Geometric condition constrained residual neural operator seismic base level reconstruction method and system

Abstract

The application discloses a kind of geometric condition constrained residual neural operator seismic datum plane reconstruction method and system, it is related to seismic exploration technical field.The method is that surface wave form is coded as path representation with acquisition geometry, physical initial record is coded as priori representation with target geometry, simultaneously with spectral domain medium encoder extraction background velocity field long-range medium information;Fusion three kinds of representation, extract target condition representation;With target condition representation, time position code and initial amplitude input coordinate query decoder, obtain correction residual;Apply energy gate, common bias removal, transverse low frequency suppression and amplitude limiting, constrained residual is superimposed to physical initial record, on the basis of retaining the main kinematic structure of physical initial record, with continuous target geometry and time coordinate query correction residual, to improve the applicability to different observation system scale and different virtual datum plane.

Description

Technical Field

[0001] This invention relates to the field of seismic exploration technology, and in particular to a method and system for reconstructing seismic reference surfaces using geometrically constrained residual neural operators. Background Technology

[0002] Seismic reference surface reconstruction is used to convert near-surface shot gather records into virtual observation records on a specified subsurface interface. This processing reduces the impact of topographic relief, low-velocity zones, and irregular acquisition geometry in subsequent migrations, velocity analyses, and inversions. In actual operations, the number of surface shot points, receiver points, and virtual target points frequently varies, accompanied by gaps, bad channels, sampling scale differences, and background velocity errors. This means that the mapping from surface records to target records is simultaneously controlled by wavefield, medium, and geometric conditions.

[0003] Existing deterministic continuation techniques can provide virtual records with basic travel time structures using propagation equations or Kirchhoff integrals. However, when the background velocity field is smooth, the observation aperture is limited, or the near-surface is complex, phase deviations, amplitude imbalances, and missing diffraction and scattering details may still exist in the results. If numerical simulation accuracy is increased indiscriminately, computational and storage costs grow rapidly with grid size, shot count, and target query count. Directly using convolutional networks to generate fixed-size output images from fixed-size input images typically embeds a set of acquisition geometry and target reference surfaces into the network structure. When the virtual target point position changes, the number of traces changes, or the target interface fluctuates, the input and output need to be rearranged, or even the model needs to be retrained. Pure generative networks also need to simultaneously recover the master travel time skeleton and detail differences, which can easily lead to non-existent events or damage to existing physical results when the training sample coverage is insufficient.

[0004] Therefore, a technical solution is needed that takes the deterministic continuation results as a priori and can query the surface waveform, background velocity field, input geometry, target geometry and time coordinates as continuous conditions, so that the model only corrects the deficiencies of the initial physical record and can adapt to variable length observation systems and different target reference surfaces. Summary of the Invention

[0005] To address the aforementioned issues, this invention discloses a geometrically constrained residual neural operator seismic reference surface reconstruction method and system. The method first reads the surface record, background velocity field, physical initial record, and surface and target observation geometry, organizing variable-length samples using an effective mask. Second, it encodes the surface waveform and acquisition geometry into trace representations, and encodes the physical initial record and target geometry into prior representations, while simultaneously extracting long-range medium information of the background velocity field using a spectral domain medium encoder. Then, it fuses the three types of representations through a context association network, extracting the target condition representation from the fused context using a target geometry query vector. Next, it queries the decoder with the target condition representation, time position encoding, and initial amplitude input coordinates to obtain the corrected residuals for each target trace and each time sampling point. Finally, it applies energy gating, common bias removal, lateral low-frequency suppression, and amplitude limiting, superimposing the constrained residuals onto the physical initial record. While preserving the main kinematic structure of the physical initial record, it queries the corrected residuals using continuous target geometry and time coordinates, thereby improving the applicability to different observation system scales and different virtual reference surfaces.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] The first aspect of this invention proposes a seismic reference surface reconstruction method using a geometrically constrained residual neural operator, comprising the following steps:

[0008] s1. Acquire multichannel seismic records, background velocity field, target virtual observation system, target virtual traces formed by pairing each source with a target virtual receiver in the system, and their target geometry, as well as the physical initial records corresponding to the target geometry; the target geometry includes the spatial coordinates of the source and the spatial coordinates of the target virtual receiver corresponding to each target virtual trace; the source can be a retained actual source or a set virtual source, and the target virtual receiver is located on the reference surface to be reconstructed.

