CN112379415A - Multi-scale full-waveform inversion method and device for reconstructed low-frequency data based on downsampling - Google Patents
Multi-scale full-waveform inversion method and device for reconstructed low-frequency data based on downsampling Download PDFInfo
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Abstract
A multi-scale full waveform inversion method for reconstructing low-frequency data based on downsampling comprises the following steps: acquiring earth surface observation data; reconstructing the data of the missing low-frequency part of the earth surface observation data by a sliding minus sampling method; carrying out data processing on the obtained reconstruction data; and constructing a background velocity model by using the processed reconstruction data through a multi-scale method, and iterating the background velocity model as an initial velocity model of the traditional full-waveform inversion to obtain an inversion result. The method comprises the steps of selecting a sampling point with the maximum cross-correlation value with real observation data by a sliding sampling reduction method to reconstruct low-frequency data through interpolation; according to the method, a high-precision speed model is obtained by utilizing the full-waveform inversion of the time domain with the full-band scale of 0-8Hz and the full-band scale of the reconstructed low-frequency data. The full waveform inversion method is used as an initial model of the traditional full waveform inversion, and the cycle skip phenomenon of the full waveform inversion is relieved.
Description
Technical Field
The invention relates to the technical field of low-frequency seismic signal recovery, in particular to a method for reconstructing a low-frequency signal lacking seismic data based on a downsampling thought and realizing full waveform inversion by combining a multi-scale thought.
Background
The Full Waveform Inversion (FWI) method relies on all the acquired waveform information to construct a model of the subsurface medium by matching the simulated data with the observed data. The generation of the simulation data requires the use of elastic wave equations of motion to describe the propagation of seismic waves in the subsurface medium. Due to the complexity of fitting data, local optimization problems based on minimizing the target functional also have a large number of local minima. These local minima will make the inversion result very biased, and the wrong inversion velocity model will also make the offset imaging result very erroneous. Under the condition of poor initial model, the phenomenon that the cycle skip phenomenon falls into the local minimum value is particularly obvious due to the huge difference between the simulation data and the observation data. The nonlinearity of full waveform inversion is reduced, the local minimum is avoided, and low-frequency data play a very important role. There are studies that show that very low frequency data (1.5-2.0Hz) play a very important role in restoring long wavelength structures underground. The prior art provides a full waveform inversion method of a Laplace domain, a large-scale low-wave-number background velocity model is constructed through a zero-frequency component of a damping wave field and is used as an initial model of the full waveform inversion of the frequency domain, and the problem that the traditional method falls into a local minimum value is solved. The gradiometer decomposes the gradient of inversion iteration into a tomography part and an offset imaging part based on the characteristic of the propagation direction of the seismic wave, and uses the tomography part to realize the inversion of the velocity background model with long wavelength, but the method can not effectively avoid the cycle skip phenomenon. There are studies to obtain a low wavenumber structure by transforming the gradient into an angle domain and eliminating a small scattering angle portion, but this method requires a large amount of three-dimensional fourier transform and thus results in low computational efficiency. Therefore, it is proposed that by introducing the time shift imaging condition in offset imaging into the inverse gradient, the low-wave-number long-wavelength extraction of the gradient in the time domain can be performed naturally without significantly increasing the amount of calculation.
Aiming at the problem of missing the inversion result influenced by low frequency at present, many scholars provide solutions from various aspects. The first type is to avoid a local minimum by improving the convexity of an objective function of a full waveform inversion optimization problem, and comprises a brand-new data transformation form based on an optimal transport theory, so that the stability and convexity of an inverse problem are improved, and the convergence radius of the inverse problem is increased. Luo and Sava proposed in 2011 a new objective function, which aims to minimize deconvolution coefficients with penalty terms between simulation data and observation data, and numerical examples also show good convexity of the objective function. The second category of methods is directed to deep learning based methods, which implement training of convolutional neural networks by means of a large number of velocity models and corresponding seismic records in pairs, so as to implement direct mapping of seismic observation records to velocity models. The third method is to perform multi-scale full waveform inversion from low frequency to high frequency by directly expanding the low frequency data. The method for expanding the low frequency mainly comprises two parts, wherein one part is a traditional algorithm, the method comprises the steps of acquiring extremely low frequency data through seismic data enveloping, obtaining an underground reflection coefficient through sparse blind inversion and further reconstructing the low frequency data. Another part is the neural network-based development in recent years, by training pairs of high-frequency and low-frequency data to achieve direct mapping of high-frequency data to low-frequency data.
