A method for suppressing power frequency electromagnetic wave background noise

Abstract

The application discloses a power frequency electromagnetic wave background noise suppression method and relates to the field of geophysical exploration signal processing. The method comprises the following steps: collecting original time series of electric field horizontal components and magnetic field horizontal components; selecting adjacent frequency bands without power frequency harmonic frequencies on both sides of a power frequency base frequency, extracting a ground electromagnetic impedance tensor from the adjacent frequency bands, and obtaining a reference impedance tensor through frequency domain interpolation; constructing a wave impedance constraint matrix and a passive propagation constraint matrix according to the reference impedance tensor; performing time-frequency transformation on the original time series, and extracting an observed complex vector at the power frequency base frequency; performing two-stage projection separation on the observed complex vector, and projecting the observed complex vector into the null space of the wave impedance constraint matrix and the passive propagation constraint matrix in sequence to obtain a natural field signal complex vector; replacing the value at the power frequency base frequency in the time-frequency transformation spectrum and performing inverse time-frequency transformation to obtain a time series after power frequency electromagnetic wave background noise suppression. The application realizes lossless separation of the amplitude and phase of a useful signal at the power frequency base frequency.

Description

Technical Field

[0001] This invention relates to the field of geophysical exploration signal processing, and more specifically, to a method for suppressing background noise of power frequency electromagnetic waves. Background Technology

[0002] Magnetotelluric sounding is a geophysical exploration method that uses natural alternating electromagnetic fields to invert underground resistivity structures. Its observation frequency band typically covers 0.001 Hz to 10 kHz, with the fundamental power frequency and its harmonic frequencies located within this effective frequency band. In single-point measurements, the amplitude of power frequency electromagnetic interference generated by the power grid near the survey area through near-field induction is often higher than the amplitude of the natural field signal, resulting in a low signal-to-noise ratio at the fundamental power frequency.

[0003] Currently, commonly used power frequency interference suppression methods include three categories: notch filters, adaptive filtering, and signal decomposition. Notch filters attenuate signal amplitude at the power frequency and its adjacent frequency bands, while introducing phase distortion, affecting the utilization of phase information in magnetotelluric inversion. Adaptive filtering methods require an additional reference channel to obtain the interference reference signal, limiting their applicability under single-point measurement conditions without a distant reference channel, and they also suffer from steady-state errors during convergence. Signal decomposition methods based on empirical mode decomposition or independent component analysis lack clear criteria for selecting noise reduction coefficients under overlapping frequency band conditions, easily leading to over-processing or under-processing.

[0004] The common shortcoming of the above methods is that they all rely on frequency position to distinguish between interference and useful signals. When power frequency interference and useful signals of the same frequency completely overlap in frequency, the process of suppressing interference will inevitably damage the useful signal. Therefore, a method for suppressing background noise of power frequency electromagnetic waves is proposed to address the above problems. Summary of the Invention

[0005] To overcome the above-mentioned defects of the prior art, embodiments of the present invention provide a method for suppressing background noise of power frequency electromagnetic waves. This method aims to address the problem that, in single-point magnetotelluric sounding scenarios, when the useful signal at the power frequency fundamental frequency overlaps with power frequency interference, existing methods damage the amplitude and phase of the useful signal at that frequency while suppressing interference.

[0006] To achieve the above objectives, this invention provides a method for suppressing background noise from power frequency electromagnetic waves, applied to single-point magnetotelluric sounding scenarios. Magnetotelluric sounding utilizes natural alternating electromagnetic fields as the field source, and inverts the resistivity structure of the subsurface medium by observing mutually orthogonal electric and magnetic field components at the Earth's surface. Power frequency interference originates from the surface power grid, acting as a near-field induction source. The electromagnetic field it generates does not satisfy the wave impedance relationship and passive propagation conditions followed by natural plane waves. This method utilizes this fundamental physical difference to separate the constrained natural field components from the unconstrained interference components in the observed signal within the physical constraint space.

[0007] The method includes the following steps.

[0008] S1 collects the original time series of the horizontal components of the electric field and the horizontal components of the magnetic field in a single-point magnetotelluric sounding scenario, which serves as input data for subsequent processing.

