CN117647838B - Angle-constrained reverse time offset imaging method - Google Patents
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Abstract
The invention discloses an angle constraint reverse time offset imaging method, which comprises the following steps: simulating seismic data based on the velocity model, observation system information and source wavelet; simulating a source wave field and a wave field of a wave detector based on the speed model, the observation system information, the source wavelet and the seismic data, and acquiring an initial reverse time migration image; performing first transformation on the initial reverse time offset image to obtain a normal vector of a reflection interface; performing the first transformation on the source wave field and the wave field of the wave detection point to obtain a unit wave vector of the wave field; and acquiring an angle constraint reverse time migration image based on the normal vector of the reflection interface and the unit wave vector of the wave field. The angle constraint reverse time migration imaging method provided by the invention can not only suppress low wave number noise, but also effectively suppress migration arc drawing, and more importantly, the method does not change the amplitude and phase information of waveforms, thereby being beneficial to subsequent seismic data interpretation.
Description
Technical Field
The invention belongs to the technical field of seismic structure imaging, and particularly relates to an angle constraint reverse time migration imaging method.
Background
Reverse time migration imaging is a method of using seismic data to obtain subsurface reflection interface morphology. The technical process is that according to a known velocity model, seismic data and observation system information, a seismic source wave field and a wave field of a wave point are respectively simulated by a numerical method, and then imaging conditions are applied to generate reflection intensity information of a subsurface interface. The imaging conditions commonly adopted at present belong to the cross-correlation category, and information can be embodied on the reverse time migration image as long as the source wave field and the wave field of the wave detection point meet the time consistency principle. The reverse time offset image not only contains effective information, but also contains a large amount of offset noise and offset false images, namely the effective information is a subset of the reverse time offset image, and if the offset noise and the offset false images cannot be effectively suppressed, construction explanation and well position deployment are misled, so that risks are brought to oil and gas exploration and development.
The Laplace denoising method is a common method for suppressing inverse time migration imaging noise, the basic idea is to perform Laplace transformation on an inverse time migration image, edges and details in the inverse time migration image can be highlighted by utilizing a second-order differential operator, high wave number information is reserved, and low wave number information is suppressed. Although the Laplace denoising method can improve the signal-to-noise ratio of the reverse time migration image, the amplitude and phase properties of the reverse time migration image are changed, and the reverse time migration image subjected to Laplace denoising cannot be used for inversion of the seismic physical parameters because the phase information corresponds to the physical parameters of the underground medium. In addition, the inverse time offset image includes not only low wave number noise but also arc offset artifacts in the form of in-phase axes, and the laplace transform cannot suppress the arc offset artifacts, but rather highlights the arc offset artifacts. The only significant information in the reverse time migration image is related to the physical process of generating the reflected wavefield at the source wavefield incident reflection interface, so migration noise and migration artifacts can be suppressed, subject to the incidence angle at the significant information being equal to the reflection angle. Therefore, there is a need for an angle-constrained reverse time shift imaging method that solves the problems of low frequency noise and arc shift artifacts in reverse time shift images.
Disclosure of Invention
In order to solve the technical problems, the invention provides an angle constraint reverse time migration imaging method which can improve migration imaging resolution, migration imaging quality and migration imaging technology service oil gas exploration and development capacity.
To achieve the above object, the present invention provides an angle-constrained reverse time offset imaging method, including:
simulating seismic data based on the velocity model, the source wavelet and the observation system information;
simulating a source wave field and a wave field of a wave detector based on the velocity model, the source wavelet, the observation system information and the seismic data, and obtaining an initial reverse time migration image;
performing first transformation on the initial reverse time offset image to obtain a normal vector of a reflection interface;
performing the first transformation on the source wave field and the wave field of the wave detection point to obtain a unit wave vector of the wave field;
and acquiring an angle constraint reverse time migration image based on the normal vector of the reflection interface and the unit wave vector of the wave field.
Optionally, obtaining the normal vector of the reflective interface includes:
performing vertical Hilbert transform on the initial reverse time offset image to obtain a first transformation result;
and acquiring a normal vector of the reflection interface based on the initial reverse time offset image and the first transformation result.
