A full waveform inversion method for marine vibroseis data with Doppler distortion

Abstract

The present invention belongs to the field of marine vibroseis data imaging, specifically, a full waveform inversion method for marine vibroseis data with Doppler distortion, constructing a time-varying spatial offset operator describing the motion of the detector and a nonlinear modeling operator based on the frequency sweep-segmentation method describing the motion of the source; deploying the time-varying spatial offset operator describing the motion of the detector and the nonlinear modeling operator based on the frequency sweep-segmentation method describing the motion of the source into a least squares fitting framework, and forming a mismatch function; iteratively solving the gradient of the velocity model parameter in the mismatch function, and obtaining a phase-corrected imaging result in the iterative process, and the present invention realizes the inversion of marine vibroseis data with Doppler distortion. It can be effective for OBN or towed marine vibroseis data sets with Doppler distortion.

Description

Technical Field

[0001] The invention belongs to the field of marine vibroseis data imaging, and in particular is a full waveform inversion method for marine vibroseis data with Doppler distortion. Background Art

[0002] Non-impulse marine sources (NIMS), such as marine controllable vibroseis sources (MVibs), are gaining popularity for seismic acquisition due to their environmental friendliness, abundant low-frequency energy output, good and repeatable waveform control level, and the ability to mix multiple phase-encoded sources. However, during the acquisition process of marine controllable vibroseis sources, since the source (and possibly the detector) are in motion, they will generate processing challenges that airgun sources do not have: Doppler shift and time-dependent source-receiver offsets acquired for the ocean bottom node (OBN). Although industry-standard phase correction methods based on spatiotemporal filtering and frequency-wavenumber (FK) domain can effectively address the interference of Doppler effect on seismic data, for low-frequency dedicated sources with long scanning time, even after phase correction, it may not be accurate to treat the data as a fixed source. Furthermore, such correction operations rely on sufficient spatial sampling to obtain ideal Doppler shift correction results without spatial aliasing. Standard seismic data processing and imaging techniques assume that the source is stationary. Failure to account for source motion in seismic imaging can result not only in phase shifts and positioning errors in imaged structures, but can also mean significant under-illumination, velocity errors, or both. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a full waveform inversion method for marine vibroseis data with Doppler distortion, so as to solve the interference of the Doppler effect in the observation records collected during the marine vibroseis acquisition process on the imaging accuracy.

[0004] The present invention is achieved in this way.

[0005] A full waveform inversion method for marine vibroseis data with Doppler distortion, the method comprising:

[0006] S1 constructs a time-varying spatial offset operator to describe the detector motion and nonlinear modeling operators based on the frequency sweep-segmentation method to describe the source motion ;

[0007] S2 describes the time-varying spatial offset operator of the detector motion and nonlinear modeling operators based on the frequency sweep-segmentation method to describe the source motion Deployed into the least squares fitting framework and formed the misfit function;

[0008] S3 iteratively solves the gradient of the velocity model parameters in the mismatch function, and obtains the imaging result after phase correction in the iterative process.

[0009] Furthermore, a nonlinear modeling operator based on the sweep-segmentation method is constructed to describe the source motion. ,include:

[0010] The sweep-segmentation method is used to simulate the wave field of earthquake source motion. Split into several swept signal segments , , ,..., , n is the total number of segments, and different swept-frequency signal segments are injected into the corresponding fixed source positions of the swept-frequency signal segments along the source motion path, where the injection positions of the swept-frequency signal segments are determined by the source moving speed and the source excitation time.

[0011] Furthermore, a time-varying spatial offset operator is constructed to describe the detector motion. , including the detector motion by introducing a time-varying spatial offset in the common shot set, expressed as formula (1):

[0012] (1) ,

[0013] in, Indicates the location of the earthquake source when it is stationary. represents the position of the detector when stationary, represents the position of the detector during motion, represents the location of the earthquake source during movement, Indicates time, represents the moving speed of the earthquake source, represents the moving speed of the detector, represents the time-varying spatial offset operator, is the marine vibroseis data with the source stationary before correlation with the swept frequency signal, Marine vibroseis data for the movement of the front detector associated with the swept frequency signal;

[0014] Time-varying spatial migration operator for: , represents the Dirichlet function.

[0015] Furthermore, the mismatch function is expressed as:

[0016] (2)

[0017] Where, T represents the continuous excitation time of the earthquake source, represents the velocity model parameters, is a wavefield limiting operator used to extract the wavefield information of the detector position. is the collected Doppler distortion seismic record, It represents that the nonlinear modeling operator based on the sweep-segmentation method acts on the velocity model parameters to generate the source motion seismic record.

