CN116774301A - Method, system, electronic equipment and medium for downward continuation of heavy magnetic bit field regularization - Google Patents

Method, system, electronic equipment and medium for downward continuation of heavy magnetic bit field regularization Download PDF

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CN116774301A
CN116774301A CN202310755872.8A CN202310755872A CN116774301A CN 116774301 A CN116774301 A CN 116774301A CN 202310755872 A CN202310755872 A CN 202310755872A CN 116774301 A CN116774301 A CN 116774301A
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CN116774301B (en
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曾小牛
李夕海
谭笑枫
牛超
刘继昊
张云
刘志刚
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Rocket Force University of Engineering of PLA
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Abstract

The invention discloses a gravity field regularized downward continuation method, a gravity field regularized downward continuation system, electronic equipment and a medium, and relates to the technical field of gravity field and geomagnetic field data measurement. The method comprises the steps of performing fast Fourier transform on the data of the heavy magnetic bit field to obtain a power spectrum of the data of the heavy magnetic bit field; taking the center of the data power spectrum of the heavy magnetic bit field as a circle center, taking integer multiples of the fundamental frequency as a radius to form a circle, and generating a plurality of annular bands; taking the radial wave number as an abscissa and taking the corresponding logarithmic value of each annular belt as an ordinate to obtain a logarithmic fractal corrected radial average power spectrum; taking a radial wave number corresponding to the minimum value of the logarithmic fractal corrected radial average power spectrum as a cut-off wave number; performing Fourier transform on the gravity field data to obtain a gravity field data Fourier spectrum; and obtaining a downward continuation result according to the cut-off wave number, the radial wave number, the data Fourier spectrum of the demagnetizing bit field and the downward continuation operator. The invention can automatically and quickly acquire the downward extension parameter of the heavy magnetic bit field, and has higher downward extension precision.

Description

Method, system, electronic equipment and medium for downward continuation of heavy magnetic bit field regularization
Technical Field
The invention relates to the technical field of gravitational field and geomagnetic field data measurement, in particular to a gravity magnetic bit field regularized downward continuation method, a gravity magnetic bit field regularized downward continuation system, electronic equipment and a gravity magnetic bit field regularized downward continuation medium.
Background
The downward extension can shorten the distance between the observation surface and the field source, and is an effective method for explaining the data of the heavy magnetic bit field and constructing a heavy magnetic auxiliary navigation reference map. It is well known that the down-extension of the magnetic gravity field amplifies the high frequency components in the measurement data, resulting in unstable down-extension results. In order to obtain more stable and accurate delayed results, different students have proposed different types of methods, which can be roughly classified into three types. The first type is a space domain method, which mainly comprises a boundary unit method, a finite element method, a spline function method, an equivalent source method and the like. In general, spatial domain methods have high accuracy, but are relatively complex to calculate. The second type of method is a wave number domain method, including wiener filtering method, compensation smoothing filtering method, regularization method, various iteration methods, and the like. The wave number domain method is simple to calculate, but aims at regular grid data generally, and the problems of fence effect, boundary effect and the like of wave number domain operation are needed to be considered. The third class of methods is the spatial wavenumber hybrid domain method that seeks to combine the advantages of the first two classes of methods.
In fact, the downward-extending instability manifests itself in the wavenumber domain in the amplification of the high frequency components of the data by the downward-extending factor. Therefore, most of the stable downdelay methods of various wave number domains are to suppress the amplification effect of the downdelay factors on high frequency by adding low-pass filters or modifying the downdelay factors, and the low-pass filters or modifying the downdelay factors have the problem of determining the cut-off wave numbers or the so-called regular parameters. The regular parameter determining method comprises an L-curve method, a C-norm method, a generalized cross checking method, a quasi-optimal method and the like. Common to these methods is that: firstly, determining a range of discrete variation of a regular parameter (in order to improve the calculation accuracy, the more and better the number of discrete values), then calculating the downward extension results of all the regular parameters in the range, and finally determining the optimal regular parameters, such as inflection points or maximum curvatures of an L-curve method, C-norm curves, minimum values of generalized cross check and quasi-optimal criterion curves, and the like, based on a certain criterion. Because of the need to traverse the range of variation of the canonical parameters, these canonical parameter determination methods are also referred to as "sequential methods", and there is a general problem of large calculation amount. The method for determining the cut-off wave number by fitting the radial spectrum curve of the radial average power spectrum of the potential field has the defect of needing to manually observe inflection points or fitting the radial spectrum although the physical meaning is clear.
