CN111142155B - Complex field weak signal recovery method based on vector surface element and electronic equipment - Google Patents

Complex field weak signal recovery method based on vector surface element and electronic equipment Download PDF

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CN111142155B
CN111142155B CN201911406030.1A CN201911406030A CN111142155B CN 111142155 B CN111142155 B CN 111142155B CN 201911406030 A CN201911406030 A CN 201911406030A CN 111142155 B CN111142155 B CN 111142155B
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gather
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target track
track
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CN111142155A (en
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徐洪斌
刘志成
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Beijing Dongfang Lianchuang Geophysical Technology Co ltd
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    • G01VGEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28Processing seismic data, e.g. for interpretation or for event detection
    • G01V1/288Event detection in seismic signals, e.g. microseismics
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01VGEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28Processing seismic data, e.g. for interpretation or for event detection
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Abstract

A complex field weak signal recovery method based on a vector bin and an electronic device are disclosed. The method can comprise the following steps: step 1: determining a target channel, and further constructing a vector surface element channel set corresponding to the target channel; step 2: performing horizontal superposition on the vector surface element gather to obtain a horizontal superposition channel; and step 3: performing Hilbert transform on the vector surface element gather, and calculating a complex field cosine phase function gather; and 4, step 4: calculating a weighting function according to the complex field cosine phase function gather; and 5: calculating a processing result of the target track according to the weighting function and the horizontal superposition track; step 6: and (5) replacing the target tracks, and repeating the steps 1-5 until all the target tracks are completed. The invention constructs the vector surface element channel set, restores the weak signal submerged by noise by adopting a complex field processing method, improves the signal-to-noise ratio of the prestack data on the basis of amplitude preservation, frequency preservation and phase preservation, meets the technical requirement of fidelity denoising, and improves the quality of the original data.

Description

Complex field weak signal recovery method based on vector surface element and electronic equipment
Technical Field
The invention belongs to the technical field of seismic exploration digital signal processing, and particularly relates to a complex field weak signal recovery method based on a vector surface element and electronic equipment.
Background
The method has the disadvantages of severe change of terrain altitude difference, poor excitation receiving condition and the like in a complex seismic exploration block, the signal-to-noise ratio of the acquired seismic data is very low, and the existing pre-stack denoising method and technology are not completely applicable and have great limitation and inadaptability.
The prior pre-stack denoising technology mainly has three problems, namely, effective weak signals can be damaged when noise is removed; secondly, the fidelity is not enough, and side effects are easy to be brought; thirdly, effective fruits are gathered on the prestack tracks, but no obvious effect is generated on the superposed section, namely the prestack effect and the poststack effect are generated. Therefore, a prestack fidelity denoising technique is urgently needed in the prestack denoising technical field, and it is necessary to develop a complex field weak signal recovery method based on a vector bin and an electronic device.
The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.
Disclosure of Invention
In view of this, the embodiment of the present disclosure provides a vector bin-based complex field weak signal recovery method and an electronic device, where a vector bin gather is constructed, a complex field processing method is adopted to recover a weak signal submerged by noise, so as to improve the signal-to-noise ratio of prestack data on the basis of amplitude preservation, frequency preservation and phase preservation, meet the requirements of fidelity denoising technology, improve the quality of original data, achieve an obvious effect on both the prestack gather and the stacking section, and substantially solve the technical bottleneck problem of conventional prestack denoising, namely "prestack effective and poststack ineffective".
The embodiment of the disclosure provides a complex field weak signal recovery method based on a vector bin, which includes: step 1: determining a target track xm(t), further constructing a vector surface element gather corresponding to the target road; step 2: performing horizontal superposition on the vector surface element gather to obtain a horizontal superposition channel; and step 3: performing Hilbert transform on the vector surface element gather, and calculating a complex field cosine phase function gather; and 4, step 4: calculating a weighting function according to the complex field cosine phase function gather; and 5: calculating a processing result of the target track according to the weighting function and the horizontal superposition track; step 6: and (5) replacing the target tracks, and repeating the steps 1-5 until all the target tracks are completed.
Preferably, the step 1 comprises: with the target track xm(t) the CMP bin in which the target track x is located is taken as a central CMP binmAnd (t) taking the offset distance and the azimuth angle as standards, screening seismic channels with the offset distance and the azimuth angle consistent with the standards from the central CMP surface element and the adjacent CMP surface elements, and constructing the vector surface element channel set.