[0009] s2. One-dimensional temporal features are extracted from the surface trace waveform, and multi-frequency position mapping is performed on the surface trace geometry. The two are fused to obtain the surface trace representation; isomorphic coding is used on the physical initial record and target geometry to obtain the prior trace representation;

[0010] s3. Perform two-dimensional spectral domain convolution and local channel mapping on the background velocity field to extract medium characterizations that represent the overall changes in the propagation medium;

[0011] s4. The medium characterization, surface trace characterization and a priori trace characterization are combined into a context sequence, and the context association network is used to establish a joint conditional characterization between surface observation, physical initial record and background velocity field under the constraint of effective trace mask.

[0012] s5. According to the first The target geometry construction target query representation of the target virtual track is used to extract the target condition representation corresponding to the target virtual track from the joint condition representation through multi-level cross-association operation;

[0013] s6. Perform multi-frequency time-position mapping for each time sampling position, and input the target condition representation, time-position mapping and corresponding initial amplitude into the coordinate query decoder to obtain the correction residual;

[0014] s7. Apply optional energy gating to the correction residual based on the local energy of the physical initial record, and apply at least one of transverse low-frequency component suppression, cross-target channel common bias removal, and bounded amplitude mapping to the correction residual to obtain a constrained residual;

[0015] s8. Combine the constrained residuals with the physical initial record to form the target datum prediction record; during the training phase, construct a joint loss containing at least two of the following: normalized waveform error, trace correlation error, local gain normalization error, normalized spectral morphology error, and temporal gradient error, and update the model parameters based on the target datum label record and the target datum prediction record; during the inference phase, input new surface seismic records, background velocity field, physical initial record, and target geometry, and output the corresponding target datum record.

[0016] A second aspect of the present invention proposes a residual neural operator seismic reference surface reconstruction system for implementing the geometric condition constraints of the method described in the first aspect, comprising: a data acquisition module, a surface trace and a priori trace characterization construction module, a medium characterization extraction module, a context association module, a target condition characterization extraction module, a coordinate time decoding module, a residual constraint processing module, and a target reference surface synthesis and training inference module; each module is configured to perform the corresponding steps of the method described in any one of the first aspects.

[0017] A third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the method described in any of the first aspects.

[0018] The beneficial effects of this invention are that the physical initial record, surface observation, and background velocity field jointly define the generation conditions of the target record: the physical initial record provides the main travel time structure, the surface waveform provides actual observational evidence, and the spectral domain medium characterization provides long-range velocity information involved in the propagation path; after contextual association, the conditions related to the target trace are extracted by the target geometry query, and then the sample-by-sample correction amount is generated by the time coordinate query. Thus, the target geometry determines the spatial location of the required correction, the time encoding determines the temporal location of the correction, and the physical initial amplitude and energy gating limit the local wave field state on which the correction is based, avoiding the decoupling of the target query and the physical reference. Lateral low-frequency suppression, common bias removal, and bounded amplitude mapping further limit the spatial trend, common offset, and amplitude range of the correction amount. Combined with the joint loss of constrained waveform, correlation, local gain, spectral morphology, and temporal gradient, the network can retain existing reflection events while correcting physical approximation errors. The effective trace mask is used for feature association, and the effective trace and time mask jointly limit the loss calculation, reducing the interference of zero-padding positions on the above condition matching, so that the same query and correction mechanism can handle different numbers of traces and sampling lengths. The aforementioned synergistic relationship provides a specific mechanism for improving the identifiability of reflection events under complex structural conditions, and the degree of improvement is evaluated through a control experiment under the same input and imaging conditions. Attached Figure Description

[0019] Figure 1 The Marmousi model provided for this invention;

[0020] Figure 2 This is a reconstructed migration profile of the reference surface obtained using traditional seismic interferometry.

[0021] Figure 3 The offset profile is reconstructed from the reference plane obtained using the trained geometric conditional residual neural operator;

[0022] Figure 4 This is a local comparison between conventional ground seismic imaging in the Inline and Crline directions and the reference plane reconstruction imaging method of this invention: where, Figure 4 (a) in the image represents the conventional ground seismic imaging results in the Inline direction; Figure 4 (b) in the figure represents the reconstruction imaging result of the reference plane by the method of the present invention in the Inline direction; Figure 4 (c) in the figure represents the conventional ground seismic imaging results in the Crline direction; Figure 4 In the figure, (d) represents the Crline direction, which is the result of the reference plane reconstruction imaging method of the present invention. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to represent selected embodiments of the invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] This invention acquires surface seismic records, background velocity fields, physical initial records corresponding to the target virtual observation geometry, and source-detector coordinates. Surface trace waveforms and their acquisition geometry are encoded into surface trace representations, and physical initial records and target geometry are encoded into a priori trace representations. Medium representations are extracted from the background velocity field using a spectral domain medium encoder. These representations are grouped into a context sequence and formed into a joint condition space via a context association network. Representations are queried based on the target virtual trace geometry, and target trace condition representations are extracted from the joint condition space through cross-association. For each time sampling point of the target trace, the target trace condition representation, time position encoding, and physical initial amplitude are input into a coordinate query decoder to obtain corrected residuals. These residuals are then subjected to energy gating, lateral low-frequency suppression, common bias removal, and amplitude limiting before being added to the physical initial records to output the target reference surface seismic record. This invention uses coarse physical extension results as a kinematic framework, allowing the learning model to focus on correcting phase, relative amplitude, and scattering details. Furthermore, different reference surfaces can be continuously queried by changing the target geometry, reducing the extrapolation risk of purely data-driven methods and the dependence on rule-based observation systems.