Optionally, the method for performing the hilbert transform in the vertical direction on the initial reverse time offset image is:
wherein,and->Spatial coordinates in horizontal and vertical directions, respectively, +.>Is imaginary unit, ++>Wave number, & gt>Is a fourier transform in the vertical direction, +.>Is an inverse fourier transform in the vertical direction, +.>Is a real number domain signal, ">Is->Hilbert transform in the vertical direction;
the method for obtaining the normal vector of the reflection interface comprises the following steps:
wherein,for instantaneous wave number +.>Is to take the real part operator and to take the real part operator,cis an analytic signal corresponding to the real number domain signal.
Optionally, obtaining a unit wave vector of the wave field includes:
performing vertical Hilbert transform on the seismic source wave field and the wave field of the wave detection point to obtain a second transformation result;
acquiring an instantaneous phase according to the source wave field, the wave field of the wave point and the second transformation result;
and obtaining a unit wave vector of the wave field by using the instantaneous phase and the derivative of the instantaneous phase with respect to time.
Optionally, the method for acquiring the instantaneous phase is as follows:
wherein,is the instantaneous phase;
the method for obtaining the unit wave vector of the wave field comprises the following steps:
wherein,is a unit wave vector, ">For taking the vector modulo, the +.>In the form of a bias operator,tis time.
Optionally, acquiring the angle-constrained reverse time offset image includes:
acquiring an angle constraint factor based on the normal vector of the reflection interface and the unit wave vector;
and acquiring an angle constraint reverse time offset image according to the angle constraint factor.
Optionally, the method for obtaining the angle constraint factor includes:
wherein,is angle constraint factor, +>Is a unit wave vector of the source wave field, +.>For the unit wave vector of the wave field of the detector point, +.>Is the normal vector of the reflection interface, +.>Is standard deviation (S)>Is an inverse cosine function, +.>Vector modulo arithmetic is taken;
the method for acquiring the angle constraint reverse time offset image according to the angle constraint factor comprises the following steps:
wherein,Iin order to obtain the imaging result, the imaging device,and->For spatial coordinates in horizontal and vertical directions, +.>For time (I)>For maximum seismic data duration, < >>For the source wave field>For wave field of wave detector>Is a cross-correlation symbol.
Compared with the prior art, the invention has the following advantages and technical effects:
the angle constraint reverse time migration imaging method provided by the invention can not only suppress low wave number noise, but also effectively suppress migration arc drawing, and more importantly, the method does not change the amplitude and phase information of waveforms, thereby being beneficial to subsequent seismic data interpretation. In addition, the method estimates the normal direction of the reflection interface and the propagation direction of the wave field through the instantaneous wave number of the wave field, and the instantaneous wave number has the advantage of accurately estimating the normal direction of the balance position between the wave crest and the wave trough, so that the error of direction estimation is reduced, and the method is beneficial to improving the reverse time migration imaging resolution.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application, illustrate and explain the application and are not to be construed as limiting the application. In the drawings:
FIG. 1 is a flow chart of an angle-constrained reverse-time offset imaging method in accordance with an embodiment of the present invention;
FIG. 2 is an angle constraint schematic of an embodiment of the present invention;
FIG. 3 is a schematic diagram of a velocity model of an embodiment of the present invention;
FIG. 4 is a schematic representation of seismic data of an embodiment of the invention;
FIG. 5 is a schematic diagram of a conventional reverse time offset image of an embodiment of the present invention;
FIG. 6 is a schematic diagram of components of instantaneous wave numbers according to an embodiment of the present invention, wherein FIG. 6 (a) is a horizontal component of instantaneous wave numbers and FIG. 6 (b) is a vertical component of instantaneous wave numbers;
FIG. 7 is a schematic diagram of information of an angle between a normal vector of a reflection interface and a reference direction according to an embodiment of the present invention;
FIG. 8 is a schematic view of components of a seismic wave vector at a time, FIG. 8 (a) being a horizontal component of the wave vector and FIG. 8 (b) being a vertical component of the wave vector, according to an embodiment of the present invention;
FIG. 9 is a schematic diagram of a reverse time shift image obtained using angle-constrained imaging conditions in accordance with an embodiment of the present invention.
Detailed Description
It should be noted that, in the case of no conflict, the embodiments and features in the embodiments may be combined with each other. The present application will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.
It should be noted that the steps illustrated in the flowcharts of the figures may be performed in a computer system such as a set of computer executable instructions, and that although a logical order is illustrated in the flowcharts, in some cases the steps illustrated or described may be performed in an order other than that illustrated herein.
