CN108802818A - The chromatography component extraction method of original gradient in a kind of full waveform inversion - Google Patents
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Abstract
本发明涉及一种全波形反演中原始梯度的层析分量提取方法，其特征在于，包括以下步骤：将全波形反演中余量的频谱划分为若干频带，每一频带均相应设定一参考频率；通过带通滤波将全波形反演中的余量划分为若干子集，并反传每一子集余量得到各个子集余量的原始梯度；针对某一子集余量的原始梯度中的某一元素，计算该元素的截断波数；根据计算的截断波数，采用高斯函数得到该元素空间域的高斯平滑滤波器；将该元素空间域的高斯平滑滤波器与该元素相乘，提取该元素的层析分量；完成对所有子集余量的原始梯度中所有元素的层析分量提取，并累加得到全波形反演中原始梯度的层析分量,本发明可广泛应用于地震数据成像反演技术领域中。
The invention relates to a method for extracting tomographic components of the original gradient in full waveform inversion, which is characterized in that it comprises the following steps: dividing the spectrum of the margin in full waveform inversion into several frequency bands, and setting a corresponding frequency band for each frequency band Reference frequency; the residual in the full waveform inversion is divided into several subsets by band-pass filtering, and the residual of each subset is back-transmitted to obtain the original gradient of each subset residual; the original gradient of a certain subset residual For an element in the gradient, calculate the truncated wavenumber of the element; according to the calculated truncated wavenumber, use the Gaussian function to obtain the Gaussian smoothing filter in the space domain of the element; multiply the Gaussian smoothing filter in the space domain of the element with the element, Extract the tomographic component of the element; complete the extraction of the tomographic component of all elements in the original gradient of all subset margins, and accumulate to obtain the tomographic component of the original gradient in the full waveform inversion. The present invention can be widely used in seismic data In the field of imaging inversion technology.
Description
Technical Field
The invention relates to a method for extracting chromatographic components of an original gradient in full waveform inversion, and relates to the technical field of seismic data imaging inversion.
Background
The full waveform inversion includes a migration mode and a tomographic mode, the refracted wave data mainly contributes to the tomographic mode, and the reflected wave data contributes to not only the tomographic mode but also the migration mode. To emphasize one of the modes, it is necessary to separate the two modes, which is critical for the reflected wave waveform inversion, because the reflected wave contributes much less to the analytic mode than to the offset mode. The researchers have proposed methods to separate these two modes, such as Born simulation, up and down wavefield separation, improved backscatter imaging conditions, and scatter angle filtering.
However, all the existing methods have disadvantages in efficiency or effect: 1) the wave equation is split into two wave equations based on the Born simulation method, one wave equation calculates an incident wave field, the other wave equation calculates a scattered wave field, and the velocity models of the two wave equations are smooth background components of the original velocity model. And generating a tomographic component and an offset component by respectively cross-correlating the incident wave and the scattered wave of the seismic source wave field with the incident wave and the scattered wave of the residual wave field. Since Born simulation requires the wave equation to be decomposed into two wave equations, the calculation amount is doubled, and more importantly, the scattered wave field calculated by the method not only includes the reflected scattered wave field but also includes the transmitted scattered wave field, so that the generated tomographic component contains a small amount of offset component, and vice versa, thereby resulting in incomplete mode decomposition. 2) The up-down wavefield separation method is based on the fact that the down-going transmitted wavefield and the up-going reflected wavefield are inclined in opposite directions in a vertical section, and thus the transmitted and reflected waves are separated by fourier transform, and a tomographic component and an offset component are generated by corresponding cross-correlation. However, the main problem of this method is that the effect is not good, and in the case of a complex model, both the transmitted wave and the reflected wave may be in the down-going or up-going direction, so the transmitted wave and the reflected wave cannot be completely separated by the up-and-down wave field separation method, and further the offset component is likely to leak into the tomographic component, and vice versa. 3) The scattering angle filtering method is to perform angle filtering based on the opening angles of the seismic source wave field and the residual wave field to realize the separation of the chromatographic component and the offset component, and when the opening angles are close to 180 degrees, the seismic source wave field and the residual wave field are in cross-correlation to generate the chromatographic component; while the remaining angles contribute to the offset component. This is based on the fact that the tomographic components are generated by the exact opposite propagation directions of the source and residual wavefields, and thus the scatter angle filtering method is a very efficient mode separation method, but it requires expensive computational costs, and is usually several times higher than the computational cost of the wavefield simulation itself. 4) The backscatter imaging condition method is a special case of scatter angle filtering, i.e. the transition band of the angle filter is from 0 to 180 degrees, and the band pass and band stop are only 0 or 180 degrees. The transition band of the angular filter for scatter angle filtering is narrow in the normal case, and the widths of the band pass and band stop are much larger than in the case of backscatter imaging conditions. Thus, although this method produces a small amount of additional computation, its separation effect is poor. In order to improve the separation effect, the backscatter imaging condition is realized by adding adaptive amplitude matching, but the computation amount of the general adaptive amplitude matching is large, and the extraction effect of weak signals such as chromatographic modes is poor.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide a method for extracting a tomographic component of an original gradient in a full waveform inversion, which can perform a thorough mode decomposition, and has a small amount of calculation and a good extraction effect.