[0025] In one embodiment, a geometrically constrained residual neural operator seismic reference surface reconstruction method is provided, comprising the following steps:

[0026] s1. Acquire multichannel seismic records, background velocity field, target virtual observation system, target virtual traces formed by pairing seismic sources with target virtual receivers in the system, and their target geometry, as well as the physical initial records corresponding to the target geometry; further includes: reading at least a portion of the sx, sy, gx, gy, selev, gelev, scalco, scalel, dt, and ns fields from the SU or SEG-Y trace header, and restoring spatial coordinates according to coordinate scale factors and elevation scale factors; when the number of surface traces, target traces, or time sampling points is inconsistent between samples, identify the real data with surface effective trace masks, target effective trace masks, and time effective masks, and perform zero-padding batch processing. Specifically, each target virtual trace is determined by a pairing relationship between a set of seismic sources and target virtual receivers, and its target geometry is a six-dimensional vector. The first three terms are the spatial coordinates of the corresponding seismic source, and the last three terms are the spatial coordinates of the virtual receiver point of the target. All coordinates use a unified coordinate system, positive elevation direction, and unit. The coordinate components perpendicular to the profile can be set to fixed values ​​in the two-dimensional model. Coordinates are divided by a unified length scale before being input into the network; in one implementation configuration, this scale is 1000m, and the surface geometry and target geometry use the same scaling.

[0027] The initial physical records are generated by Kirchhoff integral continuation, wave equation continuation, travel-time guided superposition, or other deterministic propagation operators based on the background velocity field, and have the same target trace order, time sampling interval, and number of sampling points as the target reference surface label records; the supervised correction quantity learned by the model Represented as:

[0028] ;

[0029] in, For the first Target reference plane label record, For the corresponding initial physical record, where, For the target virtual channel number, To record time; The difference between the labeled record and the initial physical record is used only as a supervisory correction during training and not as inference input.

[0030] s2. One-dimensional temporal features are extracted from the surface trace waveform, and multi-frequency position mapping is performed on the surface trace geometry. The two are then fused to obtain the surface trace representation. Isomorphic encoding is used for the initial physical record and target geometry to obtain the prior trace representation. Specifically, each waveform is treated as a single-channel time series, sequentially passed through two layers of one-dimensional convolution and GELU activation. Each convolution kernel has a length of 9, with padding lengths of 4 at both ends, maintaining a constant time sampling length. Adaptive average pooling is then performed along the time axis to obtain the fixed-length waveform features for that trace. The waveform features are concatenated with the multi-frequency position mapping results of the trace geometry, and then passed through a three-layer fully connected projection network and layer normalization to obtain the trace representation. The initial physical record uses an encoder with the same structure and independent parameters, and uses the corresponding target geometry; isomorphism does not mean that the two encoders share weights. In one implementation configuration, the number of convolutional feature channels is 48, and the dimension of the output trace representation is 96.

[0031] Multi-frequency location mapping and surface trace representation are respectively expressed as:

[0032] ;

[0033] ;

[0034] in, For geometric coordinate components, The number of frequency bands mapped to the geometric position. The first time series feature extraction result is the first time series feature extraction result. The waveform characteristics of the surface traces are shown, with double vertical lines connecting them to indicate feature splicing. For the first Source-detector geometry of a surface seismic channel. To create a learnable projection network that maps spliced ​​features to surface trace representations. To perform multi-frequency position mapping by concatenating each component of the geometric vector separately, For frequency band number, For the first A surface tunnel characterization, The surface tunnel number. For layer normalization operator; superscript For surface tunnel category labeling, the It is a positive integer, which can be selected based on the scale of position change after coordinate scaling and the validation set error; an implementation configuration takes... Another implementation configuration take Increasing the number of frequency bands will increase the dimension of position coding, but it does not necessarily improve the generalization effect. The number of frequency bands needs to be determined in conjunction with the verification results.

[0035] s3. Perform two-dimensional spectral domain convolution and local channel mapping on the background velocity field to extract medium characterizations that represent the overall changes in the propagation medium.