Preferably, the horizontal superposition lane is:
Figure BDA0002348655620000021
wherein k ism(t) is the mth target track xm(t) corresponding horizontal superimposed lanes, xi(t) is the vector bin gather, i is the track sequence number, t is the time series, n is the number of tracks or the number of coverage.
Preferably, the set of complex-field cosine-phase functions is calculated by equation (2):
Figure BDA0002348655620000022
wherein cos θi(t) is a complex field cosine phase function gather, ai(t) is the instantaneous envelope and,
Figure BDA0002348655620000023
xiand (t) is a vector bin gather.
Preferably, the weighting function is calculated by equation (3):
Figure BDA0002348655620000031
wherein, gm(t) is the weighting function, cos θ, corresponding to the mth target tracki(t) is the complex field cosine phase function gather, and n is the number of tracks or the number of covering times.
Preferably, the processing result of the target track is calculated by formula (4):
ym(t)=gm(t)km(t) (4)
wherein, ym(t) is the processing result corresponding to the mth target track, gm(t) is the weighting function corresponding to the mth target track, kmAnd (t) is a horizontal superposition track corresponding to the mth target track.
As a specific implementation manner of the embodiment of the present disclosure, an embodiment of the present disclosure further provides an electronic device, including:
a memory storing executable instructions;
a processor executing the executable instructions in the memory to perform the steps of: step 1: determining a target track xm(t), further constructing a vector surface element gather corresponding to the target road; step 2: performing horizontal superposition on the vector surface element gather to obtain a horizontal superposition channel; and step 3: performing Hilbert transform on the vector surface element gather, and calculating a complex field cosine phase function gather; and 4, step 4: calculating a weighting function according to the complex field cosine phase function gather; and 5: calculating a processing result of the target track according to the weighting function and the horizontal superposition track; step 6: and (5) replacing the target tracks, and repeating the steps 1-5 until all the target tracks are completed.
Preferably, the step 1 comprises: with the target track xm(t) the CMP bin in which the target track x is located is taken as a central CMP binmAnd (t) taking the offset distance and the azimuth angle as standards, screening seismic channels with the offset distance and the azimuth angle consistent with the standards from the central CMP surface element and the adjacent CMP surface elements, and constructing the vector surface element channel set.
Preferably, the horizontal superposition lane is:
Figure BDA0002348655620000041
wherein k ism(t) is the mth target track xm(t) corresponding horizontal superimposed lanes, xi(t) is the vector bin gather, i is the track sequence number, t is the time series, n is the number of tracks or the number of coverage.
Preferably, the set of complex-field cosine-phase functions is calculated by equation (2):
Figure BDA0002348655620000042
wherein cos θi(t) is a complex field cosine phase function gather, ai(t) is the instantaneous envelope and,
Figure BDA0002348655620000043
xiand (t) is a vector bin gather.
Preferably, the weighting function is calculated by equation (3):
Figure BDA0002348655620000044
wherein, gm(t) is the weighting function, cos θ, corresponding to the mth target tracki(t) is the complex field cosine phase function gather, and n is the number of tracks or the number of covering times.
Preferably, the processing result of the target track is calculated by formula (4):
ym(t)=gm(t)km(t) (4)
wherein, ym(t) is the processing result corresponding to the mth target track, gm(t) is the weighting function corresponding to the mth target track, kmAnd (t) is a horizontal superposition track corresponding to the mth target track.
Additional features and advantages of the invention will be set forth in the detailed description which follows.
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The above and other objects, features and advantages of the present invention will become more apparent by describing in more detail exemplary embodiments thereof with reference to the attached drawings, in which like reference numerals generally represent like parts throughout.
Fig. 1 shows a flow chart of the steps of a vector bin based complex field weak signal recovery method according to the present invention.
Fig. 2 shows a schematic diagram of vector binning construction according to one embodiment of the present invention.
Fig. 3a, 3b, and 3c respectively show a target trace, a set of vector bin traces, and a set of complex-domain cosine-phase function traces, according to an embodiment of the invention.
FIGS. 4a, 4b show a schematic of an original velocity spectrum and an original CMP gather, respectively, in accordance with an embodiment of the present invention.