Research in recent years shows that the data low frequency band of 1.5-2Hz plays a crucial role in recovering a correct background speed model. However, in practice, low frequency source and low frequency data are often difficult to obtain. When the low-frequency part needing to be extracted in the data is weak or missing, the expected effect is generally difficult to achieve by various multi-scale full waveform inversion methods. Low frequency data plays a crucial role for long wavelength structures in the inverse velocity model. Reconstructing low frequency data is important to maintain high accuracy of full waveform inversion when low frequency data is missing.
Disclosure of Invention
It is therefore an objective of the claimed invention to provide a method and apparatus for multi-scale full waveform inversion based on downsampling reconstruction of low frequency data, so as to solve at least one of the above problems.
In order to achieve the above object, as an aspect of the present invention, there is provided a multiscale full waveform inversion method for reconstructing low frequency data based on downsampling, including the following steps:
acquiring earth surface observation data;
reconstructing the data of the missing low-frequency part of the earth surface observation data by a sliding minus sampling method;
carrying out data processing on the obtained reconstruction data;
and constructing a background velocity model by using the processed reconstruction data through a multi-scale method, and iterating the background velocity model as an initial velocity model of the traditional full-waveform inversion to obtain an inversion result.
And performing acoustic wave equation finite difference forward modeling on the real model by using the seismic source wavelet with the missing low frequency to obtain the earth surface observation data.
Wherein the sliding downsampling comprises:
will observe the data dobsEqually dividing the data into N data windows with the width of h;
assuming that the sampled observed data value at the two ends of the window is diAnd di+hWherein i and i + h represent sampling points, and the sampling point selected by the downsampling is set to be k, so that the following formula is satisfied:
so that k slides within the time window, and for each determined value of k, d is passedi、dkAnd di+hAnd carrying out low-frequency interpolation with three points within the length of a time window.
Wherein the processing performed for the time window comprises:
performing cross correlation on the interpolated time window signal and real observation data in the time window, and selecting a sampling point which enables the cross correlation value to be maximum, namely an optimal sampling point; the specific formula is as follows:
wherein t represents a time value, F (-) represents an interpolation function, and cubic interpolation is carried out in a time window by utilizing three points;
and summarizing the optimal sampling points and time window boundaries of all the time windows, and carrying out interpolation reconstruction on all the data.
The data processing in the step of data processing the obtained reconstruction data includes filtering, and the filtering is used for filtering the data to a target frequency band so as to recover the model of each frequency band.
Wherein, the inversion is carried out in two scales, which are 0-8Hz and full frequency band.
Wherein, the background velocity model is used as an initial velocity model of the traditional full waveform inversion, and in the step of obtaining the inversion result after iteration, the iteration times are 100-150 times.
As another aspect of the present invention, there is provided a multiscale full waveform inversion apparatus for reconstructing low frequency data based on downsampling, including:
the data acquisition module is used for acquiring earth surface observation data;
the reconstruction module is used for reconstructing the data of the missing low-frequency part of the earth surface observation data by a sliding minus sampling method;
the data processing module is used for carrying out data processing on the obtained reconstruction data;
and the inversion module is used for constructing a background velocity model by using the processed reconstruction data through a multi-scale method, and obtaining an inversion result after iteration by using the background velocity model as an initial velocity model of the traditional full-waveform inversion.
Based on the technical scheme, compared with the prior art, the multiscale full-waveform inversion method and the multiscale full-waveform inversion device for reconstructing low-frequency data based on downsampling have at least one or part of the following beneficial effects:
(1) the method comprises the steps of selecting a sampling point with the maximum cross-correlation value with real observation data by a sliding sampling reduction method to reconstruct low-frequency data through interpolation;
(2) according to the method, a high-precision speed model is obtained by utilizing the full-waveform inversion of the time domain with the full-band scale of 0-8Hz and the full-band scale of the reconstructed low-frequency data. The full waveform inversion method is used as an initial model of the traditional full waveform inversion, and the cycle skip phenomenon of the full waveform inversion is relieved.