[0018] Further, S3 includes: expressing the mismatch function in the form of an augmented wide function, and obtaining the gradient of the velocity model parameter in the mismatch function by taking the derivative of the velocity model parameter through the augmented wide function;

[0019] The gradient of the velocity model parameters in the mismatch function is iteratively solved by the conjugate gradient method.

[0020] Furthermore, the mismatch function is expressed as an augmented wide function, and the gradient of the velocity model parameter in the mismatch function is obtained by taking the derivative of the velocity model parameter through the augmented wide function, which specifically includes:

[0021] The mismatch function is transformed into an unconstrained optimization problem using the Lagrange multiplier method, allowing the wave field excited by the source to propagate in the x and z directions:

[0022] (3) ,

[0023] in, are all adjoint states associated with the initial boundary conditions, is the Lagrangian operator associated with the wave equation, Represents the source of the earthquake in terms of source velocity Moving in the x direction, represents the nonlinear modeling operator based on the sweep-segmentation method at any time t The wave field value of the earthquake source motion, Represents the nonlinear modeling operator based on the sweep-segmentation method at the initial time The wave field value of the earthquake source motion, Indicates the expansion letter;

[0024] Will Expand by 2 step-by-step integration:

[0025] (4)

[0026] represents the value of the Lagrangian operator associated with the wave equation at time 0, represents the value of the Lagrangian operator associated with the wave equation at time T, for The wave field value of the earthquake source motion based on the nonlinear modeling operator of the sweep-segmentation method at each moment;

[0027] According to formula (3) and formula (4), the augmented function is calculated The derivative of the velocity model parameter m is:

[0028] (5)

[0029] is the adjoint state equation, expressed as:

[0030] (6),

[0031] represents the inverse time-varying spatial convolution operator that depends on the spatial sampling of the observed common shot gathers. It can be computed by the zero-lag correlation between the time derivative of the forward-propagated moving source wavefield and the back-projected wavefield residual after the inverse time-varying spatial migration.

[0032] Compared with the prior art, the present invention has the following beneficial effects: the present invention realizes the inversion of Doppler-distorted marine vibroseis data. It is effective for OBN or towed marine vibroseis data sets with Doppler distortion. Even in the scenario where the acquisition device is in high-speed motion, an underground image similar to that in a static acquisition scenario can be obtained. In addition, the method of the present invention resists spatial aliasing, and effectively avoids the interference of spatial aliasing generated by the phase correction method under rough spatial sampling conditions on the imaging results.

[0033] The method of the present invention can accurately characterize the Doppler distorted wave field collected by different acquisition devices (OBN or streamer) and obtain accurate underground images in the inversion process by deploying a nonlinear modeling operator based on the frequency sweep-segmentation method to describe the source motion and a time-varying spatial offset operator to describe the detector motion in the least squares fitting algorithm. Accurate imaging of Doppler distorted observation data can be achieved without an additional phase correction step, so it can effectively avoid the disadvantage of the traditional phase correction method being sensitive to spatial aliasing. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a flow chart of a full waveform inversion method for marine vibroseis data with Doppler distortion provided by an embodiment of the present invention;

[0035] Figure 2 is a partially scaled SEAM phase 1 velocity model diagram provided by an embodiment of the present invention;

[0036] Figure 3 The embodiments of the present invention provide (a) stationary source marine vibroseis data, (b) moving source and streamer marine vibroseis data, and (c) the difference between stationary source marine vibroseis data and moving source and streamer marine vibroseis data;

[0037] Figure 4 The embodiments of the present invention provide (a) an initial velocity model, (b) imaging results of stationary source marine vibroseis data, (c) imaging results of moving source and streamer marine vibroseis data, and (d) imaging results of motion simulation with a mobile acquisition device;

[0038] Figure 5 The embodiments of the present invention provide (a) the difference between the imaging results of stationary source marine controllable source data and the true velocity model, (b) the difference between the imaging results of moving source and towed marine controllable source data and the true velocity model, and (c) the difference between the imaging results of motion simulation with a mobile acquisition device and the true velocity model. DETAILED DESCRIPTION

[0039] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0040] like Figure 1 As shown, an implementation process of a full waveform inversion (FWI) method for Doppler-distorted marine vibroseis data. In view of the current situation that the Doppler effect exists in the data during the acquisition process of marine vibroseis, the method of the present invention makes full use of the ability of the sweep-segmentation method and the convolution expansion model to accurately simulate the movement of the source and the detector, and effectively removes the Doppler frequency shift from the full waveform inversion imaging process while ensuring the applicability and accuracy of the method. The present invention specifically includes the following steps:

[0041] S1 constructs a time-varying spatial offset operator to describe the detector motion and nonlinear modeling operators based on the frequency sweep-segmentation method to describe the source motion , where the acquisition parameters need to be set, including the acquisition speed, the type of sweep signal and the spatial sampling rate of the observation record during the acquisition process;

[0042] S2 describes the time-varying spatial offset operator of the detector motion and nonlinear modeling operators based on the frequency sweep-segmentation method to describe the source motion Deployed into the least squares fitting framework and formed the misfit function;

[0043] S3 iteratively solves the gradient of the velocity model parameters in the mismatch function, and obtains the imaging result after phase correction in the iterative process.