[0009] The horizontal component of the electric field includes the electric field in the east-west direction. and the electric field in the north-south direction The horizontal component of the magnetic field includes the east-west magnetic field. and the north-south magnetic field .

[0010] In this data acquisition scenario, no distant reference station is set up. The power frequency electromagnetic interference originates from the near-field induced interference of the power grid in the vicinity of the test area at the power frequency fundamental frequency and its harmonic frequencies.

[0011] S2, at the power frequency base frequency On each side, a neighboring frequency band without power frequency harmonics is selected. The statistical stability of the natural plane wave field source in the neighboring frequency band is used to extract the magnetotelluric impedance tensor from the electromagnetic field data of the neighboring frequency band. The reference impedance tensor at the power frequency fundamental frequency is obtained by frequency domain interpolation.

[0012] This reference impedance tensor reflects the wave impedance characteristics of the underground medium at the power frequency fundamental frequency, providing a physical benchmark for subsequent separation of natural field signals and power frequency interference.

[0013] Furthermore, adjacent frequency bands are located in Deviating from the frequency range of 2Hz to 8Hz, making the adjacent frequency bands and The response characteristics of the underground medium at each location remain similar.

[0014] The adjacent frequency band avoids the 3rd and 5th harmonic frequencies of the power frequency fundamental frequency, thus preventing low-order harmonic interference from being mixed into the impedance tensor estimation.

[0015] Furthermore, the process of extracting the magnetotelluric impedance tensor from electromagnetic field data in adjacent frequency bands is as follows: Multiple data segments are extracted within adjacent frequency bands using a sliding time window, and the impedance tensor estimate for each data segment is calculated. Calculate the median of all impedance tensor estimates, remove estimates whose Mahalanobis distance from the median exceeds a preset threshold, and filter out abnormal estimates affected by interference. The average of the retained estimates is used to obtain the average impedance tensor of the adjacent frequency band; The reference impedance tensor at the power frequency fundamental frequency is obtained by extrapolating the average impedance tensors of two adjacent frequency bands through frequency domain interpolation.

[0016] S3, construct the wave impedance constraint matrix and the passive propagation constraint matrix based on the reference impedance tensor.

[0017] The product of the wave impedance constraint matrix and the electromagnetic field vector of the natural plane wave is zero. This product relationship is equivalent to the wave impedance equation that should be satisfied between the horizontal components of the electric field and the horizontal components of the magnetic field in the natural plane wave field.

[0018] The passive propagation constraint matrix is ​​constructed from the real and imaginary parts of the reference impedance tensor, and its product with the electromagnetic field vector of the natural plane wave is zero. This product relationship expresses the propagation constraint of the natural plane wave field in a passive medium.

[0019] The wave impedance constraint matrix and the passive propagation constraint matrix impose constraints on the natural field vector from two independent physical perspectives: the wave impedance relationship and the passive propagation condition. Together, they define the constraint space for a pure signal. Signal components that deviate from this constraint space originate from near-field power frequency interference.

[0020] Furthermore, the wave impedance constraint matrix is ​​a 2x4 matrix, with the elements in the first row being... , , , The elements in the second row are as follows: , , , ,in , , , These are the four elements of the reference impedance tensor.

[0021] Furthermore, the passive propagation constraint matrix is ​​a 2x4 matrix, with the elements in the first row being... , , , The elements in the second row are as follows: , , , ,in , , , They are respectively , , , The real part.

[0022] This matrix, composed of the real elements of the reference impedance tensor, expresses the physical property that the electric and magnetic fields are in phase in the natural plane wave field as a linear constraint on each element of the electromagnetic field vector.

[0023] S4 performs time-frequency transformation on the original time series to extract the observed complex vector at the power frequency fundamental frequency.

[0024] The observation complex vector is a column vector composed of the Fourier coefficients of the horizontal components of the electric field and the horizontal components of the magnetic field at that frequency, arranged in order. This column vector contains both natural field signal components and power frequency interference components.

