Earthquake common reflection point intelligent superposition imaging method under three-dimensional structure feature constraint
By constructing a three-dimensional structural geometric model and dividing the structural zone, and by employing differentiated processing and adaptive weighting coefficient calculation, the problem of superimposed imaging of common reflection points in areas with large stratum dip angles was solved, thereby improving the signal-to-noise ratio and imaging accuracy and ensuring the accuracy of the imaging results.
Patent Information
- Application Number
- CN202511539782.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-27
- Publication Date
- 2026-01-27
AI Technical Summary
In areas with large stratigraphic dip angles, existing technologies struggle to effectively superimpose common reflection points, causing the interface reflection point positions to deviate from their true locations, reducing lateral resolution. Furthermore, conventional dip angle time difference correction is ineffective, especially in complex geological conditions, where it can easily generate oblique interference and spatial aliasing, affecting processing performance.
By constructing a three-dimensional structural geometric model, the model is divided into a smooth structural zone and abrupt structural zones. Wide azimuth gathers are used to process the smooth zone, and narrow azimuth gathers are used to process the abrupt zone. The weight of the seismic traces is calculated using an adaptive weighting coefficient formula driven by structural features. Finally, data fusion is performed to improve the signal-to-noise ratio of the stacked imaging.
It improves the signal-to-noise ratio and imaging accuracy of seismic co-reflection point stacking imaging in complex tectonic regions, ensuring that the imaging results are more consistent with the real geological features and reducing the impact of oblique interference and spatial aliasing.
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Figure CN121410801A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of seismic exploration technology. More specifically, this invention relates to an intelligent overlay imaging method for seismic common reflection points under three-dimensional structural feature constraints. Background Technology
[0002] Seismic common reflection point stacking is a seismic data processing technique. In the indoor processing stage, multiple overlay records from field observations are processed to extract common reflection points or common center point gathers. These are then subjected to a series of processing steps, including velocity analysis, dynamic and static correction, and horizontal stacking, ultimately resulting in a horizontally stacked profile or corresponding data volume that essentially reflects the subsurface geological morphology. The high-quality horizontally stacked profile obtained is a crucial foundation for seismic tectonic interpretation, velocity spectrum calculation, automatic static correction, and subsequent migration processing.
[0003] The implementation of common reflection point stacking generally involves gather extraction, dynamic correction, and stacking. Specifically, gathers from the same underground reflection point or the same central point are extracted from multiple original records obtained from field observations; these are known as CRP gathers or CMP gathers. To eliminate wave propagation time differences caused by varying source-receiver offsets, dynamic correction adjusts the travel times of each seismic wave to the self-excitation and self-reception times at their common central point, aligning the phase axes of reflected waves from the same reflection point in time, thus creating conditions for in-phase stacking. The amplitudes of all traces within the dynamically corrected common reflection point gathers are then stacked at the same sampling point. Through stacking, the signal is enhanced, while random noise and other interference are suppressed due to incoherence, significantly improving the signal-to-noise ratio and imaging quality of the seismic record.
[0004] In areas with shallow stratigraphic dips and relatively simple geological structures, reflection points below the common midpoint are concentrated, allowing for effective superposition of these reflection points, suppression of interference, and the acquisition of high-quality time profiles. However, in areas with complex geological structures and steep stratigraphic dips, true common reflection points do not exist at the dipping interface. Reflection points excited and received symmetrically about the common midpoint are dispersed within a certain range. Superposition is essentially the superposition of common reflection segments, causing the interface reflection point positions to deviate from their true locations along the downdip direction of the interface. This reduces lateral resolution, and diffracted waves cannot converge, while rotating waves cannot return to their original positions, resulting in interference bands.
[0005] In existing technologies, when the stratigraphic dip angle is large, dip time difference correction is performed on shot-receiver offset seismic records before stacking to eliminate time differences caused by stratigraphic dip in non-zero shot-receiver offset seismic traces, thereby improving the quality of horizontally stacked profiles. However, the effectiveness of dip time difference correction largely depends on the accuracy of the velocity model used, and its correction effect is poor for complex structures, such as steep structures, severe folds, and multi-directional dipping stratigraphic interweaving. Furthermore, conventional dip time difference correction is prone to oblique interference and spatial aliasing when processing areas with low coverage times, affecting the processing results.
