CN110095812B - Seismic amplitude compensation method aiming at shallow gas and diapir micro-crack influence - Google Patents

Seismic amplitude compensation method aiming at shallow gas and diapir micro-crack influence Download PDF

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CN110095812B
CN110095812B CN201910386215.4A CN201910386215A CN110095812B CN 110095812 B CN110095812 B CN 110095812B CN 201910386215 A CN201910386215 A CN 201910386215A CN 110095812 B CN110095812 B CN 110095812B
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diapir
seismic
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shallow gas
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周家雄
马光克
李雷
刘巍
张国栋
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China National Offshore Oil Corp CNOOC
CNOOC China Ltd Zhanjiang Branch
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    • 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
    • G01V1/30Analysis
    • G01V1/307Analysis for determining seismic attributes, e.g. amplitude, instantaneous phase or frequency, reflection strength or polarity
    • 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
    • G01V1/36Effecting static or dynamic corrections on records, e.g. correcting spread; Correlating seismic signals; Eliminating effects of unwanted energy
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01VGEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V2210/00Details of seismic processing or analysis
    • G01V2210/50Corrections or adjustments related to wave propagation
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    • G01MEASURING; TESTING
    • G01VGEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
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Abstract

The invention relates to a seismic amplitude compensation method aiming at shallow gas and diapir micro-fracture influence, which comprises the following steps: acquiring an amplitude influence rule of shallow gas and diapir microfractures; step two, solving an amplitude compensation coefficient of the seismic reflection datum plane; decomposing the amplitude compensation coefficient of the seismic reflection datum plane; fourthly, identifying the space distribution of shallow gas and diapir microfractures; step five, verifying the amplitude compensation coefficient of the seismic reflection datum plane; step six, constructing a seismic amplitude compensation coefficient model; and seventhly, performing amplitude compensation on the seismic body based on the seismic amplitude compensation coefficient model. The invention has the beneficial effects that: can effectively eliminate the earthquake amplitude abnormality caused by shallow gas and diapir micro-cracks and improve the fidelity of the earthquake amplitude.

Description

Seismic amplitude compensation method aiming at shallow gas and diapir micro-crack influence
Technical Field
The invention relates to an earthquake amplitude compensation method aiming at shallow gas and diapir micro-fracture influence.
Background
With the continuous deepening of oil exploration and development, the exploration and development difficulty of oil and gas fields is more and more increased, the quality requirement of seismic data is higher and higher, the seismic amplitude attribute is one of the important attributes of the seismic data, and the seismic amplitude attribute is widely applied in the aspects of high-resolution processing, construction interpretation, reservoir research, dessert prediction and the like, so that the reality significance of amplitude maintenance is great, the seismic reflection amplitude is inevitably influenced by various factors in the process of seismic wave propagation, particularly in a buried deeper stratum, a plurality of seismic amplitude compensation technologies are available at the present stage, such as spherical diffusion compensation, transmission loss amplitude compensation, surface consistency amplitude compensation, inverse Q filtering and the like, but the technologies are provided for ubiquitous amplitude influencing factors such as spherical diffusion, transmission loss, complex surface conditions or stratum absorption attenuation and the like, and for a relatively special abnormal body, for example, shallow gas and bed-breaking microcracks can cause large spatial variation of seismic reflection amplitude of the same stratum and amplitude distortion, seriously affect seismic amplitude attribute analysis and subsequent reservoir prediction results, and cannot be effectively compensated by the conventional seismic amplitude compensation method.
Disclosure of Invention
The invention aims to provide an earthquake amplitude compensation method aiming at the influence of shallow gas and diapir micro-fractures, which can effectively eliminate the amplitude abnormality caused by the shallow gas and diapir micro-fractures and improve the fidelity of earthquake amplitude.