[0036] Two-dimensional spectral domain convolution performs a Fast Fourier Transform on the background velocity field along both spatial dimensions, implements learnable complex weighted multiplication only on preset low-order spectral modes, and adds it to the pointwise local mapping; the second... The layer medium characteristics are updated as follows:

[0037] ;

[0038] in, and These are the spatial Fourier transform and the inverse Fourier transform, respectively. For spectral mode weights, For local channel mapping, It is a nonlinear function; Specifically refers to the coding layer number of the spectral domain medium. and These are the characteristics of the input and output media of this layer, respectively. This represents a complex weighted multiplication that shrinks by the input channel and accumulates by the output channel at the retained two-dimensional spectral mode positions, while unretained modes are set to zero; the nonlinear processing in the specific implementation includes group normalization and GELU activation, and random deactivation can be added during training; spatial averaging and layer normalization of the last layer features are used to obtain the medium characterization.

[0039] s4. The medium characterization, surface trace characterization and a priori trace characterization are combined into a context sequence, and the context association network is used to establish a joint conditional characterization between surface observations, physical initial records and background velocity field under the constraint of effective trace mask.

[0040] The context association network is a Transformer encoder with key-filled masks, and its mask association output is represented as follows:

[0041] ;

[0042] in, For the associated output of a single attention head, , and These are the query, key, and value matrices obtained by independent linear projection of the context sequence, respectively. The dimension of the key vector for a single attention head, indicated by the superscript. Indicates transpose. Normalize along the bond position; An additive mask that can be broadcast to the attention score matrix is ​​set to zero at the valid channel position and to negative infinity at the zero-padding channel position; the medium representation position is always valid, and the positions of the surface channel and the prior channel are determined according to their respective valid channel masks. The multi-head outputs are concatenated and linearly mapped before participating in context coding.

[0043] s5. According to the first The target geometry construction target query representation of the target virtual track is used to extract the target condition representation corresponding to the target virtual track from the joint condition representation through multi-level cross-association operations; the first The layer target condition representation is updated according to the following formula:

[0044] ;

[0045] ;

[0046] in, Specifically refers to the cross-association layer sequence number. The input of this layer The target trace condition is characterized, and the initial characterization is obtained from the target geometric encoding and projection. This is the joint conditional representation sequence output by the context association network. To perform queries based on target representation, Multi-head cross-attention operation to mask keys and values. This is the intermediate representation after summing and layer normalizing the cross-attention residuals. It is a position-by-position feedforward network; the two residual connections are applied sequentially to the cross-attention and feedforward networks.

[0047] s6. Perform multi-frequency time-position mapping for each time sampling location. Input the target condition representation, time-position mapping, and corresponding initial amplitude into the coordinate query decoder to obtain the correction residual. Specifically, divide the actual time sampling value by the time scale consistent with training to obtain the dimensionless time. and construct ,in, This is the time sampling sequence number. The number of frequency bands mapped to the time location. For time-coding operators, and geometric-coding operators Distinguishing between the two. The timescale in the implementation configuration is 1 second. The final layer target condition representation is broadcast along the time axis, and each time code is broadcast along the target track axis. These are then concatenated with the physical initial amplitude of the same target track at the same time, input into a four-layer fully connected coordinate decoder, and output point by point. The first three layers of the decoder are activated using GELU, and the last layer outputs a scalar correction value; the time encoding only provides the query position and does not change the actual sampling interval of the input record.

[0048] s7. Apply optional energy gating to the correction residual based on the local energy of the physical initial record, and apply at least one of transverse low-frequency component suppression, cross-target channel common bias removal, and bounded amplitude mapping to the correction residual to obtain a constrained residual.

[0049] Local energy gating and constrained residuals, when the three residual constraints are enabled sequentially, are expressed as follows:

[0050] ;

[0051] ;

