A method for joint one-way and multi-way full waveform inversion
Patent Information
- Application Number
- CN202610215621.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2026-02-14
- Publication Date
- 2026-09-29
- Estimated Expiration
- 2046-02-14
AI Technical Summary
[0003]在实际应用中，当初始速度模型与真实地下结构存在较大偏差时，全波形反演容易出现波形匹配困难，反演过程难以稳定收敛，尤其是在多次波发育的情况下，不同阶次多次波在传播路径和反射机制上的复杂性，容易在成像或反演过程中引入串扰伪影，从而降低反演结果的可靠性
本发明，通过在全波形反演过程中将多次波按阶次进行区分，并分别构建对应阶次的多次波全波形反演目标函数，仅对同阶次多次波的模拟记录与观测记录进行匹配，从而有效避免了不同阶次多次波之间的相互串扰，使多次波所包含的复杂传播路径信息能够被有序引入反演过程，提高了多次波全波形反演的稳定性与反演结果的物理一致性。
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Figure CN121831886B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of geological exploration technology, and in particular to a method for combined full waveform inversion of primary and secondary waves. Background Technology
[0002] Full waveform inversion, a high-resolution seismic inversion method based on the wave equation, can comprehensively utilize various waveform information such as amplitude, phase, and travel time in seismic records to achieve a detailed construction of subsurface medium velocity models. Theoretically, full waveform inversion can fully extract all the wave information contained in seismic data, and has significant advantages in seismic imaging and subsurface structure characterization, making it one of the important technical means in the current field of seismic exploration.
[0003] In practical applications, when the initial velocity model deviates significantly from the actual underground structure, full-waveform inversion is prone to waveform matching difficulties, making stable convergence of the inversion process challenging. This is especially true in the presence of multiples, where the complexity of propagation paths and reflection mechanisms of different orders of multiples can easily introduce crosstalk artifacts during imaging or inversion, thereby reducing the reliability of the inversion results. To avoid these problems, existing technologies typically employ a method of pre-removing multiples and using only primary wave data for inversion. However, this approach suffers from insufficient illumination in deep targets or areas with complex geological structures, limiting the accuracy of the underground velocity model construction. Summary of the Invention
[0004] This invention provides a method for joint full waveform inversion of primary and multiple waves. By distinguishing the order of multiple waves and introducing them into the inversion process in an orderly manner, the full waveform inversion of multiple waves and the full waveform inversion of primary waves are progressively combined while avoiding crosstalk between multiple waves of different orders. This improves the stability and convergence of the full waveform inversion process and effectively enhances the construction accuracy of the underground velocity model.
[0005] A method for joint full waveform inversion of primary and multiple waves includes the following steps: S1, In the initial stage of inversion, based on the initial velocity model, a virtual surface source is used to perform numerical simulation on the current velocity model to obtain simulated seismic records of different orders of multiple waves. S2, according to the order of multiple waves in the simulated seismic record, construct the objective function for the full waveform inversion of the corresponding order of multiple waves; S3, calculate the inversion gradient based on the objective function of the multiple full waveform inversion, and perform the multiple full waveform inversion under the condition that only multiples of the same order are matched; S4. Perform the full waveform inversion of each order of multiple waves in descending order, and use the velocity model obtained from the full waveform inversion of the previous order of multiple waves as the initial model for the full waveform inversion of the next order of multiple waves. S5. After completing the full waveform inversion of each order of multiple waves, the obtained velocity model is used as the initial model for the full waveform inversion of the first wave, and the full waveform inversion of the first wave is performed. S6. When the inversion process meets the preset convergence condition, the final underground velocity model is output, and the combined full waveform inversion results of the primary wave and multiple waves are obtained.
[0006] Optionally, S1 includes: S11. Under the current velocity model conditions, the previous order multiple wave observation record is selected as the virtual surface source input, and the multiple wave observation record is sequentially loaded to the spatial position of the corresponding receiver point to construct the virtual source conditions for multiple wave numerical simulation. S12, under the virtual source conditions, based on the wave field propagation operator corresponding to the current velocity model, the wave field excited by the virtual surface source is forward extended to simulate the propagation process of multiple wave fields in the underground medium. S13, at the receiver location, the simulated multiple wave field is received to obtain the next-order multiple simulated seismic record under the constraints of the current velocity model, represented as: ; in, This is a detector constraint operator, which is related to the spatial location of the detector point. for Observational records of first-order multiples (zero-order multiples are considered as first-order multiples). For the wave field propagation operator under the current velocity model, for Multiple-wave simulation data.