[0025] The observed complex vector is , , , The Fourier coefficients at the power frequency fundamental frequency are arranged in order to form a 4-dimensional complex column vector, and this arrangement corresponds to the columns of the wave impedance constraint matrix and the passive propagation constraint matrix.

[0026] S5 performs two-stage projection separation on the observed complex vector.

[0027] The first-level projection projects the observed complex vector onto the null space of the wave impedance constraint matrix, obtaining an intermediate signal vector. The projection result satisfies the wave impedance relationship, and the power frequency interference components in the observed complex vector that do not satisfy this relationship are separated into the complement space of the projection operator.

[0028] The second-level projection projects the intermediate signal vector onto the null space of the passive propagation constraint matrix, obtaining the separated natural field signal complex vector. The projection result simultaneously satisfies the passive propagation constraint, and the residual interference components in the intermediate signal vector that do not satisfy the constraint are further separated.

[0029] After two-stage projection separation, the observed complex vector at the power frequency fundamental frequency is decomposed into signal components that satisfy the physical constraints of the natural plane wave field and interference components that do not satisfy the constraints. The separation process does not involve frequency cut-off or amplitude attenuation.

[0030] Furthermore, the calculation method for the first-level projection is as follows: , , in, To observe complex vectors, The wave impedance constraint matrix is... For identity matrix, superscript This indicates the conjugate transpose. For the first-order projection operator, This is the intermediate signal vector.

[0031] Furthermore, the calculation method for the second-level projection is as follows: , , in, For passive propagation constraint matrix, For the second-order projection operator, It is the complex vector of the separated natural field signal.

[0032] S6 replaces the value at the fundamental frequency in the time-frequency transform spectrum with the separated natural field signal complex vector, and performs an inverse time-frequency transform to obtain the time series after suppressing the background noise of the power frequency electromagnetic wave. This replacement only applies to the fundamental frequency point; the spectral values ​​at other frequency points remain unchanged.

[0033] Furthermore, power frequency base frequency The frequencies are 50Hz or 60Hz, corresponding to different regions with different power system frequencies.

[0034] Furthermore, the method also includes: performing steps S2 to S6 on the odd harmonic frequencies of the power frequency fundamental frequency, independently constructing corresponding constraint matrices at each harmonic frequency and performing projection separation to suppress power frequency harmonic interference. The separation and replacement operations at each harmonic frequency are for different frequency points of the same spectrum and do not interfere with each other.

[0035] The technical effects and advantages of this invention are as follows: First, by constructing wave impedance constraint matrices and passive propagation constraint matrices, the interference suppression problem is transformed from a filtering operation in signal processing into a projection separation operation in a physically constrained space. Natural plane wave fields originate from upper-level ionospheric currents, and the horizontal components of their electric and magnetic fields are strictly constrained by wave impedance relationships and passive propagation conditions. In contrast, power frequency interference originates from the Earth's surface power grid, and as a near-field induction source, its generated electromagnetic field does not satisfy the aforementioned constraints. Separating the interference by utilizing this fundamental physical difference avoids the co-frequency damage problem caused by distinguishing between interference and useful signals based on frequency location.

[0036] Second, a two-stage projection separation is performed on the observed complex vector. The first-stage projection projects the observed complex vector to the null space of the wave impedance constraint matrix, ensuring the projection result satisfies the wave impedance relationship. The second-stage projection projects the intermediate signal vector to the null space of the passive propagation constraint matrix, ensuring the projection result simultaneously satisfies the passive propagation constraint. Natural field components satisfying the constraints are retained in the projection result, while power frequency interference components not satisfying the constraints are separated into the complement space of the projection operator. The entire separation process does not involve frequency cutoff or amplitude attenuation; the amplitude and phase information of the useful signal at the power frequency fundamental frequency are fully preserved, which helps improve the utilization of complete frequency band information in subsequent resistivity inversion.