FIGS. 5a, 5b show a velocity spectrum and a CMP gather after processing, respectively, in accordance with an embodiment of the present invention.
FIGS. 6a, 6b show schematic diagrams of a residual velocity spectrum and residual gathers before and after processing, respectively, according to an embodiment of the invention.
Fig. 7a, 7b show schematic diagrams of an original horizontal overlay cross section, a processed horizontal overlay cross section, respectively, according to an embodiment of the invention.
Detailed Description
Preferred embodiments of the present invention will be described in more detail below. While the following describes preferred embodiments of the present invention, it should be understood that the present invention may be embodied in various forms and should not be limited by the embodiments set forth herein.
Fig. 1 shows a flow chart of the steps of a vector bin based complex field weak signal recovery method according to the present invention.
In this embodiment, the vector bin-based complex field weak signal recovery method according to the present invention may include: step 1: determining a target track xm(t), further constructing a vector surface element gather corresponding to the target road; step 2: performing horizontal superposition on the vector surface element gather to obtain a horizontal superposition channel; and step 3: performing Hilbert transform on the vector surface element gather, and calculating a complex field cosine phase function gather; and 4, step 4: calculating a weighting function according to the complex field cosine phase function gather; and 5: calculating a processing result of the target track according to the weighting function and the horizontal superposition track; step 6: and (5) replacing the target tracks, and repeating the steps 1-5 until all the target tracks are completed.
In one example, step 1 comprises: with the target track xm(t) the CMP bin is the center CMP bin, and the target track x is usedmAnd (t) taking the offset distance and the azimuth angle as standards, screening seismic channels with the offset distance and the azimuth angle consistent with the standards from the central CMP surface element and the adjacent CMP surface elements, and constructing a vector surface element channel set.
In one example, the horizontal overlay lanes are:
Figure BDA0002348655620000061
wherein k ism(t) is the mth target track xm(t) the corresponding horizontal overlay channel, xi (t) is the vector bin gather, i is the channel sequence number, t is the time series, and n is the channel number or the coverage number.
In one example, a complex-domain cosine phase function gather is computed by equation (2):
Figure BDA0002348655620000062
wherein cos θi(t) is a complex field cosine phase function gather, ai(t) is the instantaneous envelope and,
Figure BDA0002348655620000063
xiand (t) is a vector bin gather.
In one example, the weighting function is calculated by equation (3):
Figure BDA0002348655620000064
wherein, gm(t) is the weighting function, cos θ, corresponding to the mth target tracki(t) is the complex field cosine phase function gather, and n is the number of tracks or the number of covering times.
In one example, the processing result of the target track is calculated by equation (4):
ym(t)=gm(t)km(t) (4)
wherein, ym(t) is the processing result corresponding to the mth target track, gm(t) is the weighting function corresponding to the mth target track, kmAnd (t) is a horizontal superposition track corresponding to the mth target track.
Fig. 2 shows a schematic diagram of vector binning construction according to one embodiment of the present invention.
Specifically, based on the vector bin channel set, a complex number field processing method is used for protecting strong signals, recovering weak signals, improving the signal-to-noise ratio of a target channel, and meeting the requirements of a fidelity denoising technology.
The complex field weak signal recovery method based on the vector bin can comprise the following steps:
step 1: determining a target track xm(t) with target track xm(t) the CMP bin is the center CMP bin, and the target track x is usedm(t) the offset distance and the azimuth angle are standard, seismic channels with the offset distance and the azimuth angle consistent with the standard are screened out from the central CMP surface element and the adjacent CMP surface elements, and a vector surface element channel set is constructed, wherein the surface elements are distributed in a grid mode as shown in FIG. 2, and the adjacent surface elements are 8 surface elements around the central surface element; in the construction process, certain errors are allowed to exist between the offset distance and the azimuth angle and the standard, an error range is set, the offset distance error and the azimuth angle error are controlled by the error range, the larger the error is, the more the number of channels obtained by the vector surface element is, the coverage times are increased, the signal-to-noise ratio is favorably improved, but the fidelity is favorably improved, and similarly, the number of adjacent CMP surface elements, namely the size of the vector surface element is also controlled by parameters;
step 2: performing horizontal superposition on the vector bin gather to obtain a horizontal superposition channel as a formula (1);
and step 3: performing Hilbert transform on the vector surface element gather, and calculating a complex field cosine phase function gather through a formula (2); the complex field cosine phase function gather is independent of the amplitude, the amplitude of the weak signal is equal to that of the strong signal, and the weak signal is not divided into the strong signal and the weak signal, namely the weak signal is effectively strengthened;
and 4, step 4: calculating a weighting function according to a complex field cosine phase function gather through a formula (3);
and 5: calculating a processing result of the target track according to the weighting function and the horizontal superposition track through a formula (4);
step 6: and (5) replacing the target tracks, and repeating the steps 1-5 until all the target tracks are completed.