[0007] Optionally, S2 includes: S21, the obtained multi-wave simulated seismic records are distinguished according to the multi-wave order, and the observation records of the corresponding order of multi-wave are determined. S22, For each order of multiples, a corresponding objective function for the full waveform inversion of multiples is constructed to measure the difference between the simulated data and the observed multiples data of that order. S23, during the inversion process, only the simulated records of the same order multiple waves are matched with the corresponding observation records.
[0008] Optionally, the objective function for the multiple-wave full-wave inversion is expressed as: ; in, For the first The objective function for full waveform inversion corresponding to the first-order multiple wave. This represents the L2 norm.
[0009] Optionally, S3 includes: S31, Calculate the inversion gradient of the objective function for the multiple full waveform inversion with respect to the current velocity model; S32, in the process of inverting gradient calculation, only the first... The simulated and observed records corresponding to the first multiple wave were used as matching objects; S33, Update the current velocity model based on the inverted gradient, completing the update for the first... Full waveform inversion iteration of multiple waves.
[0010] Optionally, the inversion gradient is represented as: ; in, For the first The objective function for the full waveform inversion of the first-order multiple wave with respect to the current velocity model gradient, For the first The partial derivatives of the objective function for full waveform inversion of the first-order multiple wave with respect to the current velocity model. For the first residual information of multiple wave data, For the first The first-order multiple-wave simulation records the sensitivity terms to the current velocity model. Indicates cross-correlation calculation, This represents the wave field backpropagation operator.
[0011] Optionally, S4 includes: S41, using the initial underground velocity model as the starting model for the full waveform inversion of multiples, the highest-order multiples participating in the full waveform inversion of multiples are determined. S42, with the objective function of the current order to be inverted as the constraint, call the corresponding full waveform inversion update operator to update the current velocity model and obtain the velocity model after the full waveform inversion of the current order; S43, After completing the full waveform inversion of the current order multiple, the obtained velocity model is used as the initial model for the next adjacent low-order multiple full waveform inversion, and the full waveform inversion of each order of multiple is executed in order from high to low. S44, after completing the inversion of all wave orders, outputs the subsurface velocity model that completes the full waveform inversion of all wave orders, expressed as: ; in, To complete the subsurface velocity model for full waveform inversion of all orders of multiple waves, For the initial underground velocity model, , , They are respectively the 1st, 2nd, The objective function corresponding to the first-order multiple wave is the full waveform inversion update operator with constraints.
[0012] Optionally, S5 includes: S51. After completing the full waveform inversion of each order of multiple waves, the obtained underground velocity model is used as the initial model for the full waveform inversion of the first wave, and the source wavelet is determined as the forward modeling input. S52, the source wavelet is subjected to wavefield extension, and a detector constraint is applied to extract the wavefield response, resulting in a primary wave simulated seismic record, expressed as: ; in, For the source wavelet, This is a simulated earthquake record for a single wave. S53, Match the simulated first-wave seismic record with the observed first-wave data to construct the objective function for the full waveform inversion of the first wave; S54. Calculate the inversion gradient based on the objective function of the first wave full waveform inversion, and iteratively update the underground velocity model to complete the first wave full waveform inversion.
[0013] Optionally, the convergence condition of the multi-wave full waveform inversion objective function is that when the change in the multi-wave full waveform inversion objective function is less than the multi-wave threshold in two adjacent iterations, the inversion process is determined to have reached the convergence condition, or when the number of inversion iterations of the multi-wave full waveform inversion objective function reaches the maximum number of multi-wave iterations, the inversion process is terminated. The convergence condition of the primary wave full waveform inversion objective function is as follows: when the change of the primary wave full waveform inversion objective function is less than the primary wave threshold in two adjacent iterations, the inversion process is determined to have reached the convergence condition; or when the number of inversion iterations of the primary wave full waveform inversion objective function reaches the maximum number of primary wave iterations, the inversion process is terminated.
[0014] The beneficial effects of this invention are: This invention distinguishes multiples by order during the full waveform inversion process and constructs corresponding objective functions for full waveform inversion of multiples of the same order. It only matches the simulated records and observation records of multiples of the same order, thereby effectively avoiding crosstalk between multiples of different orders. This allows the complex propagation path information contained in the multiples to be introduced into the inversion process in an orderly manner, improving the stability of full waveform inversion of multiples and the physical consistency of the inversion results.