[0006] In view of this, there is an urgent need to provide a smart overlay imaging method for seismic common reflection points under the constraint of three-dimensional structural features, so as to improve the quality of horizontal overlay profiles. Summary of the Invention
[0007] To address at least one or more of the technical problems mentioned above, this invention provides an intelligent stacking imaging method for seismic common reflection points under three-dimensional structural feature constraints, comprising: a first step, using a pre-stack time migration profile as input to construct a three-dimensional structural geometry model of the target region, and extracting structural features to generate a structural feature constraint field; a second step, dividing the target region into a structurally gentle region with a dip angle less than a preset threshold and a structurally abrupt region with a dip angle greater than a preset threshold according to the structural feature constraint field, selecting wide azimuth gathers for dynamic correction and stacking in the structurally gentle region to obtain a first stacking result; for the structurally abrupt region, iteratively adjusting the azimuth range and offset range along the structural strike for dynamic correction and stacking, selecting the common reflection point gathers in the azimuth range and offset range with the highest signal-to-noise ratio after stacking as the optimal narrow azimuth gather subset; a third step, calculating the weights of each seismic trace in the optimal narrow azimuth gather subset according to the structural feature-driven adaptive weight coefficient calculation formula, and stacking according to the weights to obtain a second stacking result.
[0008] The formula for calculating the feature-driven adaptive weight coefficients is as follows: Among them, w i Indicates the adaptive weighting coefficient. Represents the curvature gradient, coh i I represents local coherence. norm This indicates the wavefield illumination intensity, and the subscript i indicates the seismic trace number;
[0009] The fourth step involves fusing the first stacking result of the gently sculpted zone and the second stacking result of the abruptly sculpted zone to obtain a stacked image of the seismic common reflection points.
[0010] According to one embodiment of the present invention, the structural features include at least one of tilt angle, azimuth angle, curvature, and coherence.
[0011] According to one embodiment of the present invention, in the second step, the preset threshold for dividing the structurally gentle zone and the structurally abrupt zone is a stratigraphic dip angle of 15°.
[0012] According to one embodiment of the present invention, in the second step, the narrow azimuth angle range is 15° to 30° azimuth angle with the structural orientation; the offset distance range of the iterative adjustment is 1500 to 3000m offset distance.
[0013] According to one embodiment of the present invention, in the second step, the narrow azimuth angle range is an azimuth angle of 20° with the structural orientation; the offset distance range of the iterative adjustment is an offset distance of 1800 to 2500 m.
[0014] According to one embodiment of the present invention, during the iterative adjustment of the azimuth range and offset range, the number of coverage times is not less than the minimum threshold.
[0015] According to one embodiment of the present invention, the minimum threshold is 24 coverage times.
[0016] According to one embodiment of the present invention, during the iterative adjustment of the azimuth range and the offset range, the iterative step size of the azimuth is 2° to 5°, and the iterative compensation of the offset is 50 to 150m.
[0017] According to one embodiment of the present invention, in the process of iteratively adjusting the azimuth range and the offset range, the iterative step size of the azimuth is 3°, and the iterative compensation of the offset is 100m.
[0018] According to one embodiment of the present invention, in the second step, the azimuth range and offset range are iteratively adjusted and the optimal narrow azimuth aggregator subset is selected by a pre-trained neural network model.