Drawings
Fig. 1 is a flowchart of a work flow of reconstructing low-frequency data by sliding window downsampling according to an embodiment of the present invention;
FIG. 2 is a velocity model provided by an embodiment of the present invention; wherein, fig. 2(a) is a true Marmousi velocity model; FIG. 2(b) is an inverse initial velocity model;
FIG. 3 illustrates seismic source information with low frequency missing provided by an embodiment of the present invention; wherein, fig. 3(a) is a time domain; FIG. 3(b) is a frequency domain;
fig. 4 is a sampling point selection of observation data and downsampling in the reconstruction of single-channel data by the sliding time window downsampling method according to the embodiment of the present invention;
FIG. 5 is a comparison between the low frequency data recovered from the reconstruction of single-channel data and the finite difference reference data by the sliding time window downsampling method according to the embodiment of the present invention;
fig. 6 is a diagram of a comparison of frequency spectrums of single-channel reconstructed data and real single-channel data by the sliding time window downsampling method according to the embodiment of the present invention;
FIG. 7 is a graph of the inversion results of a background model using sliding time window downsampling low frequency data for FWI according to an embodiment of the present invention; FIG. 7(a) a background velocity model obtained by a multi-scale method; FIG. 7(b) is the result of a conventional FWI inversion using the background model shown in (a) as the initial model; fig. 7(c) is the result of a conventional single-scale FWI inversion.
Detailed Description
The invention discloses a low-frequency data recovery method based on a downsampling thought, which comprises the steps of firstly, equally dividing observation data into a plurality of parts, selecting sampling points in each data window, carrying out low-frequency interpolation in the length of a time window through three points, carrying out cross-correlation on a time window signal after interpolation and real observation data in the time window to screen out optimal sampling points, and finally obtaining low-frequency data through an interpolation method. Reconstructing low frequency data is important to maintain high accuracy of full waveform inversion when low frequency data is missing.
Specifically, the invention discloses a multiscale full waveform inversion method for reconstructing low-frequency data based on downsampling, which comprises the following steps:
acquiring earth surface observation data;
reconstructing the data of the missing low-frequency part of the earth surface observation data by a sliding minus sampling method;
carrying out data processing on the obtained reconstruction data;
and constructing a background velocity model by using the processed reconstruction data through a multi-scale method, and iterating the background velocity model as an initial velocity model of the traditional full-waveform inversion to obtain an inversion result.
And performing acoustic wave equation finite difference forward modeling on the real model by using the seismic source wavelet with the missing low frequency to obtain the earth surface observation data.
Wherein the sliding downsampling comprises:
will observe the data dobsEqually dividing the data into N data windows with the width of h;
assuming that the sampled observed data value at the two ends of the window is diAnd di+hWherein i and i + h represent sampling points, and the sampling point selected by the downsampling is set to be k, so that the following formula is satisfied:
so that k slides within the time window, and for each determined value of k, d is passedi、dkAnd di+hAnd carrying out low-frequency interpolation with three points within the length of a time window.
Wherein the processing performed for the time window comprises:
performing cross correlation on the interpolated time window signal and real observation data in the time window, and selecting a sampling point which enables the cross correlation value to be maximum, namely an optimal sampling point; the specific formula is as follows:
wherein t represents a time value, F (-) represents an interpolation function, and cubic interpolation is carried out in a time window by utilizing three points;
and summarizing the optimal sampling points and time window boundaries of all the time windows, and carrying out interpolation reconstruction on all the data.
The data processing in the step of data processing the obtained reconstruction data includes filtering, and the filtering is used for filtering the data to a target frequency band so as to recover the model of each frequency band.
Wherein, the inversion is carried out in two scales, which are 0-8Hz and full frequency band.
Wherein, the background velocity model is used as an initial velocity model of the traditional full waveform inversion, and in the step of obtaining the inversion result after iteration, the iteration times are 100-150 times.
The invention also discloses a multi-scale full-waveform inversion device for reconstructing low-frequency data based on downsampling, which comprises the following steps:
the data acquisition module is used for acquiring earth surface observation data;
the reconstruction module is used for reconstructing the data of the missing low-frequency part of the earth surface observation data by a sliding minus sampling method;
the data processing module is used for carrying out data processing on the obtained reconstruction data;
and the inversion module is used for constructing a background velocity model by using the processed reconstruction data through a multi-scale method, and obtaining an inversion result after iteration by using the background velocity model as an initial velocity model of the traditional full-waveform inversion.