[0052] in, This is the ratio of the root mean square energy of the sliding window at the initial physical record to the maximum sliding window energy of that channel. The lower limit of the non-zero gate. The gating index, For high-pass processing operators along the target channel direction, local low-pass components are subtracted from the input residuals; For the common bias removal operator, subtract the mean of the effective target channels of its input at the same time; The preset maximum residual amplitude; The energy gating factor is... The original corrected residuals output by the coordinate query decoder. For constrained residuals, superscript Label the constrained category; It is the hyperbolic tangent function. Take when the gate is closed The formula corresponds to the specific case where all three operations—lateral low-frequency suppression, common bias removal, and bounded amplitude mapping—are enabled. When a certain operation is disabled, the corresponding operator is replaced with an identity mapping. When bounded amplitude mapping is disabled, the result of the common bias removal step is directly output. These three operations are independently operable for different errors, not just different in execution order. Lateral low-frequency suppression is used to weaken the slowly changing strip components along the target channel direction; common bias removal is used to eliminate the offset common to all effective target channels at the same time; bounded amplitude mapping is used to limit a few abnormal correction values. The first two operations are enabled when lateral stripes and common bias exist simultaneously; the latter two operations are enabled when common bias is accompanied by local abnormal amplitudes; all three operations are enabled when all three types of problems occur simultaneously. When executed in combination, the order of energy gating, lateral low-frequency suppression, common bias removal, and bounded amplitude mapping is fixed. Each step takes the output of the previous stage as input and excludes zero-padded target channels. Adjacent target channels are sorted by spatial position and then laterally filtered. An implementation configuration uses an energy window with 81 time sampling points, a lateral smoothing window with 81 channels, and... and Enable common bias removal while disabling amplitude limiting; the window is cropped to an available odd length based on the actual recorded length and the effective target number of channels. Whether to enable it and the parameter size are selected based on the waveform fidelity of the validation set and the distribution of abnormal residuals.

[0053] s8. Combine the constrained residuals with the physical initial record to form the target datum prediction record; during the training phase, construct a joint loss containing at least two of the following: normalized waveform error, trace correlation error, local gain normalization error, normalized spectral morphology error, and temporal gradient error, and update the model parameters based on the target datum label record and the target datum prediction record; during the inference phase, input new surface seismic records, background velocity field, physical initial record, and target geometry, and output the corresponding target datum record.

[0054] The constrained residuals and the initial physical record are combined into the target datum prediction record using the following formula:

[0055] ;

[0056] in, For the first The target virtual path in the first The predicted amplitude at each time sampling point, superscript For predicting category labeling, This is the actual time corresponding to the sampling point;

[0057] The joint loss is expressed as:

[0058] ;

[0059] in, This refers to the normalized waveform error, specifically the waveform error after root mean square normalization for each channel. This refers to the correlation error, which is the correlation error after removing the mean for each channel. This refers to the local gain normalization error, which is the shape error after local root-mean-square normalization. This refers to the normalized spectral shape error, i.e., the normalized amplitude spectrum error. This refers to the temporal gradient error, which is the difference in sampling between adjacent time intervals. This refers to the residual amplitude or the transverse low-frequency regularization term. to The weights are non-negative. In one implementation configuration, the various losses are summed using pre-set fixed non-negative weights, and the weights are not dynamically and adaptively updated during training. Specifically, the weights are... , , , , , The last term being zero indicates that this configuration does not apply additional residual regularization loss, but does not mean that the aforementioned output residual constraint is turned off. The local gain normalization window takes 81 time sampling points, and each loss is calculated only for effective target traces and effective time samples. When changing the weights, the errors and imaging performance should be compared on independent validation data before fixing the selected weights and performing corresponding training.

[0060] In one embodiment, a residual neural operator seismic reference surface reconstruction system for implementing the method described in any of the above embodiments with geometrical constraints is provided, comprising:

[0061] The data acquisition module is used to acquire multichannel seismic records collected by the surface observation system, background velocity field, target virtual observation system, target virtual channels formed by pairing each source with the target virtual receiver point in the system and their target geometry, as well as the physical initial records corresponding to the target geometry;

[0062] The surface trace and prior trace representation construction module is used to extract one-dimensional temporal features from the surface trace waveform and perform multi-frequency position mapping on the surface trace geometry, and fuse the two to obtain the surface trace representation; the physical initial record and target geometry are homogeneously encoded to obtain the prior trace representation.

[0063] The medium characterization extraction module is used to perform two-dimensional spectral domain convolution and local channel mapping on the background velocity field to extract medium characterizations that represent the overall changes in the propagation medium.

[0064] The context association module is used to combine medium characterization, surface trace characterization and a priori trace characterization into a context sequence, and to use the context association network to establish a joint conditional characterization between surface observation, physical initial record and background velocity field under the constraint of effective trace mask.

[0065] The target condition characterization extraction module is used to extract the target condition based on the first condition. The target geometry construction target query representation of the target virtual track is used to extract the target condition representation corresponding to the target virtual track from the joint condition representation through multi-level cross-association operation;

[0066] The coordinate time decoding module performs multi-frequency time-position mapping for each time sampling position, and inputs the target condition representation, time-position mapping and the corresponding initial amplitude into the coordinate query decoder to obtain the correction residual.