In order to achieve the purpose, the invention adopts the following technical scheme: a method for extracting chromatographic components of an original gradient in full waveform inversion is characterized by comprising the following steps: step 1): dividing the residual frequency spectrum in the full waveform inversion into a plurality of frequency bands, wherein each frequency band is correspondingly set with a reference frequency; step 2): according to the divided frequency bands, dividing the residuals in the full waveform inversion into a plurality of subsets through band-pass filtering, and reversely transmitting the residuals of each subset to obtain the original gradient of the residuals of each subset; step 3): aiming at a certain element in the original gradient of a certain subset of margins, calculating the truncation wave number of the element according to the reference frequency corresponding to the original gradient and the P wave velocity corresponding to the element; step 4): according to the calculated truncation wave number, a Gaussian smoothing filter of the element space domain is obtained by adopting a Gaussian function; step 5): multiplying the element by a gaussian smoothing filter of the element space domain to extract a tomographic component of the element; step 6): and repeating the steps 3) to 5), finishing the extraction of the chromatographic components of all elements in the original gradient of all the subset residuals, and accumulating to obtain the chromatographic components of the original gradient in the full waveform inversion.
Further, in the step 3), for a certain element in the original gradient of a certain subset of residuals, according to the reference frequency corresponding to the original gradient and the P-wave velocity corresponding to the element, the truncated wave number of the element is calculated, which specifically includes: for a certain element in the original gradient of a certain subset of residuals, selecting the minimum opening angle of wave number vectors of a source wave field and a residual wave field of the original gradient according to the reference frequency corresponding to the original gradient and the P wave velocity corresponding to the element, and calculating the truncated wave number of the element according to the selected minimum opening angle:
wherein k istomo_maxRepresents the cutoff wave number of the element; omegacjrepresenting the reference frequency corresponding to the original gradient, v representing the P-wave velocity corresponding to the element, αminThe minimum opening angle of the wavenumber vectors of the source wavefield and the residual wavefield representing the original gradient.
Further, the minimum opening angle of the wavenumber vectors of the source wavefield and the residual wavefield of the original gradient is less than 180 degrees.
Further, the minimum opening angle of the wave number vectors of the source wavefield and the residual wavefield for the original gradient is 160 degrees.
Further, the step 4) obtains a gaussian smoothing filter of the spatial domain by using a gaussian function according to the calculated cutoff wave number, and the specific process is as follows: the gaussian function in the spatial domain is:
where | x | represents the modulus of the position vector; the fourier domain expression of the spatial domain gaussian function is:
wherein, | k | represents a vector of wave numbers, i.e., the truncated wave numbers; sigma and sigmakForm factors representing the spatial and fourier domains, respectively, the relationship between the two form factors being:
presetting a threshold, substituting the truncated wave number and the corresponding Fourier Gaussian function value, namely the threshold, into the Fourier domain expression, and calculating to obtain the shape factor sigma of the Fourier domainkAnd the shape factor sigma of the space domain is substituted into the Gaussian function of the space domain to obtain the shape factor sigma of the space domain in xiA gaussian smoothing filter G (x, x) of the spatial domain of the element(s) of (a)j，ωcj)。
Further, the threshold value is 0.3.
