CN114154111A - Bit field data downward continuation method for frequency domain continuous-fraction expansion - Google Patents
Bit field data downward continuation method for frequency domain continuous-fraction expansion Download PDFInfo
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- CN114154111A CN114154111A CN202111420104.4A CN202111420104A CN114154111A CN 114154111 A CN114154111 A CN 114154111A CN 202111420104 A CN202111420104 A CN 202111420104A CN 114154111 A CN114154111 A CN 114154111A
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Abstract
The invention discloses a bit field data downward continuation method based on frequency domain continuous fraction expansion, which comprises the following steps: s1: acquiring actually measured potential field data, wherein the actually measured potential field data comprises gravity field or magnetic field data; s2, gridding the actually measured bit field data to form bit field abnormal signals of a regular grid; s3: performing Fourier transform on the meshed actually-measured bit field data to a frequency domain, setting the calculation depth of downward continuation, multiplying the bit field data of the frequency domain by a downward continuation factor which is continuously and divisionally expanded by the frequency domain to obtain a frequency domain downward continuation calculation result of the set depth, and performing inverse Fourier transform on the frequency domain calculation result to obtain a finally-calculated downward continuation result; s4: the result obtained at S3 is plotted, and the obtained downward continuation bit field data is visually displayed. Compared with the conventional regularization downward continuation method and the Taylor series downward continuation method, the method has higher precision and stronger stability, and the high-precision continuation calculation of the bit field data can be carried out by utilizing the method.
Description
Technical Field
The invention relates to the technical field of geophysical geological resource exploration, in particular to a method for downwardly extending bit field data in a frequency domain continuous-division expansion mode.
Background
The calculation of downward continuation of the bit field data is an extremely important processing method, and can be used for enhancing weak abnormal information, improving data resolution, highlighting residual abnormality and the like. The most applied frequency domain downward continuation method has the advantages of high computational efficiency and easy implementation, but the inherent instability of the method can cause that only 2-3 point distances can be prolonged generally, and the related improvement method cannot achieve the purpose of deep continuation. In addition, the downward continuation based on the equivalent source has a slow calculation speed due to the need of solving a large linear equation system, and is not widely applied to the actual large data processing.
In order to increase the downward continuation depth and improve the calculation speed and stability, an integral iteration downward continuation method is provided by Xueshi and the like, and a series of theories and application achievements with good effects are obtained. The iterative idea is also used in a number of new methods such as taylor series expansions. The methods are obviously improved in the aspects of improving the calculation stability and precision, increasing the downward continuation depth and the like. However, as pointed out by yaohangli and the like, if the theoretical result is unstable, the iterative calculation is also converged to an unstable result if the theoretical result is converged, so that the iterative method cannot fundamentally solve the unstable problem of downward continuation.
Therefore, how to solve the instability problem of downward continuation from the theory itself is still a key problem in enhancing bit field data and improving resolution. The rational approximation method is another important means and direction for downward continuation, and in the mathematical theory, the rational approximation method has higher precision. Therefore, by adopting the continuous fraction method in rational approximation, the calculation of downward continuation with higher precision is expected to be obtained, and the stability of downward continuation can be further improved by the filtering characteristic of the method,
disclosure of Invention
The invention aims to provide a method for calculating the downward continuation of the position field data in geological resource exploration aiming at the problems in the prior art, and has practical significance for improving the accuracy of position field exploration interpretation.
The technical scheme of the invention is as follows: a method for extending downward bit field data of frequency domain continuous fraction expansion comprises the following steps:
s1: acquiring actually measured potential field data, wherein the actually measured potential field data comprises gravity field or magnetic field data;
s2, gridding the actually measured bit field data to form bit field abnormal signals of a regular grid;
s3: performing Fourier transform on the meshed actually-measured bit field data to a frequency domain, setting the calculation depth of downward continuation, multiplying the bit field data of the frequency domain by a downward continuation factor which is continuously and divisionally expanded by the frequency domain to obtain a frequency domain downward continuation calculation result of the set depth, and performing inverse Fourier transform on the frequency domain calculation result to a space domain to obtain a finally-calculated downward continuation result;
s4: the result obtained at S3 is plotted, and the obtained downward continuation bit field data is visually displayed.