[0037] Third, this method eliminates the need for a distant reference station, as interference separation can be achieved using four-component data acquired from a single measurement point. The reference impedance tensor is extracted from adjacent frequency bands on both sides of the fundamental power frequency that do not contain harmonics, eliminating the need for an additional reference channel to provide an interference reference signal. This method is suitable for magnetotelluric sounding operations without a distant reference channel, reducing the deployment requirements for field data acquisition. Attached Figure Description

[0038] Figure 1 This is a flowchart illustrating the overall implementation of the method of the present invention; Figure 2 This is a detailed flowchart of the process for obtaining the reference impedance tensor in this invention. Detailed Implementation

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0040] Example 1 As attached Figures 1 to 2 The method for suppressing background noise from power frequency electromagnetic waves is shown and applied to a single-point magnetotelluric sounding scenario. Magnetotelluric sounding utilizes natural alternating electromagnetic fields as the field source and inverts the resistivity structure of the subsurface medium by observing mutually orthogonal electric and magnetic field components at the Earth's surface.

[0041] Observational signals are often subject to strong electromagnetic interference induced by the near-field induction of the power grid at the fundamental frequency and its harmonic frequencies. This interference completely overlaps with useful underground signals in the same frequency band. Existing methods based on filtering or notch filtering inevitably damage the useful signal while suppressing the interference.

[0042] This method utilizes the fundamental physical differences between natural plane wave fields and near-field anthropogenic interference to achieve separation. Natural magnetotelluric fields are incident perpendicularly to the Earth's surface as plane electromagnetic waves. The horizontal components of their electric and magnetic fields are strictly constrained by wave impedance relationships and passive propagation conditions.

[0043] Power frequency interference originates from the surface power grid, which, as a near-field induction source, generates electromagnetic fields that do not satisfy the aforementioned constraints. Therefore, the natural field components that satisfy the constraints and the interference components that do not satisfy the constraints in the observed signal are separated in the physical constraint space, achieving lossless separation of signals of the same frequency.

[0044] The following is a detailed explanation of the method steps S1 to S6 in sequence.

[0045] Step S1 is as follows: Step S1: Collect the original time series of the horizontal components of the electric field and the horizontal components of the magnetic field in the single-point measurement scenario of magnetotelluric sounding.

[0046] Sensors were deployed at the measurement points according to the standard magnetotelluric sounding observation method. The horizontal electric field was measured using two pairs of non-polarized electrodes: one pair was deployed along the east-west direction to record the electric field in that direction. Another pair is arranged along the north-south direction to record the electric field in the north-south direction. .

[0047] The horizontal magnetic field is measured using two magnetic sensors: one is placed horizontally along the north-south direction, and the other records the magnetic field in the east-west direction. Another one was placed horizontally along the east-west direction to record the magnetic field in the north-south direction. .

[0048] Four channels are simultaneously and continuously acquired at a sampling rate of no less than 1 kHz to obtain the original time series.

[0049] This data acquisition scenario does not include a distant reference station. Power frequency electromagnetic interference originates from near-field induced interference from the power grid in the vicinity of the survey area at the fundamental power frequency and its harmonic frequencies. The fundamental power frequency is denoted as... In one implementation method 50Hz, in another implementation It is 60Hz.

[0050] Step S2 is as follows: Step S2 involves selecting a neighboring frequency band without power frequency harmonics on each side of the fundamental power frequency. The magnetotelluric impedance tensor is extracted from the electromagnetic field data, and the reference impedance tensor at the fundamental power frequency is obtained through frequency domain interpolation. This step specifically includes the following processing steps.

[0051] First, determine the frequency range of two adjacent frequency bands. Adjacent frequency bands must meet three conditions: lie in Deviating from the frequency range of 2Hz to 8Hz; It does not contain any power frequency harmonics; At the same time, avoid the 3rd and 5th harmonic frequencies of the power frequency base frequency.

[0052] by Taking 50Hz as an example, the first adjacent frequency band is selected from 46Hz to 48Hz, and the second adjacent frequency band is selected from 52Hz to 54Hz. The two frequency bands are symmetrically distributed on both sides of 50Hz, with center frequencies of 47Hz and 53Hz respectively, and avoid 150Hz and 250Hz.