Further, the reference frequency ωcjHas a frequency band range of 0.5 omegacj～2ωcj。
Further, the reference frequency ωcjIs determined by the minimum opening angle of the tomographic component and the maximum opening angle of the offset component.
Further, the minimum opening angle of the tomographic component is 160 degrees, and the maximum opening angle of the offset component is 140 degrees.
Due to the adoption of the technical scheme, the invention has the following advantages: 1. in principle, the method of the present invention requires smoothing filtering frequency by frequency, which is very efficient for full waveform inversion in the frequency domain, but for full waveform inversion in the time domain, the wavefield needs to be fourier transformed to the frequency domain and then smoothed frequency by frequency, which is inefficient for performing the fourier transform on the time domain because all the time wavefield needs to be stored, which is impractical for storing the wavefield of the three-dimensional model under current computer hardware conditions. In contrast, according to the time domain full waveform inversion, a reference frequency is set for each frequency band correspondingly, the original gradient of each subset margin is obtained according to the divided frequency bands, then, the chromatographic component is extracted for each element in the original gradient of each subset margin, and the chromatographic component in the full waveform inversion can be effectively and efficiently extracted. 2. The method has small extra calculation amount, and the extraction of the chromatographic component in the time domain only needs one to two reference frequencies under the common condition, so that the method only needs one extra back transmission at most and can be widely applied to the technical field of seismic data imaging inversion.
Drawings
FIG. 1 is a schematic diagram of the spread angle and wavenumber distribution in a conventional full waveform inversion;
FIG. 2 is a flow chart of the extraction method of the present invention;
FIG. 3 is a schematic diagram of an embodiment of the extraction method of the present invention, wherein FIG. 3(a) is a schematic diagram of a limited bandwidth source wavelet in the embodiment; FIG. 3(b) is a diagram of the original gradient of this embodiment; FIG. 3(c) is a schematic diagram of the tomographic component of the embodiment performing adaptive smoothing extraction on frequency-by-frequency in the frequency domain; FIG. 3(d) is a schematic diagram of band-pass filtering the residual using four frequency bands; FIG. 3(e) is a schematic diagram of band-pass filtering the residual using two frequency bands; FIG. 3(f) is a schematic diagram of a tomographic component for four band adaptive smoothing extraction for this embodiment; fig. 3(g) is a schematic diagram of a tomographic component for which two-band adaptive smoothing extraction is performed for this embodiment.
Detailed Description
The present invention is described in detail below with reference to the attached drawings. It is to be understood, however, that the drawings are provided solely for the purposes of promoting an understanding of the invention and that they are not to be construed as limiting the invention.
The objective function of a conventional full waveform inversion can be expressed as:
wherein d represents prediction data; d0Representing observed data; deltadIndicating a data margin; if the P-wave velocity is an inversion parameter, the gradient of the objective function to the P-wave velocity at position x is:
wherein v represents the velocity of the P-wave;representing a second derivative of a source wavefield in time; p is a radical ofrRepresenting a back-propagation residual wave field, wherein x represents a position coordinate vector, the two-dimensional model comprises two components, and the three-dimensional model comprises three components; t represents the recording time. The gradient in equation (2) is in the frequency-wavenumber domain:
wherein,represents the gradient in the wavenumber domain;andrespectively representing a source wavefield and a residual wavefield in a wavenumber domain; k is a radical ofs、krAnd k represents the wave number vectors of the source wave field, the residual wave field and the original gradient, respectively; denotes convolution in the wavenumber domain; ω represents the angular frequency.
The vector wavenumbers of the original gradient satisfy the following relationship:
k＝ks+kr(4)
in an isotropic medium:
according to equations (4) and (5), the wavenumber vector of the original gradient can be calculated by the following equation:
wherein, k represents wave number vector of original gradient, α represents spreading angle of wave number vector of source wave field and residual wave field, i.e. scattering angle, when α is atomomaxWhen, | k | represents the truncation wave number.