According to the method, a vector surface element gather is constructed, a complex number field processing method is adopted to restore a weak signal submerged by noise, the signal-to-noise ratio of prestack data is improved on the basis of amplitude preservation, frequency preservation and phase preservation, the technical requirements of fidelity denoising are met, the quality of original data is improved, obvious effects are achieved on the prestack gather and a stacking section, and the technical bottleneck problems of 'prestack effect and no poststack effect' in conventional prestack denoising are basically solved.
Application example
To facilitate understanding of the solution of the embodiments of the present invention and the effects thereof, a specific application example is given below. It will be understood by those skilled in the art that this example is merely for the purpose of facilitating an understanding of the present invention and that any specific details thereof are not intended to limit the invention in any way.
Fig. 3a, 3b, and 3c respectively show a target trace, a set of vector bin traces, and a set of complex-domain cosine-phase function traces, according to an embodiment of the invention.
The complex field weak signal recovery method based on the vector bin comprises the following steps:
step 1: determining a target track x as shown in FIG. 3am(t) with target track xm(t) the CMP bin is the center CMP bin, and the target track x is usedm(t) the offset distance and azimuth angle are standard, seismic channels with the offset distance and azimuth angle consistent with the standard are screened out from the central CMP surface element and the adjacent CMP surface elements, and a vector surface element channel set is constructed, as shown in FIG. 3 b;
step 2: performing horizontal superposition on the vector bin gather to obtain a horizontal superposition channel as a formula (1);
and step 3: performing hilbert transform on the vector bin gather, and calculating a complex field cosine phase function gather by using a formula (2), as shown in fig. 3 c;
and 4, step 4: calculating a weighting function according to a complex field cosine phase function gather through a formula (3);
and 5: calculating a processing result of the target track according to the weighting function and the horizontal superposition track through a formula (4);
step 6: and (5) replacing the target tracks, and repeating the steps 1-5 until all the target tracks are completed.
Take a certain three-dimensional work area in the western China as an example.
The name of the work area: AB 3D; full coverage area: 203 square kilometers; sampling interval: 2 ms; CMP bin size: 25m × 25 m;
processing parameters of this embodiment:
1. vector bin size: 3 x 3;
the CMP surface element where the target channel is located is taken as the center, 3 CMP surface elements are arranged In the Inline direction, 3 CMP surface elements are arranged In the Cross line direction, and 9 CMP surface elements are counted.
2. Offset error: 25 m;
the offsets are considered consistent within an error of-25 m to +25m, based on the offset of the target track.
3. Azimuth error: 30 degrees;
the azimuth is considered to be uniform within an error of-30 degrees to +30 degrees, based on the azimuth of the target track.
Fig. 4a and 4b are schematic diagrams of an original velocity spectrum and an original CMP gather, respectively, according to an embodiment of the present invention, and the signal-to-noise ratio of the acquired seismic signals is very low due to poor excitation reception conditions in a desert region.
Fig. 5a, 5b show a schematic representation of a processed velocity spectrum and CMP gather, respectively, showing a significant improvement in signal-to-noise ratio after weak signal recovery and a clear view of the velocity spectrum effective wave energy mass, in accordance with an embodiment of the present invention.
Fig. 6a, 6b show schematic diagrams of a residual velocity spectrum before and after processing and a residual gather, respectively, without significant wave event axes within the residual gather and without any significant wave energy boluses in the velocity spectrum, in accordance with an embodiment of the present invention.
Fig. 7a, 7b show schematic diagrams of an original horizontal overlay cross section, a processed horizontal overlay cross section, respectively, according to an embodiment of the invention.