In order that the objects, technical solutions and advantages of the present invention will become more apparent, the present invention will be further described in detail with reference to the accompanying drawings in conjunction with the following specific embodiments.
A multi-scale full waveform inversion method for reconstructing low-frequency data based on downsampling utilizes the idea of downsampling to reconstruct the missing low-frequency data, taking a synthesis experiment as an example, and the process comprises the following steps:
1) finite difference correction of acoustic wave equation on real model by using seismic source wavelet with low frequency missingPerforming simulation to obtain earth surface observation data dobs；
2) Will observe the data dobsEqually dividing the data into N data windows with the width of h;
3) assuming that the sampled observed data value at the two ends of the window is diAnd di+hWherein i and i + h represent sampling points, and the sampling point selected by the downsampling is set to be k, so that the following formula is satisfied:
4) so that k slides within the time window, and for each determined value of k, d is passedi、dkAnd di+hAnd carrying out low-frequency interpolation with the three points within the length of the time window, carrying out cross correlation on the interpolated time window signal and real observation data in the time window, and selecting a sampling point which enables the cross correlation value to be maximum. The specific formula is as follows:
wherein t represents a time value, F (-) represents an interpolation function, and cubic interpolation is carried out in a time window by utilizing three points;
5) as shown in fig. 1, a basic flow chart of sliding time window downsampling low frequency reconstruction is shown. The outer circulation of the flow chart is the selection of time windows, and each time window needs to determine the optimal sampling point through the internal circulation and the evaluation standard of optimal cross correlation;
6) summarizing the optimal sampling points and time window boundaries of all time windows, and carrying out interpolation reconstruction on the whole channel;
7) carrying out data processing on the reconstructed channel data, wherein the data processing mainly comprises filtering to a target frequency band and restoring a model of each frequency band;
8) the initial model is obtained by highly smoothing the real model, a background velocity model is constructed by using a multi-scale method based on reconstructed low-frequency data, and the background velocity model is used as the initial velocity model of the traditional FWI and is used for recovering a small-scale detail structure. Through frequency analysis, the inversion is carried out in two scales, 0-8Hz and full frequency band.
9) Obtaining a background velocity model through 50 times of iterative FWI inversion;
10) and (5) performing traditional FWI by taking the background velocity model as an initial model, and iterating for 100 times to obtain an inversion result.
The invention is described in detail below with reference to the figures and specific embodiments.
And (4) testing by using the Marmousi complex model, and performing rarefaction treatment on the original model because the original model is huge. As shown in fig. 2, the velocity model of this embodiment is a real velocity model and an initial velocity model, as shown in fig. 2(a) and fig. 2(b), respectively, the velocity range is from 1.5km/s to 4.5km/s, the model size is 130 × 515, and the grid distance dx-dz-12.5 m. The data acquisition system consists of 35 shots and 515 detectors, which are evenly distributed across the entire surface. In order to simulate the lack of low frequency in the actual situation, the Rake wavelet forward modeling for cutting off low frequency is used to obtain the earth surface observation data, the data recording length is 4s, the sampling time is 1ms, the frequency range is selected from 5Hz to 30Hz, and as shown in FIG. 3, the low frequency missing seismic source information provided by the embodiment is provided; the time domain and frequency domain characteristics of the low-frequency missing seismic sources are shown in fig. 3(a) and 3 (b).
1) The low-frequency reconstruction part is realized under matlab, and the multi-scale full-waveform inversion is realized under Fortran/C.
2) And performing finite difference forward modeling on the acoustic wave equation on the real Marmousi complex model by using the low-frequency-removed Rake wavelet to obtain observation data.
3) The low frequency data is constructed using the left part of the flow chart of fig. 1. Taking a trace as an example, as shown in fig. 4, the black solid line represents the observed missing low frequency data, and the open circles are the optimal sampling points extracted by the proposed method. The extracted sampling points are mainly based on cross-correlation criteria to guarantee the reliability of the recovered low-frequency data. It can be found from the figure that the sampling points are mostly at the highest point of the amplitude, and the characteristics of the reflection coefficient are also met. Interpolation is performed through the optimal sampling points (hollow circle points in fig. 4) on the entire trace data, and after the interpolation result is subjected to data processing such as filtering, the recovered low-frequency data is shown as a solid line in fig. 5.