In order to achieve the purpose, the invention adopts the following technical scheme:
a seismic amplitude compensation method aiming at shallow layer gas and diapir microfracture influence comprises the following steps:
the method comprises the following steps: establishing a geological model of shallow gas and diapir micro fractures by combining the geological condition of a site, and obtaining the amplitude influence rule of the shallow gas and the diapir micro fractures according to an earthquake forward modeling analysis method;
step two: according to the seismic reflection datum plane selection principle, respectively selecting seismic reflection datum planes on the upper surface and the lower surface of a target layer, extracting the root mean square amplitude attribute of the seismic reflection datum planes, normalizing the root mean square amplitude attribute of the seismic reflection datum planes and acquiring the reciprocal to obtain an amplitude compensation coefficient of the seismic reflection datum planes;
step three: decomposing the seismic reflection reference surface amplitude compensation coefficient obtained in the second step by using the amplitude influence rule of the shallow gas and the diapir micro-fractures obtained in the first step, wherein the seismic reflection reference surface amplitude compensation coefficient can be decomposed into a shallow gas amplitude compensation coefficient and a diapir micro-fracture amplitude compensation coefficient;
step four: constructing characteristic factor bodies of the shallow gas and the diapir micro-fractures according to the seismic reflection characteristics of the shallow gas and the diapir micro-fractures, carrying out three-dimensional hollowing on the characteristic factor bodies of the shallow gas and the diapir micro-fractures, carrying out body carving on the three-dimensional hollowed-out bodies by using a body carving technology, and identifying the space distribution of the shallow gas and the diapir micro-fractures;
step five: extracting a diapir microfracture reference surface slice according to the spatial distribution of diapir microfractures obtained in the fourth step, calculating the longitudinal cumulative thickness of shallow gas according to the spatial distribution of diapir microfractures obtained in the fourth step, calculating the correlation coefficient between the amplitude compensation coefficient of diapir microfractures obtained in the third step and the section of the diapir microfracture reference surface, calculating the correlation coefficient between the amplitude compensation coefficient of shallow gas obtained in the third step and the longitudinal cumulative thickness of shallow gas, when the correlation between the amplitude compensation coefficient of diapir microfractures and the correlation coefficient between the section of the diapir microfracture reference surface is good, and the correlation between the amplitude compensation coefficient of shallow gas and the longitudinal cumulative thickness of shallow gas is good, the amplitude compensation coefficient of the seismic reflection reference surface obtained in the second step is the final seismic reflection reference surface compensation coefficient, when the correlation between the amplitude compensation coefficient of diapir microfractures and the section of the diapir microfractures and the correlation coefficient between the section of the diapir microfracture reference surface is poor, and the amplitude compensation coefficient of the diapir microfractures and the section of the shallow gas longitudinal cumulative thickness of the diapir reference surface is, And when the correlation between the shallow layer gas amplitude compensation coefficient and the correlation coefficient of the shallow layer gas longitudinal accumulated thickness is poor, recalculating the seismic reflection reference surface amplitude compensation coefficient until the correlation of the correlation coefficient is good.
Step six: on the basis of good correlation of the correlation coefficients in the fifth step, constructing a seismic amplitude compensation coefficient model by using the upper final seismic reflection datum amplitude compensation coefficient of the target layer as the top surface and the lower final seismic reflection datum amplitude compensation coefficient of the target layer as the bottom surface through spatial interpolation;
step seven: and the seismic amplitude compensation coefficient model obtained in the sixth step is used for carrying out amplitude compensation on the seismic body.
In the first step, the earthquake forward modeling analysis method adopts wave equation forward modeling.
In the second step, the seismic reflection datum plane is selected according to the principle that a seismic reflection interface which can be continuously tracked in space is searched in a large set of mudstone with relatively stable deposition environment and stratum thickness.
In the fourth step, the characteristic factor body of diapir microfracture is a variance body, and the characteristic factor body of shallow gas is constructed according to the reflection characteristic that the shallow gas shows low frequency and strong amplitude in earthquake, and the concrete steps are as follows:
1) by Fourier transform
Figure BDA0002054935730000041
Converting the seismic volume from the time domain to the frequency domain;
2) the characteristic factor of the shallow gas is obtained by dividing the time domain seismic body by the frequency domain seismic body, and the larger the value of the characteristic factor of the shallow gas is, the higher the possibility of representing the shallow gas is.