[0044] Among them, in this embodiment, Figure 2The method of the invention is illustrated on a partially scaled version of the SEAM phase 1 model shown. In this example, a collection of 112 shots with a 15 m shot spacing is located at a depth of 0 m (sea level) from 30 to 696 m, each shot containing 48 receivers. The receiver spacing is 6 m, and the maximum and minimum shot-to-receiver offsets are 0 and 282 m, respectively. The source wavelet modeled is a 4 s linear sweep from 5 to 80 Hz, with a 1 s listening time added to the end of the signal. Two data sets are calculated for a stationary source and a source moving to the left at 6 m / s (direct waves removed), without considering interference from factors such as variable sea conditions, ghosting and multiples. Figure 3 (a) and Figure 3 (b) shows the total shot gathering of the stationary source and the moving source and streamer at a source distance of 90 m. The difference between them is shown in Figure 3 (c) in the figure shows the phase and amplitude distortion caused by the Doppler effect.

[0045] In S1, a nonlinear modeling operator based on the sweep-segmentation method is constructed to describe the source motion. ,include:

[0046] The sweep-segmentation method is used to simulate the wave field of earthquake source motion. Split into several swept signal segments , , ,..., , n is the total number of segments, and different sweep signal segments are injected into the fixed source position corresponding to the sweep signal segment along the source motion path, wherein the position of the sweep signal segment injection is determined by the source moving speed and the source excitation time. In this embodiment, the sweep signal is divided into 20 0.2s sweep signal segments (including the monitoring time), and one segment is injected every 1.2m.

[0047] Constructing a time-varying spatial migration operator to describe the detector motion , including the detector motion by introducing a time-varying spatial offset in the common shot set, expressed as formula (1):

[0048] (1) ,

[0049] in, Indicates the location of the earthquake source when it is stationary. represents the position of the detector when stationary, represents the position of the detector during motion, represents the location of the earthquake source during movement, Indicates time, represents the moving speed of the earthquake source, represents the moving speed of the detector, represents the time-varying spatial offset operator, is the marine vibroseis data with the source stationary before correlation with the swept frequency signal, is the marine vibroseis data of the front detector movement related to the sweep signal; formula (1) is the convolution expansion model.

[0050] Time-varying spatial migration operator for: , represents the Dirichlet function.

[0051] The mismatch function is expressed as:

[0052] (2)

[0053] Where, T represents the continuous excitation time of the earthquake source, represents the velocity model parameters, is a wavefield limiting operator used to extract the wavefield information of the detector position. is the collected Doppler distortion seismic record, and The meanings are the same, both representing nonlinear modeling operators based on the sweep-segmentation method.

[0054] S3 includes: expressing the mismatch function in the form of an augmented wide function, and obtaining the gradient of the velocity model parameter in the mismatch function by taking the derivative of the velocity model parameter through the augmented wide function; including:

[0055] The mismatch function is transformed into an unconstrained optimization problem using the Lagrange multiplier method, allowing the wave field excited by the source to propagate in the x and z directions:

[0056] (3) ,

[0057] in, are all adjoint states associated with the initial boundary conditions, is the Lagrangian operator associated with the wave equation, Represents the source of the earthquake in terms of source velocity Moving in the x direction, represents the nonlinear modeling operator based on the sweep-segmentation method at any time t The wave field value of the earthquake source motion, Represents the nonlinear modeling operator based on the sweep-segmentation method at the initial time The wave field value of the earthquake source motion, Indicates the expansion letter;

[0058] Will Expand by 2 step-by-step integration:

[0059] (4)

[0060] represents the value of the Lagrangian operator associated with the wave equation at time 0, represents the value of the Lagrangian operator associated with the wave equation at time T, for The wave field value of the earthquake source motion based on the nonlinear modeling operator of the sweep-segmentation method at each moment;

[0061] According to formulas (3) and (4), the augmented function is calculated The derivative of the velocity model parameter m is:

[0062] (5)

[0063] in, represents the inverse time-varying spatial convolution operator that depends on the spatial sampling of the observed common shot gathers; is the adjoint state equation, expressed as:

[0064] (6),

[0065] In the formula, and is the adjoint state and has nothing to do with the gradient solution.

[0066] Finally, the gradient of the velocity model parameters in the mismatch function is iteratively solved by the conjugate gradient method.