4) For comparison, reference data obtained using finite differences of low frequency sources is also given, indicated by the dashed line. The spectral characteristics of both are shown in fig. 6. The frequency and the phase of the low-frequency data recovered by the method are close to those of the reference data, and the frequency spectrum characteristics are uniform.
5) And using the recovered data for multi-scale full waveform inversion, wherein the initial model is obtained by highly smoothing the real model, the inversion is carried out by dividing the inversion into two scales, namely 0-8Hz and full frequency band, and the seismic source function selects the Rake wavelet of the low-frequency part.
6) After 50 iterations, a background velocity model was obtained as shown in fig. 7 (a). The low-frequency data extracted by the method can recover partial background velocity models, mainly in the shallow part and the middle part of the model.
7) The background velocity model was used as an initial model for FWI, and the results of the 100-time iterative inversion are shown in fig. 7 (b). Comparing fig. 7(c) (FWI directly with the original low frequency missing data), this approach effectively avoids local minima.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (8)
1. A multiscale full waveform inversion method for reconstructing low-frequency data based on downsampling is characterized by comprising the following steps:
acquiring earth surface observation data;
reconstructing the data of the missing low-frequency part of the earth surface observation data by a sliding minus sampling method;
carrying out data processing on the obtained reconstruction data;
and constructing a background velocity model by using the processed reconstruction data through a multi-scale method, and iterating the background velocity model as an initial velocity model of the traditional full-waveform inversion to obtain an inversion result.
2. The multiscale full waveform inversion method for undersampling-based reconstructed low frequency data according to claim 1, wherein the obtaining of surface observation data is performed by performing finite difference forward modeling of acoustic wave equation on a real model using a source wavelet with missing low frequency.
3. The method of downsampling-based multi-scale full waveform inversion of reconstructed low frequency data according to claim 1, wherein the sliding downsampling comprises:
will observe the data dobsEqually dividing the data into N data windows with the width of h;
assuming that the sampled observed data value at the two ends of the window is diAnd di+hWherein i and i + h represent sampling points, and the sampling point selected by the downsampling is set to be k, so that the following formula is satisfied:
so that k slides within the time window, and for each determined value of k, d is passedi、dkAnd di+hAnd carrying out low-frequency interpolation with three points within the length of a time window.
4. The method of multiscale full waveform inversion of downsampling-based reconstructed low frequency data according to claim 3, wherein the processing for the time window comprises:
performing cross correlation on the interpolated time window signal and real observation data in the time window, and selecting a sampling point which enables the cross correlation value to be maximum, namely an optimal sampling point; the specific formula is as follows:
wherein t represents a time value, F (-) represents an interpolation function, and cubic interpolation is carried out in a time window by utilizing three points;
and summarizing the optimal sampling points and time window boundaries of all the time windows, and carrying out interpolation reconstruction on all the data.
5. The method of claim 1, wherein the data processing in the step of data processing the obtained reconstructed data comprises filtering, and the filtering is used for filtering the data to a target frequency band so as to recover the model of each frequency band.
6. The multiscale full waveform inversion method for undersampling-based reconstructed low frequency data of claim 1, wherein the inversion is performed in two scales, 0-8Hz and full band.
7. The multiscale full waveform inversion method of the undersampling-based reconstructed low frequency data according to claim 1, wherein the background velocity model is used as an initial velocity model of the conventional full waveform inversion, and in the step of obtaining the inversion result after iteration, the number of iterations is 100-150.
8. A multiscale full waveform inversion apparatus for downsampling-based reconstruction of low frequency data, comprising:
the data acquisition module is used for acquiring earth surface observation data;
the reconstruction module is used for reconstructing the data of the missing low-frequency part of the earth surface observation data by a sliding minus sampling method;
the data processing module is used for carrying out data processing on the obtained reconstruction data;
and the inversion module is used for constructing a background velocity model by using the processed reconstruction data through a multi-scale method, and obtaining an inversion result after iteration by using the background velocity model as an initial velocity model of the traditional full-waveform inversion.
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