Disclosure of Invention
The invention aims to provide a method, a system, electronic equipment and a medium for regularized downward continuation of a heavy magnetic bit field, which can automatically and quickly acquire downward continuation parameters of the heavy magnetic bit field and have higher downward continuation precision.
In order to achieve the above object, the present invention provides the following solutions:
a method of gravity bit field regularization downstream extension, comprising:
acquiring data of a heavy magnetic bit field;
performing fast Fourier transform on the data of the magnetic re-orientation field to obtain a power spectrum of the data of the magnetic re-orientation field;
taking the center of the data power spectrum of the gravity magnetic bit field as a circle center, taking integer multiples of the fundamental frequency as a radius to form a circle, and generating a plurality of annular bands;
taking the radial wave number as an abscissa and taking the corresponding logarithmic value of each annular belt as an ordinate to obtain a logarithmic fractal corrected radial average power spectrum; the corresponding logarithmic value of the annular band is obtained by taking the logarithm of the product of the average power spectrum value of the annular band and the fractal correction spectrum;
taking a radial wave number corresponding to the minimum value of the logarithmic fractal corrected radial average power spectrum as a cut-off wave number;
performing Fourier transform on the data of the magnetic re-orientation field to obtain a Fourier spectrum of the data of the magnetic re-orientation field;
and obtaining a downward continuation result of the heavy magnetic bit field according to the cut-off wave number, the radial wave number of the heavy magnetic bit field data, the Fourier spectrum of the heavy magnetic bit field data and the downward continuation operator.
Optionally, the radial wave number is an abscissa, and a logarithmic fractal corrected radial average power spectrum is obtained by taking a logarithmic value corresponding to each annular belt as an ordinate, which specifically includes:
for any ring belt, calculating the average value of the power spectrum values of all points in the ring belt to obtain the average power spectrum value of the ring belt;
taking the logarithm of the product of the average power spectrum value of the endless belt and the fractal correction spectrum to obtain a corresponding logarithm value of the endless belt;
and taking the radial wave number as an abscissa and the logarithmic value corresponding to each annular belt as an ordinate to obtain the logarithmic fractal corrected radial average power spectrum.
Optionally, the obtaining the downward continuation result of the heavy magnetic bit field according to the cut-off wave number, the radial wave number of the heavy magnetic bit field data, the fourier spectrum of the heavy magnetic bit field data and the downward continuation operator specifically includes:
inputting the cut-off wave number and the radial wave number of the heavy magnetic bit field data into a regular low-pass filter to obtain a filtering value;
calculating the product of the filtering value, the data Fourier spectrum of the heavy magnetic bit field and the downward continuation operator to obtain a downward continuation product;
and carrying out Fourier inverse transformation on the downward continuation product to obtain a downward continuation result of the heavy magnetic bit field.
Optionally, the regular low-pass filter is:
wherein (1)>Representing canonical lowThe pass filter, h, represents the depth of downward continuation of the data of the heavy magnetic bit field, ω r Radial wave number, ω, representing the data of the gravity magnetic bit field c Represents the cut-off wave number.
A gravity bit field regularization downward continuation system, comprising:
the acquisition module is used for acquiring the data of the heavy magnetic bit field;
the data power spectrum determining module of the magnetic flux re-field is used for carrying out fast Fourier transform on the magnetic flux re-field data to obtain a data power spectrum of the magnetic flux re-field;
the ring belt generation module is used for generating a plurality of ring belts by taking the center of the data power spectrum of the heavy magnetic potential field as a circle center and taking integer multiples of the fundamental frequency as a radius as a circle;
the logarithmic fractal correction radial average power spectrum determining module is used for obtaining a logarithmic fractal correction radial average power spectrum by taking a radial wave number as an abscissa and taking a logarithmic value corresponding to each annular belt as an ordinate; the corresponding logarithmic value of the annular band is obtained by taking the logarithm of the product of the average power spectrum value of the annular band and the fractal correction spectrum;
the cut-off wave number determining module is used for taking the radial wave number corresponding to the minimum value of the logarithmic fractal correction radial average power spectrum as the cut-off wave number;
the Fourier transform module is used for carrying out Fourier transform on the data of the heavy magnetic bit field to obtain the Fourier spectrum of the data of the heavy magnetic bit field;
and the downward continuation module is used for obtaining the downward continuation result of the heavy magnetic bit field according to the cut-off wave number, the radial wave number of the heavy magnetic bit field data, the Fourier spectrum of the heavy magnetic bit field data and the downward continuation operator.