Further, the gridding calculation method in the step S2 is a minimum curvature or kriging interpolation gridding method.
Further, the method for calculating the downward continuation factor of the frequency domain continued fraction expansion in step S3 includes the following steps:
a. establishing a downward continuation factor of frequency domain continuous extension, namely performing continuous extension on the downward continuation factor:
b. selecting an expansion order suitable for downward continuation calculation according to the function characteristics of the downward continuation of the frequency domain continuous fraction expansion, wherein the function characteristics are shown in figure 1, and the previous 9 orders can be judged to have orders 1, 4, 5, 8 and 9 which can be used for downward continuation calculation according to the figure characteristics;
c. multiplying the bit field data of the frequency domain by the downward continuation factor of the frequency domain continued fraction expansion to obtain a downward continuation calculation result of the set depth plane:
wherein
Fourier transform values (ω) representing bit field data T (x', yx,ωy) Are the wave numbers in the x-and y-directions,
the number of circles,. DELTA.h, being positive indicates the distance to continue downwards.
The implementation of the invention requires a large amount of computation and requires visual display, so computer-aided computation is required. The required hardware devices include: one or more processors, storage means for storing one or more computer programs which, when executed by the one or more processors, cause the one or more processors to perform the calculations of data relating to the methods of the invention.
The invention has the beneficial effects that: the method is based on the high-precision characteristic and the stability characteristic of continuous and fractional expansion, a bit field data downward continuation method of frequency domain continuous and fractional expansion is established, and downward continuation calculation of the bit field data is realized based on the method; compared with the traditional downward continuation method, the method has the stable large-depth continuation characteristic, can effectively inhibit the noise influence in the continuation process, and obtains a more accurate continuation calculation result. Compared with the conventional downward continuation method, the method has the characteristics of larger continuation depth and higher stability, can be used for performing high-precision depth calculation of the field source, and is favorable for popularization.
Drawings
FIG. 1 is a functional characteristic of a frequency domain continuous component expansion;
FIG. 2 is a plan view of a sphere model showing gravity anomaly and a main sectional view thereof;
FIG. 3 is a main sectional view of the result of the downward continuation calculation of the abnormal gravity data of the model of FIG. 2 by using the method of the present invention and the Taylor series expansion downward continuation method;
FIG. 4 is a plan view of a magnetic anomaly of three spherical models and a main sectional view thereof;
FIG. 5 is a main sectional view of the result of the calculation of downward continuation of the magnetic force anomaly data of the model of FIG. 4 by using the method of the present invention, the regularized downward continuation method and the improved Taylor series expansion downward continuation method.
Detailed Description
Example 1
As shown in the single sphere gravity anomaly data chart of FIG. 1, the gravity anomaly is generated as shown in FIG. 2a by setting the sphere burial depth to be 100m, the sphere radius to be 20m, the density difference to be 1000kg/m ^3 and the point distance to be 10 m. For comparison, the main profile anomaly is extracted at the center position, as shown in FIG. 2 b. The method of the invention is used for downward continuation calculation, and the continuation depth is 60m (6 point distances). In order to clarify the advantages of the method of the present invention, the comparison is performed by using the conventional taylor series expansion method, and 8-order expansion is used for calculation in the comparison, so as to obtain the main section comparison result as shown in fig. 3.
Fig. 3a shows the result of the conventional taylor series expansion downward continuation method, which can be seen to have strong boundary effect, causing great interference, making the calculation accuracy low, and if the anomaly contains noise, making the anomaly submerged by the amplified noise. By adopting the method, the frequency domain conversion is firstly carried out on the original anomaly, the frequency domain is multiplied by the frequency domain factor of the method, the detailed continuation calculation can be completed, then the inverse Fourier transform returns to the space domain, the downward continuation calculation on the original anomaly is completed, and the result shown in figure 3b is obtained. The invention has more accurate advantage in downward continuation calculation compared with the traditional method.