With the aid of FIG. 2, it is explained how the angular constraint of the imaging conditions is fulfilled, assuming that the angle of the oblique configuration to the horizontal isThe unit wave vector of the source wave field at the imaging point is +.>The unit wave vector of the wave field of the wave point is +.>The normal vector of the reflection interface is +.>. Whether the angle of incidence is equal to the angle of reflection can be determined by the relationship between the vectors. In theory, when the vectorAnd->When the directions of the seismic waves are coincident, the incident angle of the seismic waves is equal to the reflection angle, the reverse time offset image is used as effective imaging, and otherwise, the reverse time offset image is eliminated. Consider vector +.>、/>And->Is subject to errors and the exact criterion of the imaging information being valid at an angle of incidence equal to the angle of reflection leads to the occurrence of marks of artificial excessive intervention in the reverse-time shifted image. To this end, a Gaussian function is introduced into the imaging conditions to relax constraints on the offset image, the mathematics of the angle-constrained imaging conditionsThe form is as follows:
（1）
in the method, in the process of the invention,and->Is the spatial coordinates in the horizontal and vertical directions, +.>Representing time->Is the maximum seismic data duration,/->Is the imaging result, < >>For the source wave field>For wave field of wave detector>Is a cross-correlation operator, angle constraint factor +.>The expression of (2) is:
（2）
in the method, in the process of the invention,is angle constraint factor, +>Is a unit wave vector of the source wave field, +.>For the unit wave vector of the wave field of the detector point, +.>Is the normal vector of the reflection interface, +.>Is standard deviation (S)>Is an inverse cosine function, +.>The vector modulo sign is taken.
The invention provides an angle constraint reverse time migration imaging method, which is shown in fig. 1 and specifically comprises the following steps:
acquiring seismic data; the seismic data are obtained based on wave equation under the condition that observation system information, a velocity model and a source wavelet are known.
The observation system information is: the spatial distribution of the seismic source and the detector;
the speed model is shown in fig. 3, and specifically includes: three velocity layers, two reflective interfaces;
the source wavelet is as follows: rake wavelets of a predetermined frequency.
Simulating a seismic source wave field based on the seismic source wavelet, the velocity model and the observation system information, and storing the seismic source wave field into a computer hard disk;
according to an observation system, a speed model and seismic data, the seismic data is used as an excitation source function according to the reverse time direction, wave fields of wave points at each moment are simulated, and meanwhile, the wave fields of the sources at corresponding moments are read for cross-correlation imaging. A conventional reverse time offset image is shown in fig. 5.
Performing first transformation on the initial reverse time offset image to obtain a normal vector of a reflection interface;
performing first transformation on the seismic source wave field and the wave field of the wave detection point to obtain a unit wave vector of the wave field;
the first transform is a hilbert transform;
and acquiring an angle constraint reverse time migration image based on the normal vector, the unit wave vector, the seismic source wave field and the wave field of the wave detection point of the reflection interface.
Further, obtaining the normal vector of the reflective interface includes:
performing vertical Hilbert transform on a conventional reverse time offset image to obtain a first transformation result;
and acquiring a normal vector of the reflection interface based on the conventional reverse time offset image and the first transformation result.
Further, the instantaneous wave number is a spatial gradient of the instantaneous phase with the ability to indicate the normal of the waveform. Both the normal vector and the unit wave vector of the reflective interface can be estimated by means of the instantaneous phase. The acquisition of real number domain signals is described belowFirstly, constructing an analytic signal corresponding to a real number domain signal ++>，
（3）
In the method, in the process of the invention,and->Is the spatial coordinates in the horizontal and vertical directions, +.>Is imaginary unit, ++>Is->Hilbert transform in the vertical direction. Hilbert transform is performed by means of a method (4) The realization of the method is realized in that,
（4）
wherein,and->Is the spatial coordinates in the horizontal and vertical directions, +.>Is imaginary unit, ++>Wave number, & gt>Is a fourier transform in the vertical direction, +.>Is an inverse fourier transform in the vertical direction, +.>Is a real number domain signal, ">Is->Hilbert transform in the vertical direction;
the mathematical expression of (2) is:
（5）
、/>are respectively at->The forward and inverse fourier transforms of the directions can be calculated using equations (6) and (7).