If the propagation directions of the source wavefield and the residual wavefield are opposite, the cross-correlation between them mainly contributes to the tomographic component of the gradient, in other words, the tomographic component in the gradient mainly originates from the source wavefield and the residual wavefield with an opening angle close to 180 degrees, and the small-angle opening angle mainly contributes to the migration component of the gradient. An effective method to separate the offset mode and the tomographic mode is based on the scattering angle filtering of equation (6). From equation (6), it can be seen that for a given frequency and velocity tomographic component, there is a specific offset componentWith a smaller number of wave numbers, as shown in FIG. 1, the wave number k of the offset componentmigWave number k of chromatographic component falling within the outer rangetomoIn the inner circle, there is a transition zone with wave number of ktransIt is thus possible to extract tomographic components by filtering with a low wavenumber, which acts equivalently to smoothing in the spatial domain.
Based on the above principle, as shown in fig. 2, the method for extracting the chromatographic component of the original gradient in the full waveform inversion provided by the invention comprises the following steps:
1. inverting the full waveform by a margin δ d (x)rT) is divided into several frequency bands, each frequency band is set with a reference frequency omegacjThe method specifically comprises the following steps:
there is a transition zone between the tomographic component and the offset component, and typically the scattering angle of the offset component is less than 140 degrees, while the opening angle of the tomographic component is greater than 160 degrees, becauseSo for a reference frequency omegacjThe frequency band of which is in the range of 0.5 omegacj～2ωcjOr the range of its frequency band is defined by the minimum opening angle a of the tomographic componenttomo_max(e.g., 160 degrees or a similar magnitude) and offset component maximum opening angle amig_max(e.g., 140 degrees or a similar magnitude) that the margin in the frequency range forms a sub-gradient that is smoothly filtered once against its reference frequency to extract its tomographic component.
2. Inverting the full waveform by band-pass filtering according to the divided frequency bands by a margin δ d (x)rT) into subsets δ d (x)r，t，ωc1)，…，δd(xr，t，ωcn) And back-propagating each subset margin to form the original gradient g (x, ω) of the respective subset marginc1)，…，g(x，ωcn)。
3. For a certainOne element g (x) in the original gradient of a subset of residualsi，ωcj) (since the numerical calculations are all discrete, the gradient of the subset margin is also discrete, and a discrete point in the gradient is an element), according to the reference frequency ω corresponding to the original gradientcjAnd the element g (x)i，ωcj) corresponding P wave velocity v, selecting minimum opening angle α of wave number vector of the original gradient seismic wave field and residual wave fieldminAnd calculating the cutoff wave number k of the element according to the formula (6)tomo_maxTo a set reference frequency ωcjAnd its corresponding P-wave velocity smoothing (k)tomo_maxcorresponding to | k |, αmincorresponding to alpha, omegacjcorresponding to ω), wherein the minimum opening angle αminLess than 180 degrees and may be set at 160 degrees.
4. From the calculated truncated wavenumber ktomo_maxThe gaussian smoothing filter of the element space domain is obtained by adopting a gaussian function design, and the method specifically comprises the following steps:
the gaussian function in the spatial domain is:
where | x | represents the modulus of the position vector; the fourier domain expression of equation (7) above is:
wherein, | k | represents a vector of wave numbers, i.e., the truncated wave numbers; sigma and sigmakForm factors representing the spatial and fourier domains, respectively, the relationship between the two form factors being:
is preset to oneA threshold value, wherein the threshold value may be 0.3 or a similar magnitude, will truncate the wave number ktomo_maAnd the corresponding Fourier Gaussian function value, namely the threshold value, is substituted into the formula (8) to obtain:
calculating to obtain a shape factor sigma of a Fourier domainkSubstituting the formula (9) into the space domain, and calculating to obtain a shape factor sigma of the space domain; then, the shape factor σ of the obtained spatial domain is substituted into the formula (7) to obtain the element g (x)i，ωcj) Gaussian smoothing filter G (x, x) in spatial domaini，ωcj)。
5. Multiplying the element by a gaussian smoothing filter of the element space domain, extracting a tomographic component of the element, and implementing adaptive smoothing on the element, where the adaptive smoothing process may be expressed as:
gtomo(x，xi，ωcj)＝G(x，xi，ωcj)g(xi，ωcj) (11)
wherein, gtomo(x，xi，ωcj) Representing a reference frequency of ωcjElement g (x) in the original gradient of the subset margin of (c)i，ωcj) The corresponding chromatographic component; g (x, x)i，ωcj) Representing a reference frequency of ωcjElement g (x) in the original gradient of the subset margin of (c)i，ωcj) A corresponding spatial domain smoothing filter; g (x)i，ωcj) Representing a reference frequency of ωcjIn the original gradient of the subset margin of (3) at xiThe elements of (1).