In the fifth step, the calculation process of the longitudinal accumulated thickness of the superficial gas is as follows:
1) assigning the unprecedented spread of the shallow gas obtained in the fourth step to a three-dimensional array;
2) carrying out space scanning on the three-dimensional array, setting the sampling point with shallow gas as 1, and setting the sampling point without shallow gas as 0;
3) and performing longitudinal accumulation on the three-dimensional array to obtain the longitudinal accumulated thickness of the superficial layer gas.
In the fifth step, the correlation coefficient calculation formula of the upper seismic reflection datum of the target layer and the lower seismic reflection datum of the target layer is as follows:
Figure BDA0002054935730000042
wherein
Figure BDA0002054935730000043
The average of A and B, respectively, the larger R represents the better correlation between the two. In the seventh step, the seismic amplitude is compensated by multiplying the seismic volume by the seismic amplitude compensation coefficient model obtained in the sixth step, and the seismic volume and the seismic amplitude compensation coefficient model have the same sampling rate, the same range and the same geodesic information. The method has the beneficial effects that: compared with the existing seismic amplitude compensation technology, the method can effectively eliminate amplitude abnormity caused by shallow gas and diapir micro-cracks, and improve the fidelity of seismic amplitude; the method ensures the rationality of seismic amplitude compensation through the decomposition and verification of the amplitude compensation coefficient of the seismic reflection reference surface under the guidance of the seismic amplitude influence rule of shallow gas and diapir microfractures.
Drawings
FIG. 1 is a schematic flow chart of an embodiment of the present invention.
FIG. 2 is a time domain seismic volume identification map of a study area in an embodiment of the invention.
FIG. 3 is a frequency domain seismic volume identification plot for a study area in an embodiment of the invention.
FIG. 4 is a shallow gas characteristic factor volume identification map of a study area in an embodiment of the invention.
FIG. 5 is a shallow gas space spread identification plot for a region of interest in an embodiment of the present invention.
FIG. 6 is a graph comparing the amplitude compensation factor of shallow gas and the cumulative thickness of shallow gas in an embodiment of the present invention.
FIG. 7 is a cross-sectional view of an amplitude compensated pre-seismic profile according to an embodiment of the present invention.
FIG. 8 is an amplitude compensated seismic section of an embodiment of the invention.
Detailed Description
The technical solution in the embodiments of the present invention will be described below with reference to the accompanying drawings.
In the embodiment, a certain gas field of the origanum marigoldianum is used as a research area, amplitude compensation is carried out on the three-dimensional seismic data body of the certain gas field of the origanum marigoldianum, a target layer of the research area is buried deeply and is influenced by overlying shallow gas and diapir microcracks, seismic reflection amplitude space change of the same stratum is large, seismic amplitude distortion is caused, and seismic amplitude attribute analysis and subsequent reservoir research are seriously influenced. As shown in fig. 1, a seismic amplitude compensation method for shallow gas and diapir microfracture effects includes the following steps:
the method comprises the following steps: and establishing a geological model of shallow gas and diapir micro-fractures by combining geological conditions of a research area, utilizing wave equation forward modeling, extracting uniform and equal-thickness seismic reflection amplitude of a target layer according to a simulation result of the wave equation forward modeling, and quantitatively analyzing the seismic reflection amplitude of the target layer to obtain an amplitude influence rule of the shallow gas and diapir micro-fractures.
In the first step, the amplitude influence law of shallow layer gas and diapir microfractures is as follows:
1) the law of the influence of the amplitude of the diapir microfracture is as follows: the diapir microcracks can cause the breaking of the earthquake homophase axis, the amplitude is weakened, a certain fuzzy area is formed, and the influence degree and the influence range of the diapir microcracks on the amplitude are positively correlated with the distribution density and the distribution range of the diapir microcracks;
2) the law of the influence of the amplitude of shallow gas is as follows: shallow gas can play the effect of sheltering from and absorbing attenuation to the reflection amplitude energy of stratum under, and the more the shallow gas cumulative thickness is, the weaker the seismic reflection amplitude of stratum under, show that shallow gas amplitude compensation coefficient is with shallow gas cumulative thickness positive correlation. Step two: according to the seismic reflection datum plane selection principle, seismic reflection datum planes are respectively selected above and below a target layer, the root mean square amplitude attribute of the seismic reflection datum planes is extracted, the root mean square amplitude attribute of the seismic reflection datum planes is normalized and the reciprocal of the root mean square amplitude attribute is taken, and the amplitude compensation coefficient of the seismic reflection datum planes is obtained.