[0015] This invention performs full waveform inversion of multiple waves sequentially from high to low order, and uses the velocity model obtained from the previous order multiple wave inversion as the initial model for the next order multiple wave inversion. This gradually guides the velocity model to approximate the actual underground structure, thereby fully utilizing the advantages of higher-order multiple waves, which have a wider illumination range and higher sensitivity to deep and complex structural areas. This effectively improves the problem of insufficient illumination of primary waves in deep targets and complex geological conditions, and enhances the construction accuracy of the underground velocity model.
[0016] This invention uses the velocity model obtained after completing the full waveform inversion of each order of multiple waves as the initial model for the full waveform inversion of the first wave. This allows the first wave inversion to be carried out under more reasonable initial model conditions, reducing the dependence of the full waveform inversion on the accuracy of the initial velocity model, reducing the risk of getting trapped in local minima, and improving the convergence and stability of the inversion process. As a result, a more reliable subsurface velocity model is obtained, providing a high-quality basic model for subsequent seismic imaging and geological interpretation. Attached Figure Description
[0017] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0018] Figure 1 This is a schematic diagram of the inversion method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the actual parameter model of an embodiment of the present invention; Figure 3 This is a schematic diagram of the initial parameter model of an embodiment of the present invention; Figure 4 This is a schematic diagram of the parameter model for the traditional first-wave full waveform inversion result according to an embodiment of the present invention; Figure 5 This is a schematic diagram of the parameter model for the second-order multiple full waveform inversion result according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the parameter model for the second-order and first-order multiple full waveform inversion results according to an embodiment of the present invention; Figure 7 This is a schematic diagram of the parameter model of the joint full waveform inversion result of the primary wave and multiple waves according to an embodiment of the present invention; Figure 8 This is a schematic diagram showing the single-track speed comparison results of an embodiment of the present invention. Detailed Implementation
[0019] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. Those skilled in the art may employ other alternative methods to implement some well-known technologies; moreover, the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.
[0020] like Figures 1-8 As shown, a method for joint full waveform inversion of primary and multiple waves includes the following steps: S1, In the initial stage of inversion, based on the initial velocity model, a virtual surface source is used to perform numerical simulation on the current velocity model to obtain simulated seismic records of different orders of multiple waves. S2, according to the order of multiple waves in the simulated seismic record, construct the objective function for the full waveform inversion of the corresponding order of multiple waves; S3, calculate the inversion gradient based on the objective function of the multiple full waveform inversion, and perform the multiple full waveform inversion under the condition that only multiples of the same order are matched; S4. Perform the full waveform inversion of each order of multiple waves in descending order, and use the velocity model obtained from the full waveform inversion of the previous order of multiple waves as the initial model for the full waveform inversion of the next order of multiple waves. S5. After completing the full waveform inversion of each order of multiple waves, the obtained velocity model is used as the initial model for the full waveform inversion of the first wave, and the full waveform inversion of the first wave is performed. S6. When the inversion process meets the preset convergence condition, the final underground velocity model is output, and the combined full waveform inversion results of the primary wave and multiple waves are obtained.
[0021] S1 includes: S11. Under the current velocity model conditions, the previous order multiple wave observation record is selected as the virtual surface source input, and the multiple wave observation record is sequentially loaded to the spatial position of the corresponding receiver point to construct the virtual source conditions for multiple wave numerical simulation. S12, under the condition of virtual seismic source, based on the wave field propagation operator corresponding to the current velocity model, the wave field excited by the virtual surface source is positively extended to simulate the propagation process of multiple wave fields in the underground medium. S13, at the receiver location, the simulated multiple wave field is received to obtain the next-order multiple simulated seismic record under the constraints of the current velocity model, represented as: ; in, This is a detector constraint operator, which is related to the spatial location of the detector point. for Observational records of first-order multiples (zero-order multiples are considered as first-order multiples). For the wave field propagation operator under the current velocity model, for Multiple-wave simulation data.
[0022] S2 includes: S21, the obtained multi-wave simulated seismic records are distinguished according to the multi-wave order, and the observation records of the corresponding order of multi-wave are determined. S22, For each order of multiples, a corresponding objective function for the full waveform inversion of multiples is constructed to measure the difference between the simulated data and the observed multiples data of that order. S23, during the inversion process, only the simulated records of the same order multiple waves are matched with the corresponding observation records.