Optionally, the determining module of the logarithmic fractal correction radial average power spectrum specifically includes:
an average power spectrum value calculation unit, configured to calculate, for any one zone, an average value of power spectrum values of all points in the zone, and obtain an average power spectrum value of the zone;
the logarithmic value calculation unit is used for taking the logarithm of the product of the average power spectrum value of the annular band and the fractal correction spectrum to obtain a logarithmic value corresponding to the annular band;
the logarithmic fractal correction radial average power spectrum determining unit is used for obtaining a logarithmic fractal correction radial average power spectrum by taking a radial wave number as an abscissa and a logarithmic value corresponding to each annular belt as an ordinate.
Optionally, the downward continuation module specifically includes:
the filtering value calculation unit is used for inputting the cut-off wave number and the radial wave number of the heavy magnetic bit field data into a regular low-pass filter to obtain a filtering value;
the downward continuation product calculation unit is used for calculating the products of the filtering value, the data Fourier spectrum of the heavy magnetic bit field and the downward continuation operator to obtain a downward continuation product;
and the downward continuation unit is used for carrying out Fourier inverse transformation on the downward continuation product to obtain a downward continuation result of the heavy magnetic field.
Optionally, the regular low-pass filter is:
wherein (1)>Represents a regular low-pass filter, h represents the depth of downward continuation of the data of the heavy magnetic bit field, omega r Radial wave number, ω, representing the data of the gravity magnetic bit field c Represents the cut-off wave number.
An electronic device, comprising:
the device comprises a memory for storing a computer program, and a processor for running the computer program to cause the electronic device to perform the method of re-magnetic bit field regularization down-continuation as described above.
A computer readable storage medium storing a computer program which when executed by a processor implements the re-magnetic bit field regularization down-continuation method described above.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
according to the method, the radial wave number is taken as an abscissa, the product of the average power spectrum value of the annular belt and the fractal correction spectrum is taken as an ordinate, the logarithmic fractal correction radial average power spectrum is obtained, the radial wave number corresponding to the minimum value of the logarithmic fractal correction radial average power spectrum is taken as a cutoff wave number, the cutoff wave number can be automatically determined, the automatic and rapid problem is solved, and the downward continuation precision is high.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flowchart of a method for regularization down-continuation of a heavy magnetic bit field according to an embodiment of the present invention;
FIG. 2 is a graph showing the variation of signal spectrum, noise spectrum and combinations thereof with radial wavenumber;
FIG. 3 is a contour plot of data of a noise-added gravity model with Gaussian white noise added;
FIG. 4 is a graph comparing radial average power spectra of the three Gaussian white noise level gravity data of FIG. 3;
FIG. 5 is a fractal corrected radial average power spectrum versus gravity data for the three Gaussian white noise levels of FIG. 3;
FIG. 6 is a graph of fractal corrected radial average power spectrum versus 2% Gaussian white noise level gravity data at different scale indices β;
FIG. 7 is a graph comparing the result of three methods of downward continuation with the theoretical gravity on the principal section;
fig. 8 is a graph comparing the residual of the three methods of downward continuation results and theoretical gravity on the main section.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
Let z axis down positive, U 0 (ω x ,ω y ) For the raw data u on the observation plane z=0 0 Fourier transform result of (x, y), U h (ω x ,ω y ) For z=h (h > 0, field source is located below z=h plane) bit field data u h The fourier transform results of (x, y) then their relationship in the wavenumber domain is:
wherein omega x And omega y Wavenumbers in x and y directions, respectively;radial wave number; />Operators are extended for downward. Due to->Amplifying characteristic of data high-frequency signal and noise, resulting in delay result U h (ω x ,ω y ) Unstable, and the greater the distance h, the more unstable the downward delay. For stable scaling, a low-pass filter L (ω r ) To suppress interference of high frequency noise, i.e
Wherein U 'is' h (ω x ,ω y ) Is a stable downward-extending result. Based on this, the embodiment of the invention provides a method for regularized downward continuation of a heavy magnetic bit field, as shown in fig. 1, the method specifically includes:
step 101: acquiring the magnetic flux field data u 0 (x,y)。
Step 102: and performing fast Fourier transform on the data of the magnetic re-orientation field to obtain a power spectrum of the data of the magnetic re-orientation field.
