method specifically comprises the following steps:

step 11, as the front end and the rear end of the original exploration signal have no previous or subsequent data for reference, the extreme value envelope line is dispersed at the end of the original exploration signal during EMD decomposition, so that the two ends of the waveform of the IMF component are distorted, and the subsequent signal processing effect is affected; therefore, the length expansion of the original exploration signal is needed to eliminate the interference of the end effect on EMD decomposition;

step 12, searching all maximum values and minimum values in the original exploration signal u (t), and obtaining an upper envelope v formed by the maximum values by using cubic spline interpolation ₁ And a lower envelope v formed by a minimum value ₂ ；

Wherein t represents the sampling time of the exploration signal, t=1, 2, l, n represents the sampling time of the exploration signal, i.e. the length of the original exploration signal, and u (t) represents the original exploration signal at the time t;

step 13, solving the upper envelope v using equation (1) ₁ And lower envelope v ₂ Mean value m of (2) ₁ (t) and then obtaining the original exploration signal and the envelope mean m by using the formula (2) ₁ Difference h of (t) ₁ (t)：

h ₁ (t)＝u(t)-m ₁ (t)(2)

Step 14, judging the difference h ₁ (t) whether the IMF requirement is met, namely the number of extreme points on the IMF function curve is equal to or different from the number of zero crossing points by no more than one;

when the IMF requirement is not satisfied, let u (t) =h ₁ (t) repeating steps 12-13 until the difference meets the IMF requirement;

when the envelope line is mean m ₁ (t) zero, difference h ₁ (t) zero or one, then the IMF component requirement is satisfied, at which point the process jumps to step 15;

step 15, h ₁ (t) as a first IMF component obtained by decomposition, let u ₁ (t)＝u(t)-h ₁ (t) repeating steps 11-14 to obtain a second IMF component h ₂ (t)；

Let u ₂ (t)＝u ₁ (t)-h ₂ (t) and so on, stopping decomposition when the termination condition is satisfied, obtaining all IMF components and residual phases, at this time

Wherein h is ₁ (t) represents the 1 st IMF component at time t, h _i (t) represents the ith IMF component at time t, i=1, 2, l, I represents the number variable of IMF components, I represents the total number of IMF components obtained by decomposition, and r (t) represents the residual phase.

The termination conditions described in step 15 are: the remaining part of the original exploration signal is a single-frequency signal or less than or equal to a preset threshold value SD.

Wherein, the liquid crystal display device comprises a liquid crystal display device,

ε∈[0.2,0.3]，u _i-1 (t)＝u _i (t)-h _i-1 (t)，u _i (t)＝u _i-1 (t)-h _i (t)，u _i-1 (t)、u _i (t) represents the remaining data after the 1 st to i-1 st IMF components and the 1 st to i th IMF components are removed from the original survey signal u (t), respectively.

According to the method, the length of the original exploration signal is expanded, the extreme point is selected to be a fixed value, the end point effect of the EMD algorithm is restrained, and the accuracy of the signals after clutter filtering is improved.

According to the time sequence characteristics of the original exploration signal, the EMD algorithm decomposes the complex signal into I eigenmode function components { h } distributed from high frequency to low frequency ₁ (t),h ₂ (t),L,h _i (t),L,h _I (t) and a residual phase r (t), the noise interference doped in the original exploration signals acquired by the known direct current method is mostly power frequency or mixed random noise, the interference signals have certain frequencies, the interference signals with frequencies can be removed by using an EMD algorithm, and almost no-frequency signals are reserved.

If the IMF component processed by the EMD algorithm has a discrete value, the result is larger than the actual value, so that the signal needs to be smoother by using a moving average to reduce the influence of the discrete value and random noise.