Example 2
To further verify the effect of the method of the present invention, the magnetic force data were calculated using three spheres with different burial depths, the sphere radius was 20m, the burial depths were 100m, 120m, and 140m, the declination and declination angles were 90 ° and 0 °, respectively, the magnetic anomaly is shown in fig. 4a, and the magnetic anomaly in the main section is shown in fig. 4 b. Comparing the calculation result of the invention with the traditional regularization downward continuation calculation result (TRDC) and the improved Taylor series expansion downward continuation calculation result (ITDC), wherein the continuation distance is 60 m. The main difference of different methods is that the continuation factors are different, the frequency domain conversion is firstly carried out on the original exception, the frequency domain factors of different methods are multiplied in the frequency domain, the detailed continuation calculation can be completed, and then the inverse Fourier transform returns to the space domain, and the downward continuation calculation on the original exception is completed. As shown in fig. 5, comparing the calculation results of different methods at a depth of 60m, it can be seen that the result obtained by the method of the present invention has a larger amplitude (CFmag in the figure) and better conforms to the theoretical value, whereas the result obtained by the regularization method (TRDCmag in the figure) and the improved taylor series expansion method (ITDCmag in the figure) both have a smaller amplitude and a larger difference from the actual theoretical value, and by calculating the root mean square error thereof, the result obtained by the method of the present invention is 3.62nT, the regularization downward extension is 5.33nT, and the improved taylor series downward extension is 5.65nT, which can be seen that the result obtained by the present invention has higher precision and highlights the advantages of the present invention.
Claims (3)
1. A method for extending downward bit field data of frequency domain continuous fraction expansion is characterized by comprising the following steps:
s1: acquiring actually measured potential field data, wherein the actually measured potential field data comprises gravity field or magnetic field data;
s2, gridding the actually measured bit field data to form bit field abnormal signals of a regular grid;
s3: performing Fourier transform on the meshed actually-measured bit field data to a frequency domain, setting the calculation depth of downward continuation, multiplying the bit field data of the frequency domain by a downward continuation factor which is continuously and divisionally expanded by the frequency domain to obtain a frequency domain downward continuation calculation result of the set depth, and performing inverse Fourier transform on the frequency domain calculation result to a space domain to obtain a finally-calculated downward continuation result;
s4: the result obtained at S3 is plotted, and the obtained downward continuation bit field data is visually displayed.
2. The method as claimed in claim 1, wherein the method for extending downward bit field data of frequency domain continuous fraction expansion comprises: the gridding calculation method in the step S2 is a minimum curvature or kriging interpolation gridding method.
3. The method as claimed in claim 1, wherein the method for extending downward bit field data of frequency domain continuous fraction expansion comprises: the method for calculating the downward continuation factor of the frequency domain continued fraction expansion in the step S3 comprises the following steps:
a. establishing a downward continuation factor of frequency domain continuous extension, namely performing continuous extension on the downward continuation factor:
b. selecting an expansion order suitable for downward continuation calculation according to the function characteristics of the downward continuation of the frequency domain continuous fraction expansion, wherein the function characteristics are shown in figure 1, and the previous 9 orders can be judged to have orders 1, 4, 5, 8 and 9 which can be used for downward continuation calculation according to the figure characteristics;
c. multiplying the bit field data of the frequency domain by the downward continuation factor of the frequency domain continued fraction expansion to obtain a downward continuation calculation result of the set depth plane:
wherein
Fourier transform values (ω) representing bit field data T (x', yx,ωy) Are the wave numbers in the x-and y-directions,
the number of circles,. DELTA.h, being positive indicates the distance to continue downwards.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115356784A (en) * | 2022-08-29 | 2022-11-18 | 西南交通大学 | Generalized minimum residual large-depth potential field downward continuation method for self-adaptive damping coefficient |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115356784A (en) * | 2022-08-29 | 2022-11-18 | 西南交通大学 | Generalized minimum residual large-depth potential field downward continuation method for self-adaptive damping coefficient |
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