Step 103: and generating a plurality of endless belts by taking the center of the data power spectrum of the magnetic flux re-positioning field as a circle center and taking integer multiples of the fundamental frequency as a radius as a circle.
Step 104: taking the radial wave number as an abscissa and taking the corresponding logarithmic value of each annular belt as an ordinate to obtain a logarithmic fractal corrected radial average power spectrum; the corresponding logarithmic value of the ring belt is the average power spectrum value P (omega) r ) Fractal correction spectrumTaking the logarithm of the product of (i.e.)>Obtained.
Step 105: taking the radial wave number corresponding to the minimum value of the logarithmic fractal corrected radial average power spectrum as a cut-off wave number omega (roughly divided by signal and noise) c 。
Step 106: for the magnetic re-bit field data u 0 (x, y) performing Fourier transform to obtain a data Fourier spectrum U of the heavy magnetic bit field 0 (ω x ,ω y )。
Step 107: and obtaining a downward continuation result of the heavy magnetic bit field according to the cut-off wave number, the radial wave number of the heavy magnetic bit field data, the Fourier spectrum of the heavy magnetic bit field data and the downward continuation operator.
In practical application, the method for obtaining the logarithmic fractal corrected radial average power spectrum by taking the radial wave number as an abscissa and taking the logarithmic value corresponding to each annular belt as an ordinate specifically comprises the following steps:
and calculating the average value of the power spectrum values of all points in any ring belt to obtain the average power spectrum value of the ring belt.
And taking the logarithm of the product of the average power spectrum value of the endless belt and the fractal correction spectrum to obtain the corresponding logarithm value of the endless belt.
And taking the radial wave number as an abscissa and the logarithmic value corresponding to each annular belt as an ordinate to obtain the logarithmic fractal corrected radial average power spectrum.
In practical application, the obtaining the downward continuation result of the heavy magnetic bit field according to the cut-off wave number, the radial wave number of the heavy magnetic bit field data, the fourier spectrum of the heavy magnetic bit field data and the downward continuation operator specifically includes:
inputting the cut-off wave number and the radial wave number of the heavy magnetic bit field data into a regular low-pass filter to obtain a filtering valueLet less than the cutoff wavenumber omega c Is only for the signal spectrum all-pass of greater than the cut-off wave number omega c Is low pass filtered.
Calculating the product of the filtering value, the data Fourier spectrum of the demagnetizing bit field and the downward continuation operator, namelyThe downward continuation product is obtained.
Inverse fourier transforming the downward continuation product, i.eAnd obtaining the downward continuation result of the heavy magnetic field.
In practical application, the regular low-pass filter is:
wherein, the liquid crystal display device comprises a liquid crystal display device,represents a regular low-pass filter, h represents the depth of downward continuation of the data of the heavy magnetic bit field, omega r Radial wave number, ω, representing the data of the gravity magnetic bit field c Represents the cut-off wave number.
The invention provides an embodiment for verifying the effectiveness of the method, which comprises the following specific steps:
spector and Grant (1970) prove that the depth h of a rectangular prism magnetic source with spatial random uncorrelated distribution and the radial average power spectrum P (omega) of the magnetic source r ) There is a simple exponential relationship:
where A is a constant determined by the source intensity. The logarithm of the two sides of the formula (4) can be obtained:
ln(P(ω r ))＝lnA-2ω r h (5)
the depth of the magnetic source is obtained by fitting a logarithmic radial average power spectrum curve in a certain wave number range and by the slope of the straight line after fitting. Thus, equation (5) and some variations thereof are widely used for estimation of the top, bottom, and centroid of a magnetic source. Subsequent researches show that the random uncorrelated magnetic source model has the problem of transition simplification, the magnetic susceptibility distribution has typical spatial self-similarity and scale invariance rules, and can be described by a fractal power law model, and the model of the formula (4) needs to be improved as follows:
wherein, beta is more than or equal to 2 and less than or equal to 4, and the scale index of the radial spectrum. For large-scale, structurally strong magnetic blocks of magnetic substrates, there is typically a fractal structure of β=2.9.