[0023] The objective function for multi-wave full waveform inversion is expressed as: ; in, For the first The objective function for full waveform inversion corresponding to the first-order multiple wave. This represents the L2 norm.
[0024] S3 includes: S31, Calculate the inversion gradient of the objective function for the multiple wave full waveform inversion with respect to the current velocity model, used to characterize the effect of the current velocity model on the first wave. Sensitivity to mismatch in multiple wavelet data; S32, in the process of inverting gradient calculation, only the first... The simulated and observed records corresponding to the first multiple wave were used as matching objects; S33, update the current velocity model based on the inverted gradient, completing the update for the first... Full waveform inversion iteration of multiple waves.
[0025] The inversion gradient is expressed as: ; in, For the first The objective function for the full waveform inversion of the first-order multiple wave with respect to the current velocity model gradient, For the first The partial derivatives of the objective function for full waveform inversion of the first-order multiple wave with respect to the current velocity model. For the first residual information of multiple wave data, For the first The first-order multiple-wave simulation records the sensitivity terms to the current velocity model. Indicates cross-correlation calculation, This represents the wave field backpropagation operator.
[0026] S4 includes: S41, using the initial underground velocity model as the starting model for the full waveform inversion of multiples, the highest-order multiples participating in the full waveform inversion of multiples are determined. S42, with the objective function of the current order to be inverted as the constraint, call the corresponding full waveform inversion update operator to update the current velocity model and obtain the velocity model after the full waveform inversion of the current order; S43, After completing the full waveform inversion of the current order multiple, the obtained velocity model is used as the initial model for the next adjacent low-order multiple full waveform inversion, and the full waveform inversion of each order of multiple is executed in order from high to low. S44, after completing the inversion of all wave orders, outputs the subsurface velocity model that completes the full waveform inversion of all wave orders, expressed as: ; in, To complete the subsurface velocity model for full waveform inversion of all orders of multiple waves, For the initial underground velocity model, , , They are respectively the 1st, 2nd, The objective function corresponding to the first-order multiple wave is the full waveform inversion update operator with constraints.
[0027] S5 includes: S51. After completing the full waveform inversion of each order of multiple waves, the obtained underground velocity model is used as the initial model for the full waveform inversion of the first wave, and the source wavelet is determined as the forward modeling input. S52, wavefield extension is performed on the source wavelet, and a detector constraint is applied to extract the wavefield response, resulting in a primary wave simulated seismic record, expressed as: ; in, For the source wavelet, This is a simulated earthquake record for a single wave. S53, matching the simulated first-wave seismic record with the observed first-wave data to construct the objective function for the full waveform inversion of the first wave; S54 calculates the inversion gradient based on the objective function of the first wave full waveform inversion and iteratively updates the underground velocity model to complete the first wave full waveform inversion.
[0028] The convergence condition of the objective function of the multi-wave full waveform inversion is that when the change of the objective function of the multi-wave full waveform inversion in two adjacent iterations is less than the multi-wave threshold, the inversion process is determined to have reached the convergence condition, or when the number of inversion iterations of the objective function of the multi-wave full waveform inversion reaches the maximum number of iterations of the multi-wave, the inversion process is terminated. The convergence condition of the objective function for the first-wave full waveform inversion is that the change in the objective function for the first-wave full waveform inversion is less than the first-wave threshold in two adjacent iterations, at which point the inversion process is considered to have reached the convergence condition, or the inversion process is terminated when the number of inversion iterations of the objective function for the first-wave full waveform inversion reaches the maximum number of iterations for the first wave.
[0029] The specific implementation method is as follows: To verify the superiority of the method of the present invention over the traditional first-wave full-wave inversion and its applicability under complex structural conditions, the present invention was applied to, for example... Figure 2 In the complex underground structural model shown, a mobile observation system with incomplete primary wave illumination was adopted. 117 seismic sources were set up for excitation and 201 receiver points were set up for reception. No seismic sources were deployed within a lateral range of 2 to 4 kilometers, thus artificially limiting the illumination range of the primary reflected waves and forming a distinct area of weak primary wave illumination.