6. Repeating the steps 3) to 5), finishing the chromatographic component extraction of all elements in the original gradient of all the subset residuals, and finally accumulating the results to obtain the chromatographic component g of the original gradient in the full waveform inversiontomo(x)：
gtomo(x)＝∑i∑jG(x，xi，ωcj)g(xi，ωcj) (12)
Wherein, G (x, x)i，ωcj) Representing a reference frequency of ωcjElement g (x) in the original gradient of the subset margin of (c)i，ωcjA corresponding spatial domain smoothing filter; g (x)i，ωcj) Representing a reference frequency of ωcjThe original gradient of the subset margin of (a) is at xiThe elements of (1).
The following describes the application process of the method for extracting the chromatographic component of the original gradient in the full waveform inversion in detail by taking a two-layer model as a specific embodiment.
As shown in FIG. 3(a), the source wavelet in this embodiment is a bandwidth limited wavelet with a spectral spread in the range of 3-20 Hz, which is represented by the dashed lines in FIGS. 3(d) and 3 (e). The observation system in this example is a point source and a detector, the source (black x in fig. 3 (b)) and the residual wavefield (white x in fig. 3 (b)) are located 2km and 6km from the left boundary, respectively, and the depth of both the source and residual wavefield is 2.5 km. As shown in fig. 3(b), the gradient of the first iteration of the full waveform inversion is shown, the offset component presents an ellipse shape, the rest part is a chromatographic component required by updating the background velocity, the chromatographic component is extracted by adopting the extraction method of the invention in the original gradient, and the minimum opening angle a of the chromatographic componenttomo_maxSet to 160 degrees. As shown in fig. 3(c), the tomographic components extracted by frequency-by-frequency adaptive smoothing are shown, but applying smoothing filtering to each frequency requires fourier transform of the entire wave field, which requires a large amount of computation, and is also inefficient in the time domain.
Since the maximum opening angle of the reflected wave is smaller than the cutoff angle, there is a transition zone in the wavenumber domain to distinguish the tomographic component from the offset component, and therefore, the minimum opening angle a of the tomographic component is settomo_max160 degrees, which is also true for most practical cases if the reflected wave opening angle is less than 140 degreesIn this case, the maximum wavenumber of the tomographic component will be less than half of the minimum wavenumber of the offset component. Therefore, under the condition of ensuring no frequency leakage between the two components, the self-adaptive smooth filtering is only applied once within the reference frequency range of 0.5-2 times.
Adaptive filtering is applied to four sets of frequency bands with reference frequencies set to 1.5Hz, 3Hz, 6Hz and 12Hz, respectively, and fig. 3(d) shows a filter for decomposing the residue into four sub-residues. The tomographic component of the gradient extracted at four reference frequencies is shown in fig. 3(f), and it can be seen that this strategy for setting the reference frequencies is the same as the filtering for each frequency separately. However, in practice, four passes of the filtered margin are required, thereby increasing the amount of computation. To reduce the amount of computation, only the reference frequencies 6Hz and 12Hz are used, since the energy of the wavelets below 3Hz or above 24Hz is very weak, so that only one additional back pass is required in practice. As shown in fig. 3(g) for tomographic components extracted with two reference frequencies, it was found that reducing the reference frequency to two has no great influence on the extraction accuracy of the tomographic components except for a slight energy leakage to the offset component between the "V" -type tomographic components. Therefore, it is effective to extract the tomographic components using two reference frequencies.