[0053] by Taking 60Hz as an example, the first adjacent frequency band is selected from 56Hz to 58Hz, and the second adjacent frequency band is selected from 62Hz to 64Hz. The center frequencies of the two bands are 57Hz and 63Hz, respectively, avoiding 180Hz and 300Hz.

[0054] Secondly, set the extraction parameters. The length of the sliding time window is denoted as... For example, 256 or 512 sampling points are taken. A 50% overlap ratio is set between adjacent time windows. The Mahalanobis distance threshold is denoted as... For example, a value between 1.5 and 4.0 is selected.

[0055] Next, the average impedance tensor is extracted for each neighboring frequency band. Taking the first neighboring frequency band as an example, the average impedance tensor of length is... The sliding time window starts from the beginning of the time-domain data corresponding to that frequency band and moves gradually along the time axis with a 50% overlap ratio. Each movement... Each sampling point is cut off to a length of The data segment was eventually extracted into multiple data segments.

[0056] Perform on each data segment Point Fourier transform. The result obtained from the transform... Among a set of discrete frequency points, the index range of frequency points corresponding to the adjacent frequency bands is located based on the frequency resolution. The values ​​within this range are then extracted. , , , Fourier coefficients of each component.

[0057] Using the four-component Fourier coefficients obtained from a single data segment within this frequency band as input, a least-squares estimation is employed to output an impedance tensor estimate. This estimate contains four complex elements, denoted as follows: , , , Each element has a real part and an imaginary part.

[0058] By traversing all sliding time window positions within the entire adjacent frequency band, a set of impedance tensor estimates is obtained. The median of this set of estimates is calculated. The four complex elements of each estimate are expanded by their real and imaginary parts to obtain an 8-dimensional real vector.

[0059] The order of arrangement is .

[0060] Calculate the covariance matrix of the 8-dimensional real vectors for all estimates. For each estimate, calculate the difference between its 8-dimensional real vector and the vector corresponding to the median. Perform a quadratic form operation on this difference vector and the inverse of the covariance matrix to obtain the Mahalanobis distance for that estimate. Eliminate estimates whose Mahalanobis distance exceeds a threshold. The estimated values ​​are then used to obtain the average impedance tensor of the adjacent frequency band by taking the arithmetic mean of the retained estimated values.

[0061] The average impedance tensor of the second adjacent frequency band is obtained by following the same operating procedure.

[0062] Finally, the two average impedance tensors are extrapolated to the frequency domain through interpolation. At this point, the average impedance tensor of the first adjacent frequency band is mapped to its center frequency, and the average impedance tensor of the second adjacent frequency band is mapped to its center frequency. For the real and imaginary parts of each element of the two average impedance tensors, linear interpolation is performed between the two center frequencies, and extrapolation is performed to... Place.

[0063] by Taking 50Hz as an example, the value at 47Hz is denoted as The value at 53Hz is denoted as The value at 50Hz. After interpolating the real and imaginary parts in this manner, the reference impedance tensor at the fundamental frequency is obtained.

[0064] Step S3 is: Step S3 constructs the wave impedance constraint matrix and the passive propagation constraint matrix based on the reference impedance tensor.

[0065] First, construct the wave impedance constraint matrix, denoted as... . It is a complex matrix with 2 rows and 4 columns.

[0066] The elements in the first row are as follows: , , , .

[0067] The elements in the second row are as follows: , , , .

[0068] Natural plane wave electromagnetic field vector Depend on , , , The Fourier coefficients are arranged in this order. When it is the natural plane wave field vector, and The product of these two equations is a zero vector. This product relationship is equivalent to the two wave impedance equations. and .

[0069] Then construct the passive propagation constraint matrix, denoted as . The real parts of each element of the reference impedance tensor are denoted as follows: , , , , respectively corresponding , , , The real part. This is a complex matrix with 2 rows and 4 columns. The elements in the first row are taken as follows: , , , The elements in the second row are taken in sequence. , , , The electromagnetic field vector of a natural plane wave. and The product of these is a zero vector.

[0070] Wave impedance constraint matrix and passive propagation constraint matrix Constraints are imposed on the natural field vectors from two independent physical perspectives, which together define the constraint space of the pure signal.