The former research mostly only considers the application of radial spectrum in magnetic source depth estimation, and rarely considers the estimation of signal and noise demarcation points. If the case where the measured data all contain noise (normally assumed to be white noise) is considered, the model of equation (6) should obviously be refined to:
wherein P is N Is the power constant corresponding to white noise. Multiplying two sides of (7)And taking the logarithm to obtain:
in the right logarithmic brackets of formula (8),is along with radial wave number omega r Monotonically decreasing function, and->Is along with radial wave number omega r Monotonically increasing functions due to A and P N Are all constant, their sum ∈ ->The approximate V-shaped is presented, and after the natural logarithm is taken, the monotonically increasing natural logarithm function does not change the approximate shape of the curve; thus, the left side of equation (8) is modeled as a fractal power law model->Data power spectrum P (ω r ) Modified log power spectrum +.>Will also generally exhibit a "V" shape. The low and medium wave number area corresponding to the left end of the V-shaped curve is composed of effective signal +.>The dominant region, and the high wavenumber region corresponding to the right end of the V-shaped curve, is defined by the noise signal +.>Dominant, therefore, the wave number corresponding to the minimum value of the V-shaped curve is taken as the cut-off wave number omega of the approximate boundary between the effective signal and the noise c Has certain rationality.
Let constant a=0.0001, source depth h=500, radial wavenumber ω r ∈[0,0.01]Noise level P N =30, β=2.9, then the radial average power spectrumFractal corrected noise spectrum->Sum of two items->And the variation of the natural logarithm result with radial wave number is shown in figure 2. As can be seen from fig. 2, the radial average power spectrum of the signalRadial wave number omega r Monotonous decrease, fractal correction noise spectrum->Radial wave number omega r Monotonically rise, the sum of them +.>Is a concave function, the curve of the function presents a V shape, and the logarithmic result of the functionAlso presenting a "V" shape. Thus (2)Can naturally take the logarithmThe wave number corresponding to the minimum value is taken as a cut-off wave number omega of approximate demarcation between the signal and the noise c 。
In order to verify the effectiveness of the automatic determination method of the filter parameters, a classical double-sphere gravity model is adopted for verification. The parameters of the two spheres are shown in table 1 (z coordinate positive downward). The number of lines M and the number of points N per line are 512, and the point distance Deltax and the line distance Deltay are 50M.
Table 1 double sphere gravity model parameter table
In the test, the gravity data at the h=0m plane is taken as the observation data, and the zero mean value, the mean square error and the gaussian white noise of which the absolute average value of the height theoretical gravity anomaly is 0.2% (0.0001 mGAL, signal to noise ratio 62.03 dB), 2% (0.001 mGAL, signal to noise ratio 42.03 dB) and 20% (0.01 mGAL, signal to noise ratio 22.03 dB) are respectively added to simulate the actual situation, so that the results are shown in fig. 3 (a), 3 (b) and 3 (c), wherein fig. 3 (a) is a noisy gravity model data contour map added with 0.2% of gaussian white noise, fig. 3 (b) is a noisy gravity model data contour map added with 2% of gaussian white noise, and fig. 3 (c) is a noisy gravity model data contour map added with 20% of gaussian white noise. The log radial average power spectrum ln (P (ω) of the noisy gravity anomaly data of fig. 3 (a) to 3 (c) was calculated respectively r ) The results are shown in fig. 4). As can be seen from fig. 4: (1) When the noise level is smaller, the corresponding logarithmic radial average power spectrum inflection point is less obvious, and the approximate demarcation points of the signal spectrum and the noise spectrum are harder to determine by visual inspection or linear fitting; (2) The smaller the noise level, the larger the radial wave number corresponding to the logarithmic radial average power spectrum inflection point. Using fractal power law modelFor the noisy gravity anomaly data radial average power spectrum P (ω) of FIGS. 3 (a) through 3 (c) r ) Modified logarithmic radial average Power Spectrum +.>As shown in fig. 5. As can be seen from fig. 5: (1) Adopts fractal power law model->The spectral line obtained after the radial average power spectrum is corrected has obvious V-shaped characteristics, and the position of the minimum value is convenient to determine; (2) As the noise level increases, the radial wave number corresponding to the minimum of the modified radial average power spectrum curve decreases in turn. Fractal power law model +.>The results using different scale indices (β=2, 2.9, 4) are shown in fig. 6. As can be seen from fig. 6: (1) The larger the scale index beta is, the more obvious the V-shaped characteristic of the curve is; (2) The minimum values of the curves under correction of different scale indexes beta are consistent, in other words, the minimum values of the corrected radial power spectrum are consistent within the range of 2-4 and are not changed along with the change of the scale indexes beta.