[0019] In this invention, differentiated processing based on structural feature constraints is employed, fully considering the impact of complex structures on the presentation of common reflection points, resulting in final imaging that better reflects real geological features. By iteratively selecting the optimal narrow azimuth gather subset with a high signal-to-noise ratio (SNR) as the objective, the SNR of the common reflection point stacked imaging can be improved. The structural feature-driven adaptive weighting coefficients comprehensively consider structural complexity, data quality, and wavefield illumination, thereby adaptively adjusting the contribution of each seismic trace in the stacking, further enhancing the SNR of the common reflection point stacked imaging. By setting two constraints—an azimuth range of ±15° to ±30° along the strike and an offset range of 1500–3000 m—the optimal narrow azimuth gather subset improves its imaging SNR under structural feature constraints. Attached Figure Description
[0020] The above and other objects, features, and advantages of exemplary embodiments of the present invention will become readily apparent upon reading the following detailed description with reference to the accompanying drawings. In the drawings, several embodiments of the invention are illustrated by way of example and not limitation, and like or corresponding reference numerals denote like or corresponding parts, wherein:
[0021] Figure 1 A schematic diagram of the steps of the intelligent superposition imaging method for seismic common reflection points under three-dimensional structural feature constraints is shown. Detailed Implementation
[0022] 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 some, not all, of the embodiments of the present 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.
[0023] It should be understood that the terms "comprising" and "including" as used in the specification and claims of this invention indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.
[0024] It should also be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used in this specification and claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations.
[0025] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
[0026] Figure 1 A schematic diagram of the steps of the intelligent superposition imaging method for seismic common reflection points under three-dimensional structural feature constraints is shown.
[0027] like Figure 1As shown, a smart stacking imaging method for seismic common reflection points under three-dimensional structural feature constraints includes: Step S1: Using a pre-stack time migration profile as input, construct a three-dimensional structural geometric model of the target area and extract structural features to generate a structural feature constraint field; Step S2: Based on the structural feature constraint field, divide the target area into a gently sloping zone with a dip angle less than a preset threshold and a structurally abruptly changed zone with a dip angle greater than a preset threshold. For the gently sloping zone, select wide azimuth gathers for dynamic correction and stacking to obtain a first stacking result; for the structurally abruptly changed zone, iteratively adjust the azimuth range and offset range within a narrow azimuth range along the structural strike for dynamic correction and stacking, selecting the common reflection point gathers within the azimuth range and offset range with the highest signal-to-noise ratio after stacking as the optimal narrow azimuth gather subset; Step S3: Calculate the weights of each seismic trace in the optimal narrow azimuth gather subset according to the structural feature-driven adaptive weight coefficient calculation formula, and stack according to the weights to obtain a second stacking result.
[0028] The formula for calculating the feature-driven adaptive weight coefficients is as follows: Among them, w i Indicates the adaptive weighting coefficient. Represents the curvature gradient, coh i I represents local coherence. norm The value represents the wavefield illumination intensity, and the subscript i represents the seismic trace number; in the fourth step S4, the first stacking result of the gently structural region and the second stacking result of the abruptly structural region are fused to obtain the seismic common reflection point stacking image.
[0029] In this invention, a pre-stack time migration profile refers to a profile formed by first time-migrating each common-migration gather in seismic data processing and then stacking them together. Pre-stack time migration profiles can better preserve amplitude characteristics and eliminate the influence of tectonic morphology on seismic wave propagation time.
[0030] In the first step, horizon and fault interpretation is performed on the pre-stack time migration profile. For example, key seismic reflection horizons are selected for tracking. Faults are identified and interpreted based on features such as discontinuities and phase axis misalignment in the seismic profile. The interpreted horizons and faults are then converted into surfaces in three-dimensional space. The horizon points are interpolated into continuous surfaces using gridding algorithms such as Kriging interpolation and inverse distance weighting. Fault interpretation is then converted into fault surfaces, and the relationship between faults and horizons is established, thus forming a preliminary model.
[0031] The initial model is then discretized into a grid, with each grid point assigned attributes such as layer number and fault identifier. Various attributes, including dip angle, azimuth angle, and curvature, are calculated or labeled on the grid model. Dip angle refers to the dip angle of the layer surface at each grid point, azimuth angle refers to the dip azimuth angle of the layer surface at each grid point, and curvature refers to the Gaussian curvature and mean curvature attributes of the layer surface. Coherence refers to the coherence of the seismic data, which can be calculated on the seismic data volume using a coherence algorithm and then mapped to the grid points, ultimately resulting in a three-dimensional structural geometric model containing layers, faults, and various structural attributes such as dip angle, azimuth angle, curvature, and coherence. Preferably, the structural features include at least one of dip angle, azimuth angle, curvature, and coherence.