The comparison result shows that the method has obvious effect no matter before or after the stack and shows extremely high fidelity.
In summary, the invention constructs the vector bin gather, reduces the weak signal submerged by noise by adopting a complex field processing method, improves the signal-to-noise ratio of prestack data on the basis of amplitude preservation, frequency preservation and phase preservation, meets the technical requirement of fidelity denoising, improves the quality of original data, has obvious effects on the prestack gather and the stacking section, and basically solves the technical bottleneck problems of 'prestack effect and no poststack effect' of the conventional prestack denoising.
It will be appreciated by persons skilled in the art that the above description of embodiments of the invention is intended only to illustrate the benefits of embodiments of the invention and is not intended to limit embodiments of the invention to any examples given.
An electronic device according to an embodiment of the present disclosure includes a memory and a processor.
The memory is to store non-transitory computer readable instructions. In particular, the memory may include one or more computer program products that may include various forms of computer-readable storage media, such as volatile memory and/or non-volatile memory. The volatile memory may include, for example, Random Access Memory (RAM), cache memory (cache), and/or the like. The non-volatile memory may include, for example, Read Only Memory (ROM), hard disk, flash memory, etc.
The processor may be a Central Processing Unit (CPU) or other form of processing unit having data processing capabilities and/or instruction execution capabilities, and may control other components in the electronic device to perform desired functions. In one embodiment of the disclosure, the processor is configured to execute the computer readable instructions stored in the memory to perform the steps of: step 1: determining a target track xm(t), further constructing a vector surface element gather corresponding to the target road; step 2: performing horizontal superposition on the vector surface element gather to obtain a horizontal superposition channel; and step 3: performing Hilbert transform on the vector surface element gather, and calculating a complex field cosine phase function gather; and 4, step 4: calculating a weighting function according to the complex field cosine phase function gather; and 5: calculating a processing result of the target track according to the weighting function and the horizontal superposition track; step 6: and (5) replacing the target tracks, and repeating the steps 1-5 until all the target tracks are completed.
In one example, the steps1 comprises: with the target track xm(t) the CMP bin is the center CMP bin, and the target track x is usedmAnd (t) taking the offset distance and the azimuth angle as standards, screening seismic channels with the offset distance and the azimuth angle consistent with the standards from the central CMP surface element and the adjacent CMP surface elements, and constructing a vector surface element channel set.
In one example, the horizontal overlay lanes are:
Figure BDA0002348655620000111
wherein k ism(t) is the mth target track xm(t) corresponding horizontal superimposed lanes, xi(t) is the vector bin gather, i is the track sequence number, t is the time series, n is the number of tracks or the number of coverage.
In one example, a complex-domain cosine phase function gather is computed by equation (2):
Figure BDA0002348655620000112
wherein cos θi(t) is a complex field cosine phase function gather, ai(t) is the instantaneous envelope and,
Figure BDA0002348655620000113
xiand (t) is a vector bin gather.
In one example, the weighting function is calculated by equation (3):
Figure BDA0002348655620000114
wherein, gm(t) is the weighting function, cos θ, corresponding to the mth target tracki(t) is the complex field cosine phase function gather, and n is the number of tracks or the number of covering times.
In one example, the processing result of the target track is calculated by equation (4):
ym(t)=gm(t)km(t) (4)
wherein, ym(t)For the processing result corresponding to the mth target track, gm(t) is the weighting function corresponding to the mth target track, kmAnd (t) is a horizontal superposition track corresponding to the mth target track.
Those skilled in the art should understand that, in order to solve the technical problem of how to obtain a good user experience, the present embodiment may also include well-known structures such as a communication bus, an interface, and the like, and these well-known structures should also be included in the protection scope of the present disclosure.
For the detailed description of the present embodiment, reference may be made to the corresponding descriptions in the foregoing embodiments, which are not repeated herein.
Having described embodiments of the present invention, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.