（6）
（7）
Formula (3) may be further represented as:
（8）
in the method, in the process of the invention,for instantaneous amplitude +.>For instantaneous phase, the mathematical expressions are respectively,
（9）
（10）
the natural logarithm taken for both sides of formula (8) is:
（11）
pair (11)Deviation-finding guideObtaining:
（12）
similarly, the pair of the formula (11)The deviation derivative can be obtained:
（13）
acquisition of real signalsThe instantaneous wave number of (2) is:
（14）
wherein,for instantaneous wave number +.>Is to take the real part operator and to take the real part operator,cis a real number domain signal->And corresponding analysis signals. If the reverse time offset image is assigned to +.>The normal vector of the reflection interface is +.>。
Further, obtaining a unit wave vector of the wave field includes:
assigning wavefields toThe instantaneous wave number is obtained using equation (14),
since the normal to the wavefront surface is not coincident with the direction of wave propagation, there is the possibility of co-directional or counter-directional. In order to accurately acquire the wave propagation direction, the instantaneous phase and time derivative corrections may be utilized,
（15）
in the method, in the process of the invention,is a unit wave vector, ">Is a vector modulo arithmetic, is->In the form of a bias operator,tis time. Assigning a source wavefield and a detector wavefield to +.>The wave vector +.>、/>。
Further, acquiring the angle-constrained reverse time offset image includes:
acquiring an angle constraint factor based on a normal vector and a unit wave vector of a reflection interface;
and acquiring an angle constraint reverse time offset image according to the angle constraint factor.
Further, an angle constraint factor is obtained by using the formula (2), and an angle constraint reverse time offset image is obtained by using the formula (1).
Examples
In order to verify the inverse time migration imaging method of the angle constraint provided by the invention, the specific implementation mode is as follows:
step 1: and simulating the seismic data. The method comprises the steps of simulating seismic data by adopting a mode of middle excitation and two sides acceptance, uniformly distributing a seismic source and detectors on the ground surface, wherein the initial positions are respectively 0.3km and 0km, 21 cannons are counted, 61 channels are counted, a Rake wavelet with a main frequency of 15Hz is selected as an excitation seismic source wavelet, a time second-order and space tenth-order finite difference method is adopted to simulate a seismic wave field based on a sound wave equation, a time sampling interval is 1ms, a space sampling interval is 10m, sampling duration is 3s, and a completely matched layer is adopted to absorb a non-physical reflection wave field at a boundary condition suppression boundary. Seismic data with shots at 2.5km are shown in fig. 4, where the event corresponds to the reflection interface in the velocity model.
Step 2: conventional reverse time offset imaging. Simulating the wave field of the seismic source at each moment according to the observation system information, the speed model and the wave source wavelet mentioned in the step 1, storing the wave field of the seismic source at each moment in a computer hard disk, taking the seismic data as an excitation source function according to the reverse time direction, simulating the wave field of the wave detection point at each moment, and simultaneously reading the wave field of the seismic source at the corresponding moment to perform cross-correlation imaging. A conventional reverse time offset image is shown in fig. 5. Since the observation system has illumination dead zones at both ends of the model, only the imaging areas of 1.2-4.2km in the horizontal direction are shown.
Step 3: and estimating the normal vector of the reflection interface. Performing Hilbert transform on the reverse time offset image in the vertical direction by using a formula (4), and assigning the reverse time offset image and the Hilbert transform result corresponding to the reverse time offset image in the vertical direction to the formula (3)And->The normal direction of the reflective interface is determined using equation (14), the two components of the vector are shown in fig. 6 (a) - (b), and for ease of illustration, the vertical direction is chosen as the reference direction, and the tilt angle is shown in fig. 7.
Step 4: and estimating the wave propagation direction. Performing Hilbert transform on the source wave field and the detector wave field in the vertical direction by using the formula (4), and assigning the source wave field and the detector wave field and their corresponding Hilbert transform results in the vertical direction to the formula (3)And->Calculating the instantaneous phases of the current wave field and the wave field at the previous moment by using a formula (10), calculating the instantaneous wave number of the current wave field by using a formula (14), and bringing the instantaneous phases and the instantaneous wave numbers into a formula (15) to obtain the unit wave vector of the wave field. The two components of the wave field wave vector at a certain moment are shown in fig. 8 (a) - (b).