[0067] The residual constraint processing module is used to perform optional energy gating on the correction residual based on the local energy of the physical initial record, and to perform at least one of transverse low-frequency component suppression, cross-target channel common bias removal and bounded amplitude mapping on the correction residual to obtain constrained residual;

[0068] The target reference surface synthesis and training inference module is used to synthesize the constrained residuals and the physical initial records into a target reference surface prediction record. During the training phase, a joint loss consisting of at least two of the following is constructed based on the target reference surface label record and the target reference surface prediction record: normalized waveform error, trace correlation error, local gain normalization error, normalized spectral morphology error, and temporal gradient error. The model parameters are then updated. During the inference phase, new surface seismic records, background velocity fields, physical initial records, and target geometry are input, and the corresponding target reference surface record is output.

[0069] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the method described in the above embodiments.

[0070] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided by this invention can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc. The geometrically constrained residual neural operator seismic reference surface reconstruction method provided by this invention is applied to... Figure 1 The test data corresponding to the Marmousi velocity model shown. Figure 1 The horizontal axis represents horizontal distance, and the vertical axis represents depth. The diagram reveals a relatively gentle layered structure on the left, a rapidly changing interface and fault in the central region (approximately 12–17 km), and an undulating reflective layer on the right. These areas are used to examine the method's reconstruction performance on target records under conditions of gentle, continuous interfaces, complex tilted structures, and lateral velocity variations.

[0071] The application process includes: organizing the surface record, corresponding acquisition geometry, and background velocity field in the same spatial coordinate system; determining the target virtual receiver points and their source pairing relationships on the reference surface to be reconstructed; preparing the initial physical record according to the target trace sequence; performing amplitude scaling processing on the record consistent with training; and establishing an effective mask according to the actual number of traces and time length. The surface waveform and acquisition geometry, and the initial physical waveform and target geometry are encoded separately, while the spectral domain medium characterization of the background velocity field is extracted. After fusion, the correction residuals are output through target geometry and time-by-time lookup at each sampling point. After processing the selected residual constraints, the correction amount is superimposed on the initial physical record to restore the corresponding amplitude scale, resulting in the target reference surface record for subsequent migration imaging. During training, the joint loss is calculated using the target-labeled record; during testing and inference, no target label is input.

[0072] Figure 2 To reconstruct the offset profile from the reference plane using traditional seismic interferometry methods, Figure 3 This is a reconstructed offset profile based on the reference plane of the method of this invention. The comparative evaluation should use the same test input, target reference plane, offset velocity field, imaging grid, and display range to avoid incorporating differences in imaging parameters or gain settings into the effectiveness of the reconstruction method. The image shows a layered region with a distance of approximately 0–9 km and a depth of approximately 3.5–4.8 km. Figure 2 Strong reflections are visible, along with adjacent wave train tails and interlayer interference. Figure 3 The main reflection bands are easier to trace laterally, and the interlayer separation is relatively clear. Within the complex central region, approximately 12–17 km apart, Figure 2 There is a strong cross-shaped energy near the inclined interface. Figure 3 The trajectory and succession of multiple tilting events are relatively easy to distinguish; however, cross-energy is still visible in some areas, and this does not mean that all imaging artifacts have been eliminated. In the right-side undulating section at a distance of approximately 18–24 km and a depth of approximately 2–4 km, Figure 3 The curvature of the reflection bands is more consistent, and the interlayer wave trains are easier to separate. The above comparison mainly supports qualitative improvements in the identifiability and continuity of the reflection structure, rather than directly equating image grayscale differences with quantitative improvements in signal-to-noise ratio.

[0073] For quantitative evaluation, the normalized waveform error, trace correlation error, and normalized spectral morphology error of the two methods should be calculated separately using the same label records within the same effective target trace and time sample range. If there is another reference imaging profile, image error and reflection structure consistency can be evaluated within the same spatial window. To distinguish between the synergistic effect of modules and the contribution of a single module, ablation comparisons can be performed with medium conditions, target geometric queries, or residual constraints turned off under the same training partition and imaging parameters.

[0074] In practical applications of 3D DAS-VSP data, the surface observations and virtual target receiver positions are first organized by shot number, receiver trace number, and spatial coordinates, unifying coordinates, elevations, time start points, sampling intervals, and amplitude processing conventions. A mask is then created using actual valid records to maintain trace sequence correspondence between the target geometry, initial physical records, and network output. The data is input into the trained network, and constrained correction residuals are obtained through geometric condition queries and time coordinate decoding. These residuals are then synthesized with the initial physical records to form the target reference surface record. Subsequently, migration imaging is performed on the reconstructed record, extracting local profiles in the Inline and Crline directions from the same location and comparing them with conventional ground seismic imaging results. For comparisons in the same direction, consistent coordinate ranges, display polarities, and gain settings should be used.