[0032] Based on the three-dimensional construction geometric model, construction features are extracted, and the three-dimensional data field formed by integrating the extracted multi-dimensional construction feature parameters is the construction constraint field. Its form is a three-dimensional grid data volume containing multiple feature parameter values for each grid point, which is used to provide spatial constraints for subsequent partitioning and intelligent weighting.
[0033] In the second step, the target region is divided into a region with gentle tectonics and a region with abrupt changes in tectonics based on the structural feature constraint field. For the region with gentle tectonics, a wide azimuth gather is used for conventional processing, while for the region with abrupt changes in tectonics, a narrow azimuth gather is used for iterative optimization of the azimuth and offset range. The optimal subset of narrow azimuth gathers is selected by comparing the signal-to-noise ratio.
[0034] Specifically, the criteria for dividing the target area are set to a preset threshold of dip angle, such as using a dip angle of 15° or 20° as the boundary.
[0035] In gently sloping areas, the dip angle of the strata is less than a preset threshold, the structure is relatively simple, the strata attitude is stable, and the structural deformation is weak. Conventional wide azimuth stacking can be used, such as conventional dynamic correction, static correction, and stacking operations, to fully utilize all-around information and obtain the first stacking result. In this invention, wide azimuth refers to an azimuth range greater than 60°. In this invention, the purpose of dynamic correction is to eliminate the difference in reflected wave propagation time caused by different shot-receiver distances. After correction, the times of the trace records at different shot-receiver distances within the common reflection point gather are converted to the self-excitation and self-reception times at their common midpoint, thereby flattening the phase axis of the reflected waves and preparing for in-phase stacking. Horizontal stacking specifically refers to the process of stacking the dynamically corrected common reflection point gathers or common midpoint gathers according to time sampling points. Its mathematical model is to superimpose the discrete amplitude values of each trace within the same dynamically corrected common depth point gather at each same time to obtain a stacked seismic trace. The above operations are prior art and will not be elaborated upon in this invention.
[0036] In areas of structural abrupt change, the dip angle of the strata exceeds a preset threshold, indicating complex geological structures. Large dip angles may indicate the presence of faults, folds, and other complex formations. Directly using wide-azimuth data could introduce interference due to wavefield differences across different azimuths, increasing imaging difficulty. This invention employs narrow-azimuth data combined with stacking along the structural strike to reduce structural influence.
[0037] In this invention, a zoned differentiated processing strategy is adopted according to the complexity of the structure, which fully considers the influence of complex structures on the presentation of common reflection points, so that the final image is more consistent with the real geological features.
[0038] In this invention, narrow azimuth angles are selected along the structural strike, ensuring relatively continuous strata and consistent seismic wave propagation paths. Seismic traces along the strike exhibit high similarity, resulting in a high signal-to-noise ratio after stacking. Illumination along the strike is more uniform, with smaller variations in reflection coefficients, more reliable amplitude relationships, and better frequency consistency. In areas of abrupt structural changes, where strata dip and azimuth angles vary significantly, using wide azimuth angles could lead to seismic traces originating from different reflection points, resulting in signal ambiguity after stacking. Narrow azimuth angles avoid this anisotropic effect. In summary, narrow azimuth gathers along the structural strike better maintain structural continuity and improve imaging accuracy in complex structural regions.
[0039] Preferably, the narrow azimuth range along the structural strike is an azimuth angle of 15° to 30° with the structural strike, that is, a range of ±15° to ±30° along the strike.
[0040] Preferably, the narrow azimuth range is an azimuth angle of 20° with the structural orientation.
[0041] Offset range is another constraint for selecting gathers for stacking in this invention. The signal-to-noise ratio (SNR) of seismic imaging is not linearly proportional to the offset range. When the offset range is too large, the stacked seismic traces will introduce new noise. This is because the improvement of SNR depends on signal consistency, i.e., whether traces at different offsets reflect the same reflection point and whether the noise is random or coherent. Imaging with too small an offset will result in significant interference from low-frequency noise such as surface waves and acoustic waves, while too large an offset may produce shadow areas or insufficient illumination, reducing signal consistency and making the imaging susceptible to multiple waves and scattering noise, with significant anisotropy effects. In this invention, an offset range of 1500–3000 m is selected for iterative adjustment, balancing the requirements of signal strength and noise suppression.