[0067] In this embodiment, a Gaussian smoothing function is used to smooth the true velocity model, and the obtained Figure 4 The initial velocity model in (a) is used to test the method of the present invention. The stationary source marine controllable source data and the moving source and towed marine controllable source data are respectively brought into the full waveform inversion to obtain the corresponding imaging results. Figure 4 (b) and Figure 4 Although the two images look similar, most of the velocity structure is fully restored. See the difference panels with the true velocity model for details. Figure 5 (a) and Figure 5 (b) in the figure shows the interference of the motion effect of the acquisition device on the accuracy of full waveform inversion.

[0068] Figure 4 (d) is the full waveform inversion image based on motion acquisition and imaging by the method of the present invention. It is almost completely consistent with the full waveform inversion image based on static acquisition and imaging. The difference between it and the true velocity model is shown in the panel Figure 5(c) in the figure demonstrates that the method of the present invention has the ability to consider the motion effect of the acquisition device during the imaging process.

[0069] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A full waveform inversion method for marine vibroseis data with Doppler distortion, characterized in that: The method includes: S1 constructs a time-varying spatial offset operator to describe the detector motion and nonlinear modeling operators based on the frequency sweep-segmentation method to describe the source motion ,include: The sweep-segmentation method is used to simulate the wave field of earthquake source motion. Split into several swept frequency signal segments , , ,..., , n is the total number of segments, and different sweep signal segments are injected into the fixed source positions corresponding to the sweep signal segments along the source motion path, wherein the injection positions of the sweep signal segments are determined by the source moving speed and the source excitation time; S2 describes the time-varying spatial offset operator of the detector motion and nonlinear modeling operators based on the frequency sweep-segmentation method to describe the source motion Deployed into the least squares fitting framework and formed the misfit function; Constructing a time-varying spatial migration operator to describe the detector motion , including the detector motion by introducing a time-varying spatial offset in the common shot set, expressed as formula (1): (1) ， in, Indicates the location of the earthquake source when it is stationary. represents the position of the detector when stationary, represents the position of the detector during motion, represents the location of the earthquake source during movement, Indicates time, represents the moving speed of the earthquake source, represents the moving speed of the detector, represents the time-varying spatial offset operator, is the marine vibroseis data with the source stationary before correlation with the swept frequency signal, Marine vibroseis data for the movement of the front detector associated with the swept frequency signal; Time-varying spatial migration operator for: , represents the Dirichlet function; S3 iteratively solves the gradient of the velocity model parameters in the mismatch function, and obtains the imaging result after phase correction in the iterative process.

2. The full waveform inversion method for marine vibroseis data with Doppler distortion according to claim 1, characterized in that: The mismatch function is expressed as: (2)， Where, T represents the continuous excitation time of the earthquake source, represents the velocity model parameters, is a wavefield limiting operator used to extract the wavefield information of the detector position. is the collected Doppler distortion seismic record, It represents that the nonlinear modeling operator based on the sweep-segmentation method acts on the velocity model parameters to generate the source motion seismic record.

3. The full waveform inversion method for marine vibroseis data with Doppler distortion according to claim 2, characterized in that: S3 includes: expressing the mismatch function in the form of an augmented wide function, and obtaining the gradient of the velocity model parameter in the mismatch function by taking the derivative of the velocity model parameter through the augmented wide function; The gradient of the velocity model parameters in the mismatch function is iteratively solved by the conjugate gradient method.

4. The full waveform inversion method for marine vibroseis data with Doppler distortion according to claim 3, characterized in that: The mismatch function is expressed as an augmented wide functional form, and the gradient of the velocity model parameter in the mismatch function is obtained by taking the derivative of the velocity model parameter through the augmented wide functional, which includes: The mismatch function is transformed into an unconstrained optimization problem using the Lagrange multiplier method, allowing the wave field excited by the source to propagate in the x and z directions: (3) ， in, are all adjoint states associated with the initial boundary conditions, is the Lagrangian operator associated with the wave equation, Represents the source of the earthquake in terms of source velocity Moving in the x direction, represents the nonlinear modeling operator based on the sweep-segmentation method at any time t The wave field value of the earthquake source motion, Represents the nonlinear modeling operator based on the sweep-segmentation method at the initial time The wave field value of the earthquake source motion, Indicates the expansion letter; Will Expand by 2 step-by-step integration: (4)， represents the value of the Lagrangian operator associated with the wave equation at time 0, represents the value of the Lagrangian operator associated with the wave equation at time T, for The wave field value of the earthquake source motion based on the nonlinear modeling operator of the sweep-segmentation method at each moment; According to formula (3) and formula (4), the augmented function is calculated The derivative of the velocity model parameter m is: (5)， is the adjoint state equation, expressed as: （6）， represents an inverse time-varying spatial convolution operator that depends on the spatial sampling of the observed common shot gathers.

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