[0075] Figure 4 (a) and (b) show the results of conventional ground seismic imaging in the inline direction and the baseline reconstruction imaging results obtained using the method of this invention, respectively. The local depth shown in the figures is approximately 4.5–6.0 km. The area marked by the blue box, with a distance of approximately 1.5–4.2 km and a depth of approximately 5.1–5.3 km, is... Figure 4 The reflected wave group in (a) exhibits segmentation and local misalignment along the transverse direction. Figure 4 The corresponding reflection zone in (b) can be continuously tracked over a longer distance, and the relationship between the local bending morphology and the changes in adjacent strata is easier to identify. This performance reflects the improvement in the continuity of reflection events between target traces, and does not take the increase in the amplitude of a single reflection as the basis for the effect. Figure 4 In the diagram, (c) and (d) show the corresponding results in the Crline direction, with a depth of approximately 2.5–3.5 km. The blue box is located at a distance of approximately 1.2–2.0 km and a depth of approximately 2.6–2.8 km. Figure 4 (c) Shallow weak events are difficult to track continuously and are adjacent to strong reflected wave trains. Figure 4 Within the middle (d) frame, relatively continuous changes in weak reflections can be identified, and the separation between weak events and adjacent strong reflections is easier to discern. The two sets of figures demonstrate that the method of this invention improves the traceability of reflection events in different directions within the actual data window shown; however, its applicability is still affected by the acquisition aperture, background velocity accuracy, and training sample coverage, and cannot be extrapolated from local comparisons to achieve the same improvement across all depths in the entire region.

[0076] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A seismic reference surface reconstruction method using geometrically constrained residual neural operators, characterized in that, Includes the following steps: s1. Acquire multichannel seismic records, background velocity field, target virtual observation system, target virtual channels formed by pairing each seismic source with the target virtual receiver point in the system and their target geometry, and physical initial records corresponding to the target geometry; s2. One-dimensional temporal features are extracted from the surface trace waveform, and multi-frequency position mapping is performed on the surface trace geometry. The two are fused to obtain the surface trace representation; isomorphic coding is used on the physical initial record and target geometry to obtain the prior trace representation; s3. Perform two-dimensional spectral domain convolution and local channel mapping on the background velocity field to extract medium characterizations that represent the overall changes in the propagation medium; s4. The medium characterization, surface trace characterization and a priori trace characterization are combined into a context sequence, and the context association network is used to establish a joint conditional characterization between surface observation, physical initial record and background velocity field under the constraint of effective trace mask. s5. According to the first The target geometry construction target query representation of the target virtual track is used to extract the target condition representation corresponding to the target virtual track from the joint condition representation through multi-level cross-association operation; s6. Perform multi-frequency time-position mapping for each time sampling position, and input the target condition representation, time-position mapping and corresponding initial amplitude into the coordinate query decoder to obtain the correction residual; s7. Apply optional energy gating to the correction residual based on the local energy of the physical initial record, and apply at least one of transverse low-frequency component suppression, cross-target channel common bias removal, and bounded amplitude mapping to the correction residual to obtain a constrained residual; s8. Combine the constrained residuals with the physical initial record to form the target datum prediction record; During the training phase, a joint loss consisting of at least two of the following is constructed based on the target reference surface label record and the target reference surface prediction record: normalized waveform error, trace correlation error, local gain normalization error, normalized spectral morphology error, and temporal gradient error. The model parameters are then updated. During the inference phase, new surface seismic records, background velocity fields, physical initial records, and target geometry are input, and the corresponding target reference surface record is output.

2. The geometrically constrained residual neural operator seismic reference surface reconstruction method as described in claim 1, characterized in that, Step s1 further includes: reading at least a portion of the sx, sy, gx, gy, selev, gelev, scalco, scalel, dt, and ns fields from the SU or SEG-Y trace header, and restoring the spatial coordinates according to the coordinate scale factor and the elevation scale factor; when the number of surface traces, target traces, or time sampling points are inconsistent between samples, the real data is identified by the surface effective trace mask, the target effective trace mask, and the time effective mask, and zero-padding batch processing is performed. The initial physical records are generated by Kirchhoff integral continuation, wave equation continuation, travel-time guided superposition, or other deterministic propagation operators based on the background velocity field, and have the same target trace order, time sampling interval, and number of sampling points as the target reference surface label records; the supervised correction quantity learned by the model Represented as: ； in, For the first Target reference plane label record, For the corresponding initial physical record, For the target virtual path number, To record time; This is the difference between the tag record and the initial physical record.