The above embodiments are only used for illustrating the present invention, and the structure, connection mode, manufacturing process, etc. of the components may be changed, and all equivalent changes and modifications performed on the basis of the technical solution of the present invention should not be excluded from the protection scope of the present invention.
Claims (9)
1. A method for extracting chromatographic components of an original gradient in full waveform inversion is characterized by comprising the following steps:
step 1): dividing the residual frequency spectrum in the full waveform inversion into a plurality of frequency bands, wherein each frequency band is correspondingly set with a reference frequency;
step 2): according to the divided frequency bands, dividing the residuals in the full waveform inversion into a plurality of subsets through band-pass filtering, and reversely transmitting the residuals of each subset to obtain the original gradient of the residuals of each subset;
step 3): aiming at a certain element in the original gradient of a certain subset of margins, calculating the truncation wave number of the element according to the reference frequency corresponding to the original gradient and the P wave velocity corresponding to the element;
step 4): according to the calculated truncation wave number, a Gaussian smoothing filter of the element space domain is obtained by adopting a Gaussian function;
step 5): multiplying the element by a gaussian smoothing filter of the element space domain to extract a tomographic component of the element;
step 6): and repeating the steps 3) to 5), finishing the extraction of the chromatographic components of all elements in the original gradient of all the subset residuals, and accumulating to obtain the chromatographic components of the original gradient in the full waveform inversion.
2. The method as claimed in claim 1, wherein the step 3) of calculating, for an element in the original gradient of a subset of the residuals, the truncated wavenumber of the element according to the reference frequency corresponding to the original gradient and the P-wave velocity corresponding to the element comprises:
for a certain element in the original gradient of a certain subset of residuals, selecting the minimum opening angle of wave number vectors of a source wave field and a residual wave field of the original gradient according to the reference frequency corresponding to the original gradient and the P wave velocity corresponding to the element, and calculating the truncated wave number of the element according to the selected minimum opening angle:
wherein k istomo_maxRepresents the cutoff wave number of the element; omegacjrepresenting the reference frequency corresponding to the original gradient, v representing the P-wave velocity corresponding to the element, αminThe minimum opening angle of the wavenumber vectors of the source wavefield and the residual wavefield representing the original gradient.
3. The method of claim 2, wherein the minimum opening angle of the wavenumber vectors of the source wavefield and the residual wavefield of the original gradient is less than 180 degrees.
4. The method of claim 3, wherein the minimum opening angle of the wavenumber vectors of the source wavefield and the residual wavefield of the original gradient is 160 degrees.
5. The method for extracting chromatographic components of original gradients in full waveform inversion as claimed in claim 1, wherein the step 4) is to use a gaussian function to obtain a gaussian smoothing filter of a spatial domain according to the calculated truncated wavenumber, and the specific process is as follows:
the gaussian function in the spatial domain is:
where | x | represents the modulus of the position vector; the fourier domain expression of the spatial domain gaussian function is:
wherein, | k | represents a vector of wave numbers, i.e., the truncated wave numbers; sigma and sigmakForm factors representing the spatial and fourier domains, respectively, the relationship between the two form factors being:
presetting a threshold, substituting the truncated wave number and the corresponding Fourier Gaussian function value, namely the threshold, into the Fourier domain expression, and calculating to obtain the shape factor sigma of the Fourier domainkAnd the shape factor sigma of the space domain is substituted into the Gaussian function of the space domain to obtain the shape factor sigma of the space domain in xiA gaussian smoothing filter G (x, x) of the spatial domain of the element(s) of (a)i，ωcj)。
6. The method of claim 5, wherein the threshold is 0.3.
7. The method of claim 2, wherein the reference frequency ω is a frequency of the original gradient in the full waveform inversioncjHas a frequency band range of 0.5 omegacj～2ωcj。
8. The method of claim 2, wherein the reference frequency ω is a frequency of the original gradient in the full waveform inversioncjIs determined by the minimum opening angle of the tomographic component and the maximum opening angle of the offset component.
9. The method of claim 8, wherein the minimum opening angle of the tomographic component is 160 degrees and the maximum opening angle of the offset component is 140 degrees.
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| CN108802818B (en) | 2019-06-25 |
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