Next, we take the noisy gravity data at the h=0m plane as the observation data, then use the Ti khonov regular low-pass filter (equation (3), method 1), the modified Tikhonov regular low-pass filter (equation (4), method 1) and the modified derivative iteration method (Wang Ze et al, 2022), method 3) to extend it down 1000m (20 times the point distance), and let the resulting extension value u be c And a true gravitational field value u at a height of 1000m t Using mean square error (Root mean square error, RMSE)
And Relative Error (RE)
To calculate and compare the extension errors.
By means of FIG. 5, the corresponding low-pass filter cutoff wave number omega can be determined from the minimum corresponding to the corrected radial average power spectrum curve added with 0.2%, 2%, 20% different noise level gravity data c Sequentially 1.10X10 -3 、9.38×10 -4 、6.64×10 -4 Let the low-pass filter at these cut-off wave numbers omega c At 0.5, the relation between the regular parameter and the cut-off wave number is utilizedThe corresponding regular parameters can be found to be 6.57 multiplied by 10 respectively -7 、7.65×10 -6 、2.38×10 -4 . Two low pass filters and improved derivative iteration related parameters and extended error pairs at three noise levels are shown in tables 2, 3 and 4.
For visual comparison of the extension effect, the values of the extension data obtained after the downward extension by the three methods and the values of the real gravity data on the h=1000m plane on the main sections above the two centers are put together, which are compared with each other as shown in fig. 7 (a), fig. 7 (b) and fig. 7 (c), wherein fig. 7 (a) is a comparison graph of the downward extension result obtained by processing the 0.2% gaussian white noise gravity observation data by the three methods and the theoretical gravity on the main section, fig. 7 (b) is a comparison graph of the downward extension result obtained by processing the 2% gaussian white noise gravity observation data by the three methods and the theoretical gravity on the main section, and fig. 7 (c) is a comparison graph of the downward extension result obtained by processing the 20% gaussian white noise gravity observation data by the three methods and the theoretical gravity on the main section; the differences between the three continuation results and the true values are shown in fig. 8 (a), fig. 8 (b) and fig. 8 (c), wherein fig. 8 (a) is a graph of a comparison of a downward continuation result obtained by processing 0.2% gaussian white noise gravity observation data by three methods with a residual error of theoretical gravity on a main section, fig. 8 (b) is a graph of a comparison of a downward continuation result obtained by processing 2% gaussian white noise gravity observation data by three methods with a residual error of theoretical gravity on a main section, and fig. 8 (c) is a graph of a comparison of a downward continuation result obtained by processing 20% gaussian white noise gravity observation data by three methods with a residual error of theoretical gravity on a main section. As can be seen from tables 2 to 4 and fig. 7 to 8: (1) The regularization method adopts the corresponding regularization parameters obtained by the gravity bit field regularization downward continuation method, the downward continuation result is superior to the improved derivative iteration method, and the effectiveness of the method is verified; (2) At low noise levels, the downdelay of the regular low-pass filter is less than that of the modified regular low-pass filter (i.e., equation 3), but as the noise level increases, the advantages of the modified regular low-pass filter gradually increase.
TABLE 2 comparison of theoretical gravity model data plus 0.2% noise
TABLE 3 comparison of theoretical gravity model data plus 2% noise
TABLE 4 comparison of theoretical gravity model data plus 20% noise
The invention also provides a re-magnetic bit field regularization downward continuation system aiming at the method, which comprises the following steps:
and the acquisition module is used for acquiring the data of the heavy magnetic bit field.
And the data power spectrum determination module of the magnetic flux re-field is used for carrying out fast Fourier transform on the magnetic flux re-field data to obtain a data power spectrum of the magnetic flux re-field.
And the ring belt generating module is used for generating a plurality of ring belts by taking the center of the data power spectrum of the heavy magnetic bit field as a circle center and taking integer multiples of the fundamental frequency as a radius as a circle.
The logarithmic fractal correction radial average power spectrum determining module is used for obtaining a logarithmic fractal correction radial average power spectrum by taking a radial wave number as an abscissa and taking a logarithmic value corresponding to each annular belt as an ordinate; the corresponding logarithmic value of the endless belt is obtained by taking the logarithm of the product of the average power spectrum value of the endless belt and the fractal correction spectrum.
And the cut-off wave number determining module is used for taking the radial wave number corresponding to the minimum value of the logarithmic fractal corrected radial average power spectrum as the cut-off wave number.
And the Fourier transform module is used for carrying out Fourier transform on the data of the heavy magnetic bit field to obtain the Fourier spectrum of the data of the heavy magnetic bit field.