Assuming each IMF component h _i (t) are all derived from the real data h _i ' and random noise e (t), i.e. h _i (t)＝h _i ' t) +e t, in order to suppress random noise interference and obtain a more accurate signal, smoothing and filtering are required for each IMF component; in particular, IMF components with random noise across the appropriate cells are considered to be stationary, and averaging across the cells reduces the interference of random noise e (t) on the real data, and thus each IMF component is processed as follows:

intercepting m exploration signals in the IMF component according to sampling time to form a cell interval, enabling the intermediate value between the cells to be equal to the average value of the cell interval, sliding the cell interval on the time sequence of the IMF component according to step length=1, repeatedly calculating the intermediate value between the cells, and iteratively processing each data of the IMF component to obtain the IMF component after the sliding average.

For example, when m=7, i.e. the length between cells is 7, the average of these 7 data is used as the 4 th number between cells, i.e.

Let m=2n+1, then k=n+1, h _k (t) represents h _i (t) Signal data obtained by moving average, h _k The number of (t) and h _i (t) are equal in number.

Obtained by the above process

Compared with the original data u (t), the method reduces the interference of random noise, has smoother data curve, removes peak interference generated by the detection equipment, and reduces the influence of random interference on the exploration result.

After moving average, the exploration signal is still subject to fluctuation, so that the most conforming function matching of data is obtained by minimizing the square sum of errors, unknown data is obtained by using a least square method to make data prediction, the square sum of errors of the data and actual data is minimized, the exploration signal is fitted on a curve, the curve with the minimum data error is obtained, the data is more concentrated, and the influence of discrete data on the exploration data is greatly reduced; since the data measured in multiple cycles by resistivity method is theoretically a straight line, the use of least squares fitting can make the exploration signal maximally approximate to the true value.

Each IMF component h after the moving average _k (t) each contains N sample data, using [ (1, h) _k (1))，L，(t，h _k (t)，L，(N，h _k (N))]The representation is that curve fitting is performed on these data points, assuming a curve equation of f (x) =a ₀ +a ₁ x+L+a _n x ⁿ (N < N), substituting the data points into the above equation yields the following form equation:

A ^T Ax＝A ^T b

wherein a is ₀ 、a ₁ 、a _n Each representing a coefficient of curve fit, a representing a relationship matrix,

representing the first and nth unknowns, respectively, of the first data point equation,/->

Representing the first and nth unknowns of the nth data point equation, respectively, T representing the transpose of the matrix, x= (a) ₀ ,a ₁ ,L,a _n ) ^T ，b＝(y ₀ ,y ₁ ,L,y _n ) ^T ，y ₀ 、y ₁ 、y _n Respectively representing a first predicted value, a 2 nd predicted value and an n+1st predicted value obtained by fitting;

pre-let f (x) =a ₀ +a ₁ x+L+a _n x ⁿ (N < N) satisfies the least square method, the coefficient determinant |C of the form equation ^T C|noteq0, C is the coefficient matrix of the formal equation; the discrete points in the data can be concentrated on one curve by using the least square method, so that the data is more concentrated, and the influence of the data value dispersion on the result is reduced.

Example 1

As shown in fig. 1 (a), a two-dimensional resistivity forward modeling is performed by using MATLAB, a model of 40 x 30M is built, wherein an abnormal body with a size of 4 x 4M and a resistance r1=0.1Ω exists, a ground simulation resistor r2=5Ω is provided, an electrode a and an electrode B are power supply electrodes, an electrode M and an electrode N are measurement electrodes, the lengths of the power supply electrodes and the measurement electrodes are changed according to quadrupole sounding, MN voltage values are measured, in order to remove direct current component noise, the resistivity method instrument uses an electrode a for +u and an electrode B for-U in the first half period, and uses an electrode a for-U and an electrode B for +u in the second half period, so as to obtain theoretical data, as shown in fig. 1 (B).