[0042] Under the two constraints of "azimuth range of ±15° to ±30° along the strike" and "offset range of 1500 to 3000m", the azimuth range and offset range are adjusted respectively. For the common reflection point gathers within each adjusted range, dynamic correction and stacking are performed. The signal-to-noise ratio of the multiple stacked data are compared, and the azimuth range and offset range of the common reflection point gather corresponding to the stacked data with the highest signal-to-noise ratio are selected as the optimal narrow azimuth gather subset.
[0043] During the iterative adjustment process, the number of coverage iterations should be kept at a minimum threshold. Preferably, the minimum threshold is 24 coverage iterations. This setting can prevent distortion of the superposition results caused by selecting too small an azimuth angle or offset, ensuring that the superposition results have statistical significance.
[0044] During the iterative adjustment of the azimuth range and offset range, the iterative step size of the azimuth is 2° to 5°, and the iterative compensation of the offset is 50 to 150m.
[0045] Preferably, during the iterative adjustment of the azimuth range and offset range, the iterative step size of the azimuth is 3°, and the iterative compensation of the offset is 100m.
[0046] Preferably, the azimuth range and offset range can be iteratively adjusted and the optimal narrow azimuth aggregator subset can be selected using a pre-trained neural network model.
[0047] In this invention, by iteratively selecting the optimal narrow azimuth angle channel subset with the goal of high signal-to-noise ratio, the signal-to-noise ratio of co-reflection point superposition imaging can be improved.
[0048] In the third step, for each seismic trace in the optimal narrow azimuth trace subset, weights are set based on structural characteristics. Specifically, factors affecting the weight coefficients include curvature gradient, local coherence, and wavefield illumination intensity.
[0049] The formula for calculating the feature-driven adaptive weight coefficients is as follows: Among them, w i Indicates the adaptive weighting coefficient. Represents the curvature gradient, coh i I represents local coherence. norm The value indicates the intensity of the wave field illumination, and the subscript i indicates the seismic trace number.
[0050] Among them, curvature gradient is the rate of change vector of curvature in space, reflecting the degree of structural complexity; a larger gradient indicates more drastic structural changes. Local coherence is a measure of the waveform similarity of seismic traces within a local spatial range. Wavefield illumination intensity reflects the degree to which subsurface points are adequately illuminated by seismic waves. The structural feature-driven adaptive weighting coefficients comprehensively consider structural complexity, data quality, and wavefield illumination intensity, thereby adaptively adjusting the contribution of each seismic trace in the stacking process and further improving the signal-to-noise ratio of common reflection point stacking imaging.
[0051] Finally, the seismic traces from the optimal narrow azimuth trace set are superimposed according to their weights to obtain a second superposition result. This second superposition result reflects the morphology of the tectonic abrupt change zone. Through data optimization driven by tectonic features, dynamic weight allocation, and intelligent superposition, the imaging resolution and tectonic boundary clarity of complex geological targets are significantly improved.
[0052] In the fourth step, the first and second overlay results are fused to obtain the final imaging result. During the fusion process, the partition boundaries can use a gradual transition to avoid abrupt changes.
[0053] In this invention, differentiated processing based on structural feature constraints is employed, fully considering the impact of complex structures on the presentation of common reflection points, resulting in final imaging that better reflects real geological features. By iteratively selecting the optimal narrow azimuth gather subset with a high signal-to-noise ratio (SNR) as the objective, the SNR of the common reflection point stacked imaging can be improved. The structural feature-driven adaptive weighting coefficients comprehensively consider structural complexity, data quality, and wavefield illumination, thereby adaptively adjusting the contribution of each seismic trace in the stacking, further enhancing the SNR of the common reflection point stacked imaging. By setting two constraints—an azimuth range of ±15° to ±30° along the strike and an offset range of 1500–3000 m—the optimal narrow azimuth gather subset improves its imaging SNR under structural feature constraints.