[0071] Step S4 is: Step S4 performs time-frequency transformation on the original time series to extract the observed complex vector at the power frequency fundamental frequency.

[0072] In one implementation, a short-time Fourier transform is used for time-frequency transformation. The original four-component time series is input into the short-time Fourier transform. The time window length is related to that in step S2. To maintain consistency, the overlap ratio of adjacent time windows should both be 50%.

[0073] The transformation outputs at each frequency point within each time window , , , The Fourier coefficients, for each time window, in Frequency extraction , , , Fourier coefficients, according to , , , The order of these elements forms a 4-dimensional complex column vector, denoted as the observation complex vector. .

[0074] In another implementation, the time-frequency transformation employs continuous wavelet transform. Morlet wavelet is selected as the mother wavelet, and the original time series is input into the continuous wavelet transform, outputting wavelet coefficients at each time point and scale on the time-scale plane.

[0075] The correspondence between scale and frequency is determined by the center frequency of the mother wavelet and the sampling interval of the signal. At the corresponding scale, extract point by point along the time axis. , , , wavelet coefficients, according to , , , The sequential arrangement constitutes the observation complex vector at that point in time. .

[0076] In this embodiment, the acquisition of the reference impedance tensor in step S2 still adopts the short-time Fourier transform, so as to take advantage of the short-time Fourier transform's equal resolution in the frequency domain to accurately locate the adjacent frequency band boundary.

[0077] Step S5 is as follows: Step S5 performs two-stage projection separation on the observed complex vector.

[0078] The first-level projection projects the observed complex vector onto the null space of the wave impedance constraint matrix, removing components that do not satisfy the wave impedance relationship.

[0079] The second-level projection further projects the intermediate results onto the null space of the passive propagation constraint matrix, obtaining a complex vector of the natural field signal that simultaneously satisfies two physical constraints.

[0080] When step S4 uses the short-time Fourier transform, each time window corresponds to an observation complex vector. Projection separation is performed independently in each time window. When continuous wavelet transform is used, each time point corresponds to an observation complex vector. Projection separation is performed independently at each time point. The projection calculation process is exactly the same in both cases.

[0081] The processing procedure for the first-level projection is as follows.

[0082] Calculate the first-order projection operator : ; in It is a 4th order identity matrix. The wave impedance constraint matrix constructed in step S3, with superscript... This indicates the conjugate transpose.

[0083] When calculating, first find The conjugate transpose matrix . It is 2 rows and 4 columns. The matrix has 4 rows and 2 columns. Calculate the matrix product. This yields a 2x2 square matrix. Inverting this 2x2 square matrix gives us its inverse matrix. .Will Multiplying by the inverse matrix yields a 4x2 matrix. Then, right-multiply this 4x2 matrix... This results in a 4x4 square matrix. Using a 4th-order identity matrix Subtracting the 4th order square matrix yields the first-order projection operator. .

[0084] Will With the observation complex vector Multiply to obtain the intermediate signal vector : ; The order of the elements in the text and Consistent, corresponding sequentially , , , After the first level of projection, satisfy This means that the wave impedance relationship has been satisfied.

[0085] The processing procedure for the second-level projection is as follows.

[0086] Calculate the second-order projection operator : ; in The passive propagation constraint matrix constructed in step S3, It is a 4th order identity matrix.

[0087] The calculation steps are the same as for the first-level projection. First, calculate... conjugate transpose .calculate We obtain a 2x2 matrix and then inverse it. .calculate This results in a 4x2 matrix. Then multiply it by the right matrix. We obtain a 4x4 square matrix Using the identity matrix Subtracting this square matrix yields the second-order projection operator. .

[0088] Will With intermediate signal vector Multiplying them together yields the complex vector of the natural field signal. : ; The order of the elements in the text and Consistent. After the second level of projection, Simultaneously satisfy and .