The direct current resistivity method inevitably suffers from earth current interference, weather interference, industrial strong interference, gaussian random noise, polarization of an underground medium, and the like when electrodes are arrayed. In order to simulate external interference, sinusoidal noise and random noise of 50Hz, 100Hz and 250Hz are respectively added into theoretical data to simulate the scattered current of electricity leakage on the ground and the sudden noise caused by external uncertain current, so as to obtain simulation data, and the simulation result is shown in fig. 2, wherein fig. 2 is simulation data of a positive period after noise addition, wherein (a) represents simulation data with a signal-to-noise ratio of 5, (b) represents simulation data with a signal-to-noise ratio of 20, (c) represents simulation data with a signal-to-noise ratio of 30, and (d) represents simulation data with a signal-to-noise ratio of 40.

From fig. 1 and fig. 2, it can be known that the analog voltage value without random interference is a uniform straight line, the analog data shows periodicity and randomness after noise is added, the random interference has sudden interference caused by industrial interference, mechanical construction and the like, and the voltage value is in a saw-tooth shape and is severely jumped when the random interference occurs.

Decomposing the simulation data in the step (a) in fig. 2 by adopting an empirical mode decomposition method to obtain a frequency spectrum shown in fig. 3 and a plurality of eigenmode function (IMF) components shown in fig. 4; as shown in fig. 3, the interference energy below 250Hz is strongest, and in addition, noise responds in various scales and frequency ranges, the noise frequency range covers the whole signal, and the noise frequency range shows irregularities, which are consistent with the interference type of actual exploration data. As shown in fig. 4, the analog data shown in (a) of fig. 2 is decomposed into 9 IMF components, and the theoretical value of the electrical data is a constant value, so that it is known that noise mainly exists in IMF1, IMF2, IMF3 and IMF4 components, IMF1 is separated first, the highest frequency is the highest, and noise interference is the strongest, while the residual phase IMF9 approaches to a straight line and accords with the data characteristic of the direct current method, but the value of IMF9 has a larger difference from the theoretical data, and IMF9 loses effective information, so that only the residual phase cannot be reserved as denoised data.

Discarding IMF components with different frequencies respectively, and recombining the residual IMF components to obtain a recombined signal shown in fig. 5, wherein E1 is a recombined signal of the residual IMF components after discarding the IMF1 component and the IMF2 component, E2 is a recombined signal of the residual IMF components after discarding the IMF1 component, the IMF2 component and the IMF3 component, the comparison error between the recombined signal and theoretical data is 5.4%, E3 is a recombined signal of the residual IMF components after discarding the IMF1 component, the IMF2 component, the IMF3 component and the IMF4 component, the comparison error between the recombined signal and theoretical data is 7.1%, and E4 is a residual phase IMF9 component, the comparison error between the recombined signal and theoretical data is-8.7%; from the above analysis, it can be seen that: if only discarding high-frequency noise can achieve a certain denoising effect, the real voltage information is weakened at the same time; if only the residual phase is reserved, the error is negative, which means that the effective information is abandoned too much, the reserved exploration data is incomplete, the data characteristics are incomplete, and the abnormal body prediction abnormality can be caused by using the method as inversion.

Therefore, the exploration signals captured by the resistivity exploration equipment comprise various frequency electric signals existing in the earth, EMD is decomposed and then exists in each IMF component, the denoising effect of resistivity data cannot be met by using EMD decomposition filtering, and effective signals are lost only by removing specific IMF components, so that moving average and least square fitting are needed to be carried out on each IMF component, the denoising effect is improved, the integrity of the exploration signals is ensured, and the exploration accuracy is improved.

The IMF component of fig. 4 is subjected to a moving average and least squares fit to yield the component shown in fig. 6, from which it can be seen that: the components become smoothed after removing the background noise, and the data becomes constant after removing the noise interference as expected. The last IMF components are not changed before and after processing, which means that noise interference hardly exists in the last IMF components, and the last IMF components are not necessarily processed; the noise interference in the IMF component can be basically removed by the moving average and least square fitting, and the effective information is comprehensively reserved.