[0030] Under the aforementioned geological conditions and observation system, the embodiment first uses the traditional first-wave full waveform inversion method to perform... Figure 3 The initial velocity model shown is subjected to 30 iterations of inversion to obtain... Figure 4 The results of the full waveform inversion for the first wave are shown. Due to the limitations of the first wave illumination, the overall error of the inversion results is relatively large, with local velocity update errors and unclear thin-layer and fault interfaces. Especially in the weak illumination region of 3 to 4 kilometers, the velocity model can hardly be updated effectively.
[0031] To address the aforementioned issues, this invention incorporates the full waveform inversion of multiples into the traditional full waveform inversion process for first-order multiples by constructing objective functions corresponding to different orders of multiples. In this embodiment, starting with the full waveform inversion of second-order multiples, a first-order multiple is used as a virtual surface source, and simulated data of second-order multiples are obtained based on wavefield propagation operators. The objective function is defined in the least squares sense, with the criterion being minimizing the L2 error between the observed and simulated data of second-order multiples. To ensure consistency in the number of model updates during the inversion process, each inversion stage undergoes 10 iterations, for a total of 30 updates. The full waveform inversion results of second-order multiples are shown below. Figure 5 As shown, the inversion effect is significantly improved in the 3 to 4 km range.
[0032] The inversion results of the second-order multiple full waveform are used as the initial model for the inversion of the first-order multiple full waveform. An objective function corresponding to the first-order multiple is constructed and iterated, yielding the following inversion results: Figure 6As shown, the accuracy of velocity modeling is further improved. Finally, the full waveform inversion results of the multiple waves are used as the initial model for the full waveform inversion of the primary wave for iteration, obtaining the joint full waveform inversion results of the primary and multiple waves (e.g., Figure 7 (As shown). Compared with the results obtained by the traditional full-waveform inversion method using only the first wave, the joint full-waveform inversion method proposed in this invention can effectively compensate for the insufficient illumination of the first wave and provide richer reflection information constraints for the inversion process. Even with a relatively small number of iterations, the obtained velocity model is significantly closer to the true velocity model, reducing the dependence of the inversion results on the initial model to a certain extent.
[0033] To further demonstrate the advantages of the present invention, Figure 8 This paper presents a comparison of single-channel velocities obtained through traditional primary wave full waveform inversion and joint full waveform inversion. The velocity versus depth curves at lateral positions of 1 km, 2 km, and 3 km show that, under different primary wave illumination conditions, the joint inversion method generally provides more accurate velocity updates, and the results show significantly higher agreement with the actual velocity model.
[0034] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.
[0035] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A method for joint full-waveform inversion of primary and multiple waves, characterized in that, Includes the following steps: S1, In the initial stage of inversion, based on the initial velocity model, a virtual surface source is used to perform numerical simulation on the current velocity model to obtain simulated seismic records of different orders of multiple waves. S2, according to the order of multiple waves in the simulated seismic record, construct the objective function for the full waveform inversion of the corresponding order of multiple waves; S3, calculate the inversion gradient based on the objective function of the multiple full waveform inversion, and perform the multiple full waveform inversion under the condition that only multiples of the same order are matched; S4, following the order of the multiple wavelets from high to low, sequentially perform the full waveform inversion of each order of multiple wavelets, and use the velocity model obtained from the previous order of the full waveform inversion of the multiple wavelets as the initial model for the next order of the full waveform inversion of the multiple wavelets. Specifically, this includes: S41, using the initial underground velocity model as the starting model for the full waveform inversion of multiples, the highest-order multiples participating in the full waveform inversion of multiples are determined. S42, with the objective function of the current order to be inverted as the constraint, call the corresponding full waveform inversion update operator to update the current velocity model and obtain the velocity model after the full waveform inversion of the current order; S43, After completing the full waveform inversion of the current order multiple, the obtained velocity model is used as the initial model for the next adjacent low-order multiple full waveform inversion, and the full waveform inversion of each order of multiple is executed in order from high to low. S44, after completing the inversion of all wave orders, outputs the subsurface velocity model that completes the full waveform inversion of all wave orders, expressed as: ； in, To complete the subsurface velocity model for full waveform inversion of all orders of multiple waves, For the initial underground velocity model, , , They are respectively the 1st, 2nd, The objective function corresponding to the first-order multiple wave is the full-waveform inversion update operator with constraints; S5. After completing the full waveform inversion of each order of multiple waves, the obtained velocity model is used as the initial model for the full waveform inversion of the first wave, and the full waveform inversion of the first wave is performed. S6. When the inversion process meets the preset convergence condition, the final underground velocity model is output, and the combined full waveform inversion results of the primary wave and multiple waves are obtained.