[0089] After two stages of projection separation The four elements represent the time window or the point in time. The electromagnetic complex coefficients that satisfy all physical constraints of the natural plane wave field. Observation complex vector. The power frequency interference component induced by the near-field power grid, because it does not satisfy the above constraints, is separated into the complement space of the projection operator during the projection process. This separation process does not involve frequency cutoff or amplitude attenuation. The amplitude and phase information of the useful signal at the frequency point are completely preserved.

[0090] Step S6 is: Step S6 replaces the value at the fundamental frequency of the original spectrum with the complex vector of the separated natural field signal, performs inverse time-frequency transformation, and obtains the output time series after suppressing the background noise of the power frequency electromagnetic wave.

[0091] In the short-time Fourier transform method, for the original spectrum of each time window, find The location corresponding to the frequency point. Place this position... , , , The Fourier coefficients of the four components are respectively replaced with The first, second, third, and fourth elements. The Fourier coefficients at all other frequency points remain unchanged.

[0092] After all time windows have been replaced, an inverse short-time Fourier transform is performed. The time window length for the inverse transform is taken as... The overlap ratio of adjacent time windows is set to 50%. The overlapping and addition method is used when synthesizing time-domain signals. The time-domain segments obtained from the inverse transform of each time window are placed into the output buffer in chronological order. For the overlapping region between adjacent time windows, since the overlap ratio is 50%, each sampling point in the overlapping region belongs to both the preceding and following time windows. The values ​​of these two time windows at that sampling point are added together, divided by 2, and averaged to obtain the final output value for that sampling point. The synthesized complete time series is the output result.

[0093] In the continuous wavelet transform method, for each time point at... The wavelet coefficients at the corresponding scale will , , , The wavelet coefficients are replaced with The first, second, third, and fourth elements are replaced. The wavelet coefficients at other scales remain unchanged. After replacing all time points, an inverse continuous wavelet transform is performed to obtain the output result.

[0094] In another implementation, the above processing flow is extended to The odd harmonic frequencies. The processing of each harmonic frequency is performed independently from the fundamental frequency processing. The separation and replacement operations at each frequency point are performed on different frequency points of the same spectrum without interference.

[0095] With the third harmonic frequency and the 5th harmonic frequency Let's take an example to illustrate. for Three times that, in The two sides are selected from adjacent frequency bands, and the frequency band selection rules are the same as those for the two sides. The processing is the same, that is, it is located in It deviates from the 2Hz to 8Hz range and does not overlap with other processed frequencies. Taking 50Hz as an example, The Hz frequency is set to 150Hz, with adjacent frequency bands ranging from 146Hz to 148Hz and from 152Hz to 154Hz. Within these adjacent frequency bands, the impedance tensor is extracted and extrapolated following the same procedure as in step S2. The harmonic reference impedance tensor at that location. Construct from this harmonic reference impedance tensor as described in step S3. The corresponding wave impedance constraint matrix and passive propagation constraint matrix. Following step S4... Extract the observed complex vector. Perform two-stage projection separation as described in step S5 to obtain... The complex vector of the natural field signal at that location. Replace the original spectrum with this complex vector of the signal. The value at the frequency point.

[0096] for 5 times, with Taking 50Hz as an example, The frequency is 250Hz, and the adjacent frequency bands are 246Hz to 248Hz and 252Hz to 254Hz, processed using the same procedure. If higher-order odd harmonics need to be processed, the same logic applies, selecting suitable adjacent frequency bands on both sides of each harmonic frequency and performing the above steps sequentially. After all the spectrum replacements at all target frequency points are completed, a unified inverse short-time Fourier transform is performed to obtain the output result that simultaneously suppresses the power frequency fundamental frequency and its multiple odd harmonic interferences.