The IMF components after the moving average and least square fitting are recombined to obtain a recombined signal as shown in fig. 7, and comparing the recombined signal with theoretical data, it can be seen that: the data after denoising has been removed and has frequency noise, the whole data tends to smooth, the data has very big degree near theoretical value, the noise suppression degree in this data has reached the scope that does not exert an influence on the data inversion.

Example 2

The denoising processing is performed on the acquired signals with the signal to noise ratios of 20, 30 and 40 by using the denoising method, and the denoising result is shown in fig. 8, which can be seen from the graph: along with the increase of the noise ratio, the suppression effect of the method on noise is more obvious, when the signal-to-noise ratio of the acquired signals reaches more than 40, voltage value data obtained by noise reduction basically fluctuates in a small range, the type and the position of an abnormal body can be accurately predicted by inversion based on the voltage value data, the problem of false abnormal body or large position deviation of the abnormal body can not occur, the method has important significance in exploration engineering, and the accuracy of exploration and the safety of engineering construction can be improved.

Example 3

The conventional arithmetic average method and the application are used for carrying out noise reduction treatment on the voltage data with different sampling rates, and the treatment results are shown in table 1, and can be seen from table 1: although the influence of noise on the exploration signal can be reduced by increasing the sampling rate, the error of the exploration signal and theoretical data is reduced, the noise reduction effect is limited, and the noise reduction effect is slowly improved along with the increase of the sampling rate; the noise reduction method provided by the application can effectively reduce the error between the exploration signal and the theoretical data, so that the effective data in the exploration signal can be reserved to a greater extent, the authenticity of the exploration signal is ensured, and the accuracy of exploration is improved.

Table 1 comparison of final treatment results

Treatment method	Theoretical voltage value	Voltage value after denoising treatment	Error of
				Arithmetic mean of 50Hz sampling rate	1.076	0.931	-13.5％
Arithmetic mean of 100Hz sampling rate	1.076	1.208	12.3％
				Arithmetic mean of 300Hz sampling rate	1.076	1.141	6.1％
500Hz sampling rate arithmetic mean	1.076	1.139	5.9％
				The application (500 Hz)	1.076	1.089	1.23％

Example 4

The high-density electric method instrument is used for carrying out field exploration on the ground under the building training floor of the school, AB is set to be 6 meters, MN is set to be 3 meters, sampling interval is 250 mu s, sampling period is 5s, electrode AB is powered by dry battery 30V, four-period measurement is carried out, sampling data are shown in fig. 9, noise data are severely fluctuated, and noise with fixed frequency and noise with high randomness are doped.

Frequency analysis of the sampled data found: the interference frequency of data obtained by resistivity exploration is mainly frequency multiplication of 50Hz, because the teaching experiment area where the exploration area is located is provided with large-scale electric equipment and grounding wires, and a large amount of power frequency interference can be generated. There are also some disturbances with less energy distributed in all areas, which are caused by the influence of solar motion and also the polarization effect of underground substances, etc., and the energy of the disturbances is less irregular and circulated.

The measured data were noise reduced to obtain a measured voltage, based on which the measured current and apparent resistivity ratio was calculated using formulas (3), (4), where the device coefficient k= 7.069, and the calculation results are shown in table 2.

Where ρ represents apparent resistivity, DU represents a potential difference between the measurement electrode M and the measurement electrode N, I represents AN actual measurement current, AM represents a distance between the electrode a and the electrode M, AN represents a distance between the electrode a and the electrode N, BM represents a distance between the electrode B and the electrode M, and BN represents a distance between the electrode B and the electrode N.

Table 2 apparent resistivity data

As can be seen from table 2, apparent resistivity is large when the noise suppression processing is not performed on the raw data; meanwhile, the superposition of noise and an artificial electric field enhances the measurement voltage between the electrodes MN, and the apparent resistivity is larger than the actual apparent resistivity.