2. The method for joint full waveform inversion of primary and multiple waves according to claim 1, characterized in that, S1 includes: S11. Under the current velocity model conditions, the previous order multiple wave observation record is selected as the virtual surface source input, and the multiple wave observation record is sequentially loaded to the spatial position of the corresponding receiver point to construct the virtual source conditions for multiple wave numerical simulation. S12, under the virtual source conditions, based on the wave field propagation operator corresponding to the current velocity model, the wave field excited by the virtual surface source is forward extended to simulate the propagation process of multiple wave fields in the underground medium. S13, at the receiver location, the simulated multiple wave field is received to obtain the next-order multiple simulated seismic record under the constraints of the current velocity model, represented as: ； in, For the detector constraint operator, for Multiple wave observation records, For the wave field propagation operator under the current velocity model, for Multiple-wave simulation data.
3. The method for joint full waveform inversion of primary and multiple waves according to claim 2, characterized in that, S2 includes: S21, the obtained multi-wave simulated seismic records are distinguished according to the multi-wave order, and the observation records of the corresponding order of multi-wave are determined. S22, For each order of multiples, a corresponding objective function for the full waveform inversion of multiples is constructed to measure the difference between the simulated data and the observed multiples data of that order. S23, during the inversion process, only the simulated records of the same order multiple waves are matched with the corresponding observation records.
4. The method for joint full waveform inversion of primary and multiple waves according to claim 3, characterized in that, The objective function for the multiple wave full waveform inversion is expressed as: ； in, For the first The objective function for full waveform inversion corresponding to the first-order multiple wave. This represents the L2 norm.
5. The method for joint full waveform inversion of primary and multiple waves according to claim 4, characterized in that, S3 includes: S31, Calculate the inversion gradient of the objective function for the multiple full waveform inversion with respect to the current velocity model; S32, in the process of inverting gradient calculation, only the first... The simulated and observed records corresponding to the first multiple wave were used as matching objects; S33, Update the current velocity model based on the inverted gradient, completing the update for the first... Full waveform inversion iteration of multiple order waves.
6. The method for joint full waveform inversion of primary and multiple waves according to claim 5, characterized in that, The inversion gradient is expressed as: ； in, For the first The objective function for the full waveform inversion of the first-order multiple wave with respect to the current velocity model gradient, For the first The partial derivatives of the objective function for full waveform inversion of the first-order multiple wave with respect to the current velocity model. For the first Data residuals of multiple waves For the first The first-order multiple-wave simulation records the sensitivity terms to the current velocity model. Indicates cross-correlation calculation, This represents the wave field backpropagation operator.
7. The method for joint full waveform inversion of primary and multiple waves according to claim 6, characterized in that, S5 includes: S51. After completing the full waveform inversion of each order of multiple waves, the obtained underground velocity model is used as the initial model for the full waveform inversion of the first wave, and the source wavelet is determined as the forward modeling input. S52, the source wavelet is subjected to wavefield extension, and a detector constraint is applied to extract the wavefield response, resulting in a primary wave simulated seismic record, expressed as: ； in, For the source wavelet, This is a simulated earthquake record for a single wave. S53, Match the simulated first-wave seismic record with the observed first-wave data to construct the objective function for the full waveform inversion of the first wave; S54. Calculate the inversion gradient based on the objective function of the first wave full waveform inversion, and iteratively update the underground velocity model to complete the first wave full waveform inversion.
8. The method for joint full waveform inversion of primary and multiple waves according to claim 7, characterized in that, The convergence condition of the multi-wave full waveform inversion objective function is as follows: when the change of the multi-wave full waveform inversion objective function in two adjacent iterations is less than the multi-wave threshold, the inversion process is determined to have reached the convergence condition; or when the number of inversion iterations of the multi-wave full waveform inversion objective function reaches the maximum number of multi-wave iterations, the inversion process is terminated. The convergence condition of the primary wave full waveform inversion objective function is as follows: when the change of the primary wave full waveform inversion objective function is less than the primary wave threshold in two adjacent iterations, the inversion process is determined to have reached the convergence condition; or when the number of inversion iterations of the primary wave full waveform inversion objective function reaches the maximum number of primary wave iterations, the inversion process is terminated.