[0054] While numerous embodiments of the invention have been shown and described herein, it will be apparent to those skilled in the art that such embodiments are provided by way of example only. Many modifications, alterations, and alternatives will occur to those skilled in the art without departing from the spirit and essence of the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed in the practice of the invention. The appended claims are intended to define the scope of protection of the invention and therefore cover equivalents or alternatives within the scope of these claims.
Claims
1. A method for intelligent overlay imaging of seismic common reflection points under three-dimensional structural feature constraints, characterized in that, include: The first step is to use the pre-stack time-migration profile as input to construct a three-dimensional structural geometry model of the target region and extract structural features to generate a structural feature constraint field. The second step involves dividing the target region into a gently sloping region with a dip angle less than a preset threshold and a region with abrupt changes in slope greater than a preset threshold, based on the structural feature constraint field. For regions with gentle tectonics, wide azimuth gathers are selected for dynamic correction and stacking to obtain the first stacking result; For the structural change zone, the azimuth range and offset range are iteratively adjusted within a narrow azimuth range along the structural trend for dynamic correction and superposition. The common reflection point gathers within the azimuth range and offset range with the highest signal-to-noise ratio after superposition are selected as the optimal narrow azimuth gather subset. The third step involves calculating the weights of each seismic trace in the optimal narrow azimuth trace subset based on the adaptive weighting coefficient formula driven by structural features, and then superimposing the weights to obtain the second superposition result. The formula for calculating the adaptive weight coefficients driven by the constructed features is as follows: Among them, w i Indicates the adaptive weighting coefficient. Represents the curvature gradient, coh i I represents local coherence. norm This indicates the wavefield illumination intensity, and the subscript i indicates the seismic trace number; The fourth step involves fusing the first stacking result of the gently sculpted zone and the second stacking result of the abruptly sculpted zone to obtain a stacked image of the seismic common reflection points.
2. The intelligent superposition imaging method for seismic common reflection points under three-dimensional structural feature constraints according to claim 1, characterized in that, The structural features include at least one of tilt angle, azimuth angle, curvature, and coherence.
3. The intelligent superposition imaging method for seismic common reflection points under three-dimensional structural feature constraints according to claim 1, characterized in that, In the second step, the preset threshold for dividing the gently sculpted zone into the abruptly sculpted zone is a stratigraphic dip angle of 15°.
4. The intelligent superposition imaging method for seismic common reflection points under three-dimensional structural feature constraints according to claim 1, characterized in that, In the second step, the narrow azimuth range is an azimuth angle of 15° to 30° with the structural strike; The offset range for iterative adjustment is 1500–3000 m.
5. The intelligent superposition imaging method for seismic common reflection points under three-dimensional structural feature constraints according to claim 4, characterized in that, In the second step, the narrow azimuth range is defined as an azimuth angle of 20° with the structural strike. The offset range for iterative adjustment is 1800–2500 m.
6. The intelligent superposition imaging method for seismic common reflection points under three-dimensional structural feature constraints according to claim 1, characterized in that, During the iterative adjustment of the azimuth range and offset range, the number of coverage iterations shall not be less than the minimum threshold.
7. The intelligent superposition imaging method for seismic common reflection points under three-dimensional structural feature constraints according to claim 6, characterized in that, The minimum threshold is 24 coverage times.
8. The intelligent superposition imaging method for seismic common reflection points under three-dimensional structural feature constraints according to claim 1, characterized in that, During the iterative adjustment of the azimuth range and offset range, the iterative step size of the azimuth is 2° to 5°, and the iterative compensation of the offset is 50 to 150m.
9. The intelligent superposition imaging method for seismic common reflection points under three-dimensional structural feature constraints according to claim 8, characterized in that, During the iterative adjustment of the azimuth range and offset range, the iterative step size of the azimuth is 3°, and the iterative compensation of the offset is 100m.
10. The intelligent superposition imaging method for seismic common reflection points under three-dimensional structural feature constraints according to claim 1, characterized in that, In the second step, the azimuth range and offset range are iteratively adjusted and the optimal narrow azimuth aggregator subset is selected using a pre-trained neural network model.