With the increase of the sampling rate, the increase of the measured data can properly suppress noise, so that the apparent resistivity is reduced, the influence of the noise on the exploration data can be reduced by using the noise reduction method, the apparent resistivity is closer to an actual value, and the method is used for inversion, so that false abnormal bodies or inaccurate position ranges of the abnormal bodies can be avoided, the accuracy of exploration prediction is improved, and economic loss or danger is reduced.

It is noted that relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.

Although embodiments of the present application have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the application, the scope of which is defined in the appended claims and their equivalents.

Claims (6)

1. A method for noise reduction of resistivity survey signals, comprising the steps of:

s1, decomposing a resistivity method exploration signal by adopting an empirical mode decomposition method to obtain a plurality of IMF components;

s2, fitting a plurality of IMF components by using a moving average and a least square method;

and S3, superposing the processing result of the step S2 to obtain a recombined signal.

2. The method of noise reduction of a resistivity survey signal of claim 1, wherein step 1 includes:

step S11, searching to obtain the maximum value and the minimum value in the original exploration signal u (t), and obtaining an upper envelope v formed by the maximum value by using cubic spline interpolation ₁ And a lower envelope v formed by a minimum value ₂ ；

Step S12, calculating the mean value of the upper envelope curve and the lower envelope curve, and the difference h between the original exploration signal and the mean value ₁ (t)；

Step S13, judging the difference h ₁ (t) whether the IMF component condition is satisfied, if so, jumping to step S14, if not, letting u (t) =h ₁ (t) repeating the steps S11-S12 until the difference value meets the IMF condition;

step S14, let h ₁ (t) as a first IMF component, let u ₁ (t)＝u(t)-h ₁ (t) repeating steps S11-S13 to obtain a second IMF component h ₂ (t)；

Let u ₂ (t)＝u ₁ (t)-h ₂ And (t) and the like, stopping decomposing when the termination condition is met, and obtaining all IMF components and residual phases.

3. The method of noise reduction of a resistivity survey signal of claim 2, wherein step S1 further includes length expanding the raw survey signal prior to step S11.

4. A method of noise reduction of a resistivity survey signal in accordance with claim 2, wherein the termination condition is: the rest part of signals are single-frequency signals or smaller than a threshold value SD;

wherein I represents the number variable of IMF components, I represents the total number of IMF components obtained by decomposition, i=1, 2, l, I, u _i-1 (t)、u _i (t) represents the residual data after removal of the 1 st to i-1 st IMF components and the 1 st to i th IMF components from the original survey signal u (t), respectively, ε [0.2,0.3 ]]。

5. The method of noise reduction of a resistivity survey signal of claim 1, wherein each IMF component is processed in step S2 as follows:

and intercepting part of exploration signals in the IMF component according to the sampling time to form a cell interval, enabling the intermediate value between the cells to be equal to the average value of the cell interval, sliding the cell interval on the time sequence of the IMF component according to the step length=1, and processing each data of the IMF component to obtain the IMF component after the sliding average.

6. The method of noise reduction of resistivity survey signals of claim 5, wherein the step S2 further includes the step of:

curve fitting is performed on N data points of each moving average processed IMF component, assuming a curve equation of f (x) =a ₀ +a ₁ x+L+a _n x ⁿ (N < N), substituting N data points into the curve equation to obtain a form equation:

A ^T Ax＝A ^T b

wherein a is ₀ 、a ₁ 、a _n All represent coefficients of curve fitting, x ⁿ Respectively representing the first and nth unknowns of the curve equation, a represents the relationship matrix, T represents the transpose of the matrix, x= (a) ₀ ,a ₁ ,L,a _n ) ^T ，b＝y ₀ ,y ₁ ,L,y _n ^T ，y ₀ 、y ₁ 、y _n Respectively representing a first predicted value, a 2 nd predicted value and an n+1st predicted value obtained by fitting;

let coefficient determinant |C of formal equation ^T C|noteq0, C is a coefficient matrix representing the equation.

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