In the second step, the selection of the seismic reflection datum plane is subject to the following conditions:
1) the method needs to be found in a large set of mudstone, and compared with sandstone, the large set of mudstone has weak hydraulic power, relatively stable deposition environment and relatively stable stratum thickness in the deposition process;
2) the stratum interface can be continuously tracked;
in order to ensure that the conditions are met, the selection of the seismic reflection datum plane is not limited to the response of a single stratum interface, but can be the response of a set of strata, and when a stratum interface which can be tracked and explained in a whole area is difficult to find in the whole area, the seismic reflection datum plane can be formed by splicing a plurality of stratum interfaces.
Step three: and decomposing the seismic reflection reference surface amplitude compensation coefficient obtained in the step two by using the amplitude influence rule of the shallow gas and the diapir micro-fractures obtained in the step one, wherein the seismic reflection reference surface amplitude compensation coefficient can be decomposed into a shallow gas amplitude compensation coefficient and a diapir micro-fracture amplitude compensation coefficient.
Step four: the method comprises the steps of constructing characteristic factor bodies of shallow gas and diapir micro-fractures according to seismic reflection characteristics of the shallow gas and the diapir micro-fractures, carrying out three-dimensional hollowing on the characteristic factor bodies of the shallow gas and the diapir micro-fractures, carrying out body carving on the three-dimensional hollowed-out bodies by utilizing a body carving technology, and identifying the space distribution of the shallow gas and the diapir micro-fractures.
In the fourth step, the characteristic factor of the shallow gas needs to be constructed through the seismic reflection characteristics of the shallow gas, and through the analysis of the drilled well data and the seismic data of the research area, the shallow gas is found to be characterized by strong amplitude and low frequency in the earthquake, so that the characteristic factor of the shallow gas can be constructed by dividing the amplitude by the frequency, and the specific process is as follows:
1) by Fourier transform
Figure BDA0002054935730000071
Converting the seismic volume from the time domain to the frequency domain, wherein FIG. 2 is an identification diagram of the seismic volume in the time domain, and FIG. 3 is an identification diagram of the seismic volume in the frequency domain;
2) the time domain seismic volume is divided by the frequency domain seismic volume to obtain the characteristic factor volume of the shallow gas, and fig. 4 is an identification diagram of the characteristic factor volume of the shallow gas.
The spatial distribution of shallow gas can be identified by utilizing the three-dimensional hollowing and body carving technology, and fig. 5 is an identification diagram of the spatial distribution of the shallow gas; the characteristic factor body of the diapir microcracks is a variance body, is extracted through body attributes according to a time domain earthquake body, and the space distribution of the diapir microcracks can be identified by utilizing a three-dimensional hollow and body carving technology.