3. The geometrically constrained residual neural operator seismic reference surface reconstruction method as described in claim 2, characterized in that, In step s2, the multi-frequency location mapping and surface trace representation are respectively expressed as: ； ； in, For geometric coordinate components, The number of frequency bands mapped to the geometric position. The first time series feature extraction result is the first time series feature extraction result. The surface waveform features are represented by double vertical lines, indicating feature splicing. For the first Source-detector geometry of a surface seismic channel. To create a learnable projection network that maps spliced ​​features to surface trace representations. To perform multi-frequency position mapping by concatenating each component of the geometric vector separately, For frequency band number, For the first A surface tunnel characterization, The surface tunnel number. For layer normalization operator; superscript Mark the surface passage category.

4. The geometrically constrained residual neural operator seismic reference surface reconstruction method as described in claim 3, characterized in that, In step s3, the two-dimensional spectral domain convolution performs a fast Fourier transform on the background velocity field along both spatial dimensions, implements learnable complex weight multiplication only on preset low-order spectral modes, and adds it to the pointwise local mapping; The layer medium characteristics are updated as follows: ； in, and These are the spatial Fourier transform and the inverse Fourier transform, respectively. For spectral mode weights, For local channel mapping, It is a nonlinear function; Specifically refers to the coding layer number of the spectral domain medium. and These are the characteristics of the input and output media of this layer, respectively. This represents a complex weighted multiplication that contracts by input channel and accumulates by output channel at the retained two-dimensional spectral mode positions, while unretained modes are set to zero; The medium characterization is obtained by spatial averaging and layer normalization of the characteristics of the last layer.

5. The seismic reference surface reconstruction method with geometrically constrained residual neural operators as described in claim 4, characterized in that, In step s4, the context association network is a Transformer encoder with key-filled masks, and its mask association output is represented as follows: ； in, For the associated output of a single attention head, , and These are the query, key, and value matrices obtained by independent linear projection of the context sequence, respectively. The dimension of the key vector for a single attention head, indicated by the superscript. Indicates transpose. Normalize along the bond position; It is an additive mask that can be broadcast to the attention score matrix, with zeros at the valid channel positions and negative infinity at the zero-padding channel positions.

6. The geometrically constrained residual neural operator seismic reference surface reconstruction method as described in claim 5, characterized in that, In step s5, the first The layer target condition representation is updated according to the following formula: ； ； in, Specifically refers to the cross-association layer sequence number. The input of this layer The target trace condition is characterized, and the initial characterization is obtained from the target geometric encoding and projection. This is the joint conditional representation sequence output by the context association network. To perform queries based on target representation, Multi-head cross-attention operation to mask keys and values. This is the intermediate representation after summing and layer normalizing the cross-attention residuals. It is a position-by-position feedforward network; the two residual connections are applied sequentially to the cross-attention and feedforward networks.

7. The seismic reference surface reconstruction method with geometrically constrained residual neural operators as described in claim 6, characterized in that, In step s7, the local energy gating and constrained residuals are represented as follows when the three residual constraints are enabled sequentially: ； ； in, This is the ratio of the root mean square energy of the sliding window at the initial physical record to the maximum sliding window energy of that channel. The lower limit of the non-zero gate. The gating index, For high-pass processing operators along the target channel direction, local low-pass components are subtracted from the input residuals; For the common bias removal operator, subtract the mean of the effective target channels of its input at the same time; The preset maximum residual amplitude; The energy gating factor is... The original corrected residuals output by the coordinate query decoder. For constrained residuals, superscript Label the constrained category; It is the hyperbolic tangent function. Take when the gate is closed .

8. The seismic reference surface reconstruction method with geometrically constrained residual neural operators as described in claim 7, characterized in that, In step s8, the constrained residuals and the initial physical record are combined into the target datum prediction record using the following formula: ； in, For the first The target virtual path in the first The predicted amplitude at each time sampling point, superscript For predicting category labeling, This is the actual time corresponding to the sampling point; The joint loss is expressed as: ； in, This refers to the normalized waveform error, specifically the waveform error after root mean square normalization for each channel. This refers to the correlation error, which is the correlation error after removing the mean for each channel. This refers to the local gain normalization error, which is the shape error after local root-mean-square normalization. This refers to the normalized spectral shape error, i.e., the normalized amplitude spectrum error. This refers to the temporal gradient error, which is the difference in sampling between adjacent time intervals. This refers to the residual amplitude or the transverse low-frequency regularization term. to The weights are non-negative.

9. A residual neural operator seismic reference surface reconstruction system for implementing the geometric condition constraints of the method according to any one of claims 1 to 8, characterized in that, include: The method comprises a data acquisition module, a surface path and prior path representation construction module, a medium representation extraction module, a context association module, a target condition representation extraction module, a coordinate time decoding module, a residual constraint processing module, and a target reference surface synthesis and training inference module; each module is configured to perform the corresponding steps of the method described in any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method described in any one of claims 1 to 8.

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