And the downward continuation module is used for obtaining the downward continuation result of the heavy magnetic bit field according to the cut-off wave number, the radial wave number of the heavy magnetic bit field data, the Fourier spectrum of the heavy magnetic bit field data and the downward continuation operator.
As an optional implementation manner, the logarithmic fractal correction radial average power spectrum determining module specifically includes:
and the average power spectrum value calculation unit is used for calculating the average value of the power spectrum values of all points in any ring belt to obtain the average power spectrum value of the ring belt.
And the logarithmic value calculation unit is used for taking the logarithm of the product of the average power spectrum value of the endless belt and the fractal correction spectrum to obtain the logarithmic value corresponding to the endless belt.
The logarithmic fractal correction radial average power spectrum determining unit is used for obtaining a logarithmic fractal correction radial average power spectrum by taking a radial wave number as an abscissa and a logarithmic value corresponding to each annular belt as an ordinate.
As an optional implementation manner, the downward continuation module specifically includes:
and the filtering value calculation unit is used for inputting the cut-off wave number and the radial wave number of the heavy magnetic bit field data into a regular low-pass filter to obtain a filtering value.
And the downward continuation product calculation unit is used for calculating the products of the filtering value, the data Fourier spectrum of the heavy magnetic bit field and the downward continuation operator to obtain downward continuation products.
And the downward continuation unit is used for carrying out Fourier inverse transformation on the downward continuation product to obtain a downward continuation result of the heavy magnetic field.
As an alternative embodiment, the regular low-pass filter is:
wherein (1)>Represents a regular low-pass filter, h represents the depth of downward continuation of the data of the heavy magnetic bit field, omega r Radial wave number, ω, representing the data of the gravity magnetic bit field c Represents the cut-off wave number.
The embodiment of the invention also provides electronic equipment, which comprises:
the device comprises a memory and a processor, wherein the memory is used for storing a computer program, and the processor runs the computer program to enable the electronic device to execute the gravity magnetic bit field regularization downward continuation method.
The embodiment of the invention also provides a computer readable storage medium, which stores a computer program, and the computer program realizes the downward continuation method of the heavy magnetic bit field regularization when being executed by a processor.
The invention has the following technical effects:
the invention starts from a fractal corrected bit field radial average power spectrum theoretical model, based on the characteristics of fractal corrected logarithmic radial spectrum curves, provides a gravity bit field regularized downward extension method, and can automatically determine downward extension parameters (cut-off wave numbers) by solving the minimum value of the fractal corrected radial spectrum curves, thereby solving the problems of automatic and rapid acquisition of the gravity bit field downward extension parameters and having higher downward extension precision.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.

Claims (10)

1. A method for regularized downstream extension of a magnetic flux field, comprising:
acquiring data of a heavy magnetic bit field;
performing fast Fourier transform on the data of the magnetic re-orientation field to obtain a power spectrum of the data of the magnetic re-orientation field;
taking the center of the data power spectrum of the gravity magnetic bit field as a circle center, taking integer multiples of the fundamental frequency as a radius to form a circle, and generating a plurality of annular bands;
taking the radial wave number as an abscissa and taking the corresponding logarithmic value of each annular belt as an ordinate to obtain a logarithmic fractal corrected radial average power spectrum; the corresponding logarithmic value of the annular band is obtained by taking the logarithm of the product of the average power spectrum value of the annular band and the fractal correction spectrum;
taking a radial wave number corresponding to the minimum value of the logarithmic fractal corrected radial average power spectrum as a cut-off wave number;
performing Fourier transform on the data of the magnetic re-orientation field to obtain a Fourier spectrum of the data of the magnetic re-orientation field;
and obtaining a downward continuation result of the heavy magnetic bit field according to the cut-off wave number, the radial wave number of the heavy magnetic bit field data, the Fourier spectrum of the heavy magnetic bit field data and the downward continuation operator.
2. The method for regularized downstream extension of the gravity-magnetic bit field according to claim 1, wherein the obtaining the logarithmic fractal corrected radial average power spectrum by taking the radial wave number as the abscissa and the corresponding logarithmic value of each endless belt as the ordinate specifically comprises:
for any ring belt, calculating the average value of the power spectrum values of all points in the ring belt to obtain the average power spectrum value of the ring belt;
taking the logarithm of the product of the average power spectrum value of the endless belt and the fractal correction spectrum to obtain a corresponding logarithm value of the endless belt;
and taking the radial wave number as an abscissa and the logarithmic value corresponding to each annular belt as an ordinate to obtain the logarithmic fractal corrected radial average power spectrum.