[0097] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of 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 suppressing background noise of power frequency electromagnetic waves, characterized in that, include: S1, collect the original time series of the horizontal components of the electric field and the horizontal components of the magnetic field in the single-point measurement scenario of magnetotelluric sounding; S2, Select a neighboring frequency band without power frequency harmonic frequencies on both sides of the power frequency fundamental frequency, extract the magnetotelluric impedance tensor from the electromagnetic field data of the neighboring frequency band, and obtain the reference impedance tensor at the power frequency fundamental frequency through frequency domain interpolation. S3, construct the wave impedance constraint matrix and the passive propagation constraint matrix based on the reference impedance tensor; The product of the wave impedance constraint matrix and the natural plane wave electromagnetic field vector is zero, and the passive propagation constraint matrix is ​​constructed from the real and imaginary parts of the reference impedance tensor and its product with the natural plane wave electromagnetic field vector is zero. S4, Perform time-frequency transformation on the original time series to extract the observed complex vector at the power frequency fundamental frequency. The observed complex vector is a column vector composed of the Fourier coefficients of the electric field horizontal component and the magnetic field horizontal component at that frequency arranged in order. S5, perform two-stage projection separation on the observed complex vector. The first-level projection projects the observed complex vector onto the null space of the wave impedance constraint matrix to obtain the intermediate signal vector. The second-level projection projects the intermediate signal vector onto the null space of the passive propagation constraint matrix to obtain the separated natural field signal complex vector; S6 replaces the value at the fundamental frequency of the power frequency in the time-frequency transform spectrum with the complex vector of the separated natural field signal, and performs inverse time-frequency transform to obtain the time series after suppressing the background noise of the power frequency electromagnetic wave.

2. The method for suppressing background noise of power frequency electromagnetic waves according to claim 1, characterized in that, In step S2, the adjacent frequency band is located within the frequency range of 2Hz to 8Hz away from the power frequency fundamental frequency, and the adjacent frequency band avoids the 3rd and 5th harmonic frequencies of the power frequency fundamental frequency.

3. The method for suppressing background noise of power frequency electromagnetic waves according to claim 2, characterized in that, Step S2 involves extracting the magnetotelluric impedance tensor from electromagnetic field data in adjacent frequency bands, including: Multiple data segments are extracted within the adjacent frequency band using a sliding time window, and the impedance tensor estimate for each data segment is calculated. Calculate the median of all impedance tensor estimates and discard estimates whose Mahalanobis distance from the median exceeds a preset threshold; The average of the retained estimates is used to obtain the average impedance tensor of the adjacent frequency band.

4. The method for suppressing background noise of power frequency electromagnetic waves according to claim 1, characterized in that, The wave impedance constraint matrix mentioned in step S3 is a 2-row, 4-column matrix. The elements in the first row are as follows: , , , , The elements in the second row are as follows: , , , , in , , , These are the four elements of the reference impedance tensor.

5. The method for suppressing background noise of power frequency electromagnetic waves according to claim 1, characterized in that, The passive propagation constraint matrix mentioned in step S3 is a 2-row, 4-column matrix. The elements in the first row are as follows: , , , , The elements in the second row are as follows: , , , , in , , , They are respectively , , , The real part.

6. The method for suppressing background noise of power frequency electromagnetic waves according to claim 1, characterized in that, The calculation method for the first-level projection in step S5 is as follows: ， ， in To observe complex vectors, The wave impedance constraint matrix is... For identity matrix, superscript This indicates the conjugate transpose. For the first-order projection operator, This is the intermediate signal vector.

7. The method for suppressing background noise of power frequency electromagnetic waves according to claim 6, characterized in that, The calculation method for the second-level projection in step S5 is as follows: ， ， in For passive propagation constraint matrix, For the second-order projection operator, It is the complex vector of the separated natural field signal.

8. The method for suppressing background noise of power frequency electromagnetic waves according to claim 1, characterized in that, The power frequency base frequency is 50Hz or 60Hz.

9. The method for suppressing background noise of power frequency electromagnetic waves according to claim 1, characterized in that, The horizontal component of the electric field is the electric field in the east-west direction. and the electric field in the north-south direction The horizontal component of the magnetic field is an east-west oriented magnetic field. and the north-south magnetic field The observed complex vector is composed of , , , A 4-dimensional complex column vector composed of Fourier coefficients at the power frequency fundamental frequency.

10. The method for suppressing background noise of power frequency electromagnetic waves according to claim 1, characterized in that, The method further includes: For the odd harmonic frequencies of the power frequency fundamental frequency, steps S2 to S6 are performed respectively to suppress power frequency harmonic interference.

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