Claims (8)

1. A complex field weak signal recovery method based on vector bin is characterized by comprising the following steps:
step 1: determining a target track xm(t), further constructing a vector surface element gather corresponding to the target road;
step 2: performing horizontal superposition on the vector surface element gather to obtain a horizontal superposition channel;
and step 3: performing Hilbert transform on the vector surface element gather, and calculating a complex field cosine phase function gather;
and 4, step 4: calculating a weighting function according to the complex field cosine phase function gather;
and 5: calculating a processing result of the target track according to the weighting function and the horizontal superposition track;
step 6: replacing the target tracks, and repeating the steps 1-5 until all the target tracks are completed;
wherein the weighting function is calculated by equation (3):
Figure FDA0002623343610000011
wherein, gm(t) is the weighting function, cos θ, corresponding to the mth target tracki(t) is a complex field cosine phase function gather, n is the number of tracks or the number of covering times, i is a track serial number, and t is a time sequence;
wherein the processing result of the target track is calculated by formula (4):
ym(t)=gm(t)km(t) (4)
wherein, ym(t) is the processing result corresponding to the mth target track, gm(t) is the weighting function corresponding to the mth target track, kmAnd (t) is a horizontal superposition track corresponding to the mth target track.
2. The vector bin-based complex field weak signal recovery method according to claim 1, wherein the step 1 comprises:
with the target track xm(t) the CMP bin in which the target track x is located is taken as a central CMP binmAnd (t) taking the offset distance and the azimuth angle as standards, screening seismic channels with the offset distance and the azimuth angle consistent with the standards from the central CMP surface element and the adjacent CMP surface elements, and constructing the vector surface element channel set.
3. The vector bin-based complex field weak signal recovery method according to claim 1, wherein the horizontal superposition channel is:
Figure FDA0002623343610000021
wherein k ism(t) is the mth target track xm(t) corresponding horizontal superimposed lanes, xi(t) is the vector bin gather, i is the track sequence number, t is the time series, n is the number of tracks or the number of coverage.
4. The vector bin-based complex field weak signal recovery method according to claim 1, wherein the complex field cosine phase function gather is calculated by formula (2):
Figure FDA0002623343610000022
wherein cos θi(t) is a complex field cosine phase function gather, ai(t) is the instantaneous envelope and,
Figure FDA0002623343610000023
xiand (t) is a vector bin gather.
5. An electronic device, characterized in that the electronic device comprises:
a memory storing executable instructions;
a processor executing the executable instructions in the memory to perform the steps of:
step 1: determining a target track xm(t), further constructing a vector surface element gather corresponding to the target road;
step 2: performing horizontal superposition on the vector surface element gather to obtain a horizontal superposition channel;
and step 3: performing Hilbert transform on the vector surface element gather, and calculating a complex field cosine phase function gather;
and 4, step 4: calculating a weighting function according to the complex field cosine phase function gather;
and 5: calculating a processing result of the target track according to the weighting function and the horizontal superposition track;
step 6: replacing the target tracks, and repeating the steps 1-5 until all the target tracks are completed;
wherein the weighting function is calculated by equation (3):
Figure FDA0002623343610000031
wherein, gm(t) is the addition corresponding to the mth target trackWeight function, cos θi(t) is a complex field cosine phase function gather, n is the number of tracks or the number of covering times, i is a track serial number, and t is a time sequence;
wherein the processing result of the target track is calculated by formula (4):
ym(t)=gm(t)km(t) (4)
wherein, ym(t) is the processing result corresponding to the mth target track, gm(t) is the weighting function corresponding to the mth target track, kmAnd (t) is a horizontal superposition track corresponding to the mth target track.
6. The electronic device of claim 5, wherein the step 1 comprises:
with the target track xm(t) the CMP bin in which the target track x is located is taken as a central CMP binmAnd (t) taking the offset distance and the azimuth angle as standards, screening seismic channels with the offset distance and the azimuth angle consistent with the standards from the central CMP surface element and the adjacent CMP surface elements, and constructing the vector surface element channel set.
7. The electronic device of claim 5, wherein the horizontal overlay channel is:
Figure FDA0002623343610000041
wherein k ism(t) is the mth target track xm(t) corresponding horizontal superimposed lanes, xi(t) is the vector bin gather, i is the track sequence number, t is the time series, n is the number of tracks or the number of coverage.
8. The electronic device of claim 5, wherein the complex-domain cosine-phase function gather is computed by equation (2):
Figure FDA0002623343610000042
wherein cos θi(t) is a complex field cosine phase function gather, ai(t) is the instantaneous envelope and,
Figure FDA0002623343610000043
xiand (t) is a vector bin gather.
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