Step 5: angle-constrained reverse time-shift imaging. In the conventional reverse time migration imaging process, based on the normal vector of the reflection interface in the step 3 and the unit wave vectors of the source wave field and the wave field of the wave point in the step 4, an angle constraint factor is calculated by using a formula (2), wherein the standard deviation in the formula takes 5 degrees, and then an angle constraint reverse time migration image is generated by using a formula (1), as shown in fig. 9.
The foregoing is merely a preferred embodiment of the present application, but the scope of the present application is not limited thereto, and any changes or substitutions easily conceivable by those skilled in the art within the technical scope of the present application should be covered in the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (3)
1. An angle-constrained reverse time offset imaging method, comprising:
simulating seismic data based on the velocity model, the source wavelet and the observation system information;
simulating a source wave field and a wave field of a wave detector based on the velocity model, the source wavelet, the observation system information and the seismic data, and obtaining an initial reverse time migration image;
performing first transformation on the initial reverse time offset image to obtain a normal vector of a reflection interface;
acquiring the normal vector of the reflection interface comprises:
performing vertical Hilbert transform on the initial reverse time offset image to obtain a first transformation result;
acquiring a normal vector of a reflection interface based on the initial reverse time offset image and a first transformation result;
the method for performing Hilbert transform on the initial reverse time offset image in the vertical direction comprises the following steps:
wherein (1)>And->Spatial coordinates in horizontal and vertical directions, respectively, +.>Is imaginary unit, ++>Wave number, & gt>Is a fourier transform in the vertical direction, +.>Is an inverse fourier transform in the vertical direction, +.>Is a real number domain signal, ">Is->Hilbert transform in the vertical direction;
the method for obtaining the normal vector of the reflection interface comprises the following steps:
wherein (1)>For instantaneous wave number +.>Is to take the real part operator and to take the real part operator,cis an analytic signal corresponding to the real number domain signal;
performing the first transformation on the source wave field and the wave field of the wave detection point to obtain a unit wave vector of the wave field;
acquiring a unit wave vector of the wave field includes:
performing vertical Hilbert transform on the seismic source wave field and the wave field of the wave detection point to obtain a second transformation result;
acquiring an instantaneous phase according to the source wave field, the wave field of the wave point and the second transformation result;
obtaining a unit wave vector of the wave field by using the instantaneous phase and the derivative of the instantaneous phase with respect to time;
the method for acquiring the instantaneous phase comprises the following steps:
wherein (1)>Is the instantaneous phase;
the method for obtaining the unit wave vector of the wave field comprises the following steps:
wherein (1)>Is a unit wave vector, ">In order to take the vector modulo the symbol,/>in the form of a bias operator,ttime is;
and acquiring an angle constraint reverse time migration image based on the normal vector of the reflection interface and the unit wave vector of the wave field.
2. The method of angle-constrained reverse time shift imaging of claim 1, wherein obtaining the angle-constrained reverse time shift image comprises:
acquiring an angle constraint factor based on the normal vector of the reflection interface and the unit wave vector;
and acquiring an angle constraint reverse time offset image according to the angle constraint factor.
3. The method for reverse time migration imaging of claim 2, wherein the method for obtaining the angle constraint factor is:
wherein (1)>Is angle constraint factor, +>Is a unit wave vector of the source wave field, +.>For the unit wave vector of the wave field of the detector point, +.>Is the normal vector of the reflection interface, +.>Is the standard deviation of the two-dimensional image,is an inverse cosine function, +.>Vector modulo arithmetic is taken;
the method for acquiring the angle constraint reverse time offset image according to the angle constraint factor comprises the following steps:
wherein (1)>Andfor spatial coordinates in horizontal and vertical directions, +.>For time (I)>For maximum seismic data duration, < >>For the source wave field>For wave field of wave detector>Is a cross-correlation operator.
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| CN112904426A (en) * | 2021-03-27 | 2021-06-04 | 中国石油大学(华东) | Decoupling elastic wave reverse time migration method, system and application |
| CN115598704A (en) * | 2022-11-08 | 2023-01-13 | 西安交通大学（Cn） | Method and device for generating amplitude-preserving angle gather based on least square reverse time migration and readable storage medium |
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| CN112904426A (en) * | 2021-03-27 | 2021-06-04 | 中国石油大学(华东) | Decoupling elastic wave reverse time migration method, system and application |
| CN115598704A (en) * | 2022-11-08 | 2023-01-13 | 西安交通大学（Cn） | Method and device for generating amplitude-preserving angle gather based on least square reverse time migration and readable storage medium |
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