Step five: on the basis of the shallow layer gas amplitude compensation coefficient and the diapir microfracture amplitude compensation coefficient obtained in the third step, according to the space distribution of diapir microfractures obtained in the fourth step, a diapir microfracture reference surface slice is extracted, the longitudinal accumulated thickness of shallow layer gas is calculated, then the correlation coefficient of the diapir microfracture amplitude compensation coefficient and the diapir microfracture reference surface slice obtained in the third step and the correlation coefficient of the shallow layer gas amplitude compensation coefficient and the longitudinal accumulated thickness of the shallow layer gas obtained in the third step are calculated, the two correlation coefficients are verified, and the final seismic reflection reference surface amplitude compensation coefficient is obtained, and the specific process is as follows:
1) and (3) verifying the amplitude compensation coefficient of the diapir microfracture: according to the amplitude influence rule of the diapir microfractures obtained in the step one, the influence degree and the influence range of the diapir microfractures on the amplitude are positively correlated with the distribution density and the distribution range of the diapir microfractures, so on the basis of the diapir microfracture amplitude compensation coefficient obtained in the step three, the feature factor daughter of the diapir microfractures is taken as a data body, the seismic reflection reference surface variance cube slice is extracted, then the correlation coefficient of the feature factor daughter slice of the diapir microfractures and the diapir microfracture amplitude compensation coefficient is calculated, and the calculation formula of the correlation coefficient is as follows:
Figure BDA0002054935730000081
wherein
Figure BDA0002054935730000082
The average values of A and B are respectively, and the larger R is, the better the correlation between the two is represented;
2) and (3) verifying the shallow layer air amplitude compensation coefficient: according to the shallow gas amplitude influence rule obtained in the step one, the shallow gas amplitude compensation coefficient is positively correlated with the shallow gas accumulated thickness, so that the accuracy of the shallow gas amplitude compensation coefficient can be verified through the correlation between the shallow gas accumulated thickness and the shallow gas amplitude compensation coefficient, the shallow gas spatial distribution is assigned to a three-dimensional array on the basis of the shallow gas spatial distribution obtained in the step four, the three-dimensional array is spatially scanned, the sample point with shallow gas is set to be 1, the sample point without shallow gas is set to be 0, then the three-dimensional array is longitudinally accumulated, the longitudinal accumulated thickness of the shallow gas can be obtained, as shown in fig. 6, the shallow gas amplitude compensation coefficient is positively correlated with the shallow gas accumulated thickness, the correlation coefficient is as high as 0.87, the result of the shallow gas amplitude compensation coefficient is correct, if the correlation coefficient is poor, the step two is required to be returned, and recalculating the amplitude compensation coefficient of the seismic reflection datum until the correlation coefficient has good correlation.
Step six: and according to the method of the final seismic reflection datum amplitude compensation coefficient obtained in the step five, constructing a seismic amplitude compensation coefficient model by using the upper final seismic reflection datum amplitude compensation coefficient of the target layer as the top surface and the lower final seismic reflection datum amplitude compensation coefficient of the target layer as the bottom surface through spatial interpolation.
Step seven: and in the amplitude compensation process, the seismic body and the seismic amplitude compensation model have the same sampling rate, the same range and the same measuring net information, as shown in figure 7, before the amplitude compensation, the seismic event axis is fuzzy under the influence of overlying shallow gas and diapir microcracks, and the amplitude space change is abnormal, as shown in figure 8, after the amplitude compensation, the amplitude attribute is more consistent with the reflection coefficient of the drilled stratum, so that the method has good application effect in actual data.

Claims (7)

1. A seismic amplitude compensation method aiming at shallow layer gas and diapir micro-crack influence is characterized by comprising the following steps:
the method comprises the following steps: establishing a geological model of shallow gas and diapir micro fractures by combining the geological condition of a site, and obtaining the amplitude influence rule of the shallow gas and the diapir micro fractures according to an earthquake forward modeling analysis method;
step two: according to the seismic reflection datum plane selection principle, respectively selecting seismic reflection datum planes on the upper surface and the lower surface of a target layer, extracting the root mean square amplitude attribute of the seismic reflection datum planes, normalizing the root mean square amplitude attribute of the seismic reflection datum planes and acquiring the reciprocal to obtain an amplitude compensation coefficient of the seismic reflection datum planes;
step three: decomposing the seismic reflection reference surface amplitude compensation coefficient obtained in the second step by using the amplitude influence rule of the shallow gas and the diapir micro-fractures obtained in the first step, wherein the seismic reflection reference surface amplitude compensation coefficient is decomposed into a shallow gas amplitude compensation coefficient and a diapir micro-fracture amplitude compensation coefficient;