3. The method for regularized downward continuation of the magnetic field according to claim 1, wherein the obtaining the downward continuation result of the magnetic field according to the cut-off wave number, the radial wave number of the magnetic field data, the fourier spectrum of the magnetic field data and the downward continuation operator specifically comprises:
inputting the cut-off wave number and the radial wave number of the heavy magnetic bit field data into a regular low-pass filter to obtain a filtering value;
calculating the product of the filtering value, the data Fourier spectrum of the heavy magnetic bit field and the downward continuation operator to obtain a downward continuation product;
and carrying out Fourier inverse transformation on the downward continuation product to obtain a downward continuation result of the heavy magnetic bit field.
4. The method of claim 1, wherein the regular low-pass filter is:
the regular low-pass filter, h represents the depth of downward continuation of the data of the heavy magnetic bit field, omega r Radial wave number, ω, representing the data of the gravity magnetic bit field c Representing cut-off wave number。
5. A gravity bit field regularization downward continuation system, comprising:
the acquisition module is used for acquiring the data of the heavy magnetic bit field;
the data power spectrum determining module of the magnetic flux re-field is used for carrying out fast Fourier transform on the magnetic flux re-field data to obtain a data power spectrum of the magnetic flux re-field;
the ring belt generation module is used for generating a plurality of ring belts by taking the center of the data power spectrum of the heavy magnetic potential field as a circle center and taking integer multiples of the fundamental frequency as a radius as a circle;
the logarithmic fractal correction radial average power spectrum determining module is used for obtaining a logarithmic fractal correction radial average power spectrum by taking a radial wave number as an abscissa and taking a logarithmic value corresponding to each annular belt as an ordinate; the corresponding logarithmic value of the annular band is obtained by taking the logarithm of the product of the average power spectrum value of the annular band and the fractal correction spectrum;
the cut-off wave number determining module is used for taking the radial wave number corresponding to the minimum value of the logarithmic fractal correction radial average power spectrum as the cut-off wave number;
the Fourier transform module is used for carrying out Fourier transform on the data of the heavy magnetic bit field to obtain the Fourier spectrum of the data of the heavy magnetic bit field;
and the downward continuation module is used for obtaining the downward continuation result of the heavy magnetic bit field according to the cut-off wave number, the radial wave number of the heavy magnetic bit field data, the Fourier spectrum of the heavy magnetic bit field data and the downward continuation operator.
6. The gravity bit field regularization downward continuation system of claim 5, wherein the logarithmic fractal correction radial average power spectrum determination module specifically comprises:
an average power spectrum value calculation unit, configured to calculate, for any one zone, an average value of power spectrum values of all points in the zone, and obtain an average power spectrum value of the zone;
the logarithmic value calculation unit is used for taking the logarithm of the product of the average power spectrum value of the annular band and the fractal correction spectrum to obtain a logarithmic value corresponding to the annular band;
the logarithmic fractal correction radial average power spectrum determining unit is used for obtaining a logarithmic fractal correction radial average power spectrum by taking a radial wave number as an abscissa and a logarithmic value corresponding to each annular belt as an ordinate.
7. The gravity field regularized down-continuation system according to claim 5, characterized in that the down-continuation module comprises in particular:
the filtering value calculation unit is used for inputting the cut-off wave number and the radial wave number of the heavy magnetic bit field data into a regular low-pass filter to obtain a filtering value;
the downward continuation product calculation unit is used for calculating the products of the filtering value, the data Fourier spectrum of the heavy magnetic bit field and the downward continuation operator to obtain a downward continuation product;
and the downward continuation unit is used for carrying out Fourier inverse transformation on the downward continuation product to obtain a downward continuation result of the heavy magnetic field.
8. The gravity bit field regularization downward continuation system of claim 5, wherein the regularized low pass filter is:
the regular low-pass filter, h represents the depth of downward continuation of the data of the heavy magnetic bit field, omega r Radial wave number, ω, representing the data of the gravity magnetic bit field c Represents the cut-off wave number.
9. An electronic device, comprising:
a memory for storing a computer program that runs the computer program to cause the electronic device to perform the gravity bit field regularization downward continuation method according to any of claims 1-4.
10. A computer readable storage medium, characterized in that it stores a computer program which, when executed by a processor, implements the re-magnetic bit field regularization downward continuation method of any of claims 1-4.
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