step four: constructing characteristic factor bodies of the shallow gas and the diapir micro-fractures according to the seismic reflection characteristics of the shallow gas and the diapir micro-fractures, carrying out three-dimensional hollowing on the characteristic factor bodies of the shallow gas and the diapir micro-fractures, carrying out body carving on the three-dimensional hollowed-out bodies by using a body carving technology, and identifying the space distribution of the shallow gas and the diapir micro-fractures;
step five: extracting a diapir microfracture reference surface slice according to the spatial distribution of diapir microfractures obtained in the fourth step, calculating the longitudinal cumulative thickness of shallow gas according to the spatial distribution of diapir microfractures obtained in the fourth step, calculating the correlation coefficient between the amplitude compensation coefficient of diapir microfractures obtained in the third step and the section of the diapir microfracture reference surface, calculating the correlation coefficient between the amplitude compensation coefficient of shallow gas obtained in the third step and the longitudinal cumulative thickness of shallow gas, when the correlation between the amplitude compensation coefficient of diapir microfractures and the correlation coefficient between the section of the diapir microfracture reference surface is good, and the correlation between the amplitude compensation coefficient of shallow gas and the longitudinal cumulative thickness of shallow gas is good, the amplitude compensation coefficient of the seismic reflection reference surface obtained in the second step is the final seismic reflection reference surface compensation coefficient, when the correlation between the amplitude compensation coefficient of diapir microfractures and the section of the diapir microfractures and the correlation coefficient between the section of the diapir microfracture reference surface is poor, and the amplitude compensation coefficient of the diapir microfractures and the section of the shallow gas longitudinal cumulative thickness of the diapir reference surface is, When the correlation between the shallow layer gas amplitude compensation coefficient and the correlation coefficient of the shallow layer gas longitudinal accumulated thickness is poor, recalculating the seismic reflection reference surface amplitude compensation coefficient until the correlation of the correlation coefficient is good;
step six: on the basis of good correlation of the correlation coefficients in the fifth step, constructing a seismic amplitude compensation coefficient model by using the upper final seismic reflection datum amplitude compensation coefficient of the target layer as the top surface and the lower final seismic reflection datum amplitude compensation coefficient of the target layer as the bottom surface through spatial interpolation;
step seven: and the seismic amplitude compensation coefficient model obtained in the sixth step is used for carrying out amplitude compensation on the seismic body.
2. The method for compensating seismic amplitude for shallow gas and diapir microfracture effects of claim 1, wherein in the first step, the method for seismic forward modeling analysis uses wave equation forward modeling.
3. The method as claimed in claim 1, wherein in the second step, the seismic reflection datum is selected by finding a spatially continuous traceable seismic reflection interface in a large set of mudstone with relatively stable deposition environment and formation thickness.
4. The method for compensating the seismic amplitude according to the shallow gas and the influence of diapir microfractures as claimed in claim 1, wherein in the fourth step, the characteristic factor entity of the diapir microfractures is a variance entity, and the characteristic factor entity of the shallow gas is constructed according to the reflection characteristic that the shallow gas shows low frequency and strong amplitude in the earthquake, and the concrete steps are as follows:
1) by Fourier transform
Figure FDA0002387156540000021
Converting the seismic volume from the time domain to the frequency domain;
2) the characteristic factor of the shallow gas is obtained by dividing the time domain seismic body by the frequency domain seismic body, and the larger the value of the characteristic factor of the shallow gas is, the higher the possibility of representing the shallow gas is.
5. The method for compensating seismic amplitude for shallow gas and diapir microfracture effects of claim 1, wherein in step five, the calculation of the longitudinal cumulative thickness of shallow gas is as follows:
1) assigning the spatial distribution of the shallow gas obtained in the fourth step to a three-dimensional array;
2) carrying out space scanning on the three-dimensional array, setting the sampling point with shallow gas as 1, and setting the sampling point without shallow gas as 0;
3) and performing longitudinal accumulation on the three-dimensional array to obtain the longitudinal accumulated thickness of the superficial layer gas.
6. The method for compensating seismic amplitude for shallow gas and diapir microfracture effects of claim 1, wherein in the fifth step, the correlation coefficient calculation formula of the upper seismic reflection datum of the target layer and the lower seismic reflection datum of the target layer is as follows:
Figure FDA0002387156540000022
Figure FDA0002387156540000023
wherein
Figure FDA0002387156540000024
The average of A and B, respectively, the larger R represents the better correlation between the two.
7. The method as claimed in claim 1, wherein in the seventh step, the seismic amplitude is compensated by multiplying the seismic body by the seismic amplitude compensation coefficient model obtained in the sixth step, and the seismic body and the seismic amplitude compensation coefficient model have the same sampling rate, the same range and the same geodesic information.
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