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<< Click to Display Table of Contents >> Navigation: Migration > Check Rikatti equations method |
This module performs velocity model updating in the depth domain using the Riccati (Rikatti) equations method. It is an interactive tomographic tool that refines an existing depth velocity model by analyzing the moveout residuals measured on depth-migrated common image gathers (CIGs). The Riccati equations provide a relationship between the observed differential moveout (DM) and the required velocity perturbation, allowing the velocity field to be updated in a mathematically rigorous way.
The workflow begins with loading the seismic CIG data and a starting depth velocity model. The user interactively navigates through the survey bins and, for each selected bin, picks DM corrections by placing points on a semblance panel displayed in both time and depth domains. When satisfied with the picking, the user triggers the solver to apply the Riccati-based inversion and update the velocity model. The result is a corrected depth velocity gather that can be passed on to subsequent depth migration workflows.
Use this module when depth migration gathers show residual moveout that indicates systematic velocity errors. The module supports both DM picking with optional corridor constraints, and automatic picking driven by semblance analysis, making it suitable for both detailed manual velocity analysis and semi-automated large-scale updates.
The SEG-Y file handle referencing the depth-domain common image gathers (CIGs) to be analyzed. These gathers should already be depth-migrated. The module reads traces bin by bin as the user navigates the survey, so the file must remain accessible during the interactive session.
The trace header database corresponding to the input SEG-Y data. It provides the bin coordinates, inline/crossline numbers, offset information, and datum values required to correctly index and load gathers. All data must be referenced to a constant datum surface, which is verified automatically when the input is loaded.
The starting interval velocity model in the depth domain, provided as a gather with traces organized by bin position and samples representing velocity values at successive depth levels. This model serves as the reference from which the Riccati solver computes corrections. The datum of the velocity model must match the datum of the seismic data; a mismatch will result in an error at initialization.
The storage item that holds the differential moveout picks made by the user on the semblance panel. Each pick specifies the velocity perturbation needed at a given depth level and bin location. These picks are the primary input to the Riccati inversion and drive the velocity update.
An optional secondary picking item used to define corridor constraints around the DM picks. When corridors are enabled (see the Use corridor for auto picking parameter), the semblance-based automatic picker searches only within the corridor bounds defined here. Corridors help prevent the auto-picker from jumping to spurious semblance peaks in noisy or complex areas.
The time sampling interval (in seconds) used when the depth CIG is converted to the time domain for semblance analysis. The default value is 0.004 s (4 ms). Finer values increase the resolution of the semblance display but also increase computation time and memory. Changing this parameter triggers re-computation of the time-domain CIG.
The maximum two-way time (in seconds) to include in the time-domain CIG display. The default is 4 s. Set this to cover the full depth range of interest after conversion from depth to time. Values that are too short will clip deep reflections from the semblance panel; unnecessarily large values waste memory.
The near-surface reference velocity (in m/s) used during the depth-to-time conversion of the CIG and during static datum correction. The default is 4000 m/s. Set this value to represent the typical velocity in the near-surface layer or at the datum level of the dataset. An incorrect V0 will shift the depth-to-time conversion and cause misalignment between the time-domain semblance and the actual reflection events.
The reference datum elevation (in m) for displaying the depth CIG and the time tables. This value is automatically set from the input data datum when the data is loaded and generally does not need to be changed manually. Modifying it will shift the displayed CIG and time tables relative to the depth axis.
When enabled (default: on), the module recomputes all internal ray-traced grids and pre-computed storage before each solve. This ensures that the solver always uses the latest velocity model and grid parameters. Disable this option only if the velocity model and grid settings have not changed since the previous solve and you want to save the time spent re-computing the storage — for example, when iterating only the DM picks without changing any other settings.
This group controls how the root-mean-square (RMS) velocity is calculated from the depth velocity model. The RMS velocity is a key intermediate quantity used by the Riccati solver to relate depth-domain velocity perturbations to the observed moveout residuals. The three parameters below define the offset range over which the regression is performed.
The minimum source-receiver offset (in m) to include in the RMS velocity regression. The default is 200 m. Near-offset traces may be affected by direct-wave interference or noise; excluding them using this parameter can improve the stability and accuracy of the computed RMS velocity.
The maximum source-receiver offset (in m) to include in the RMS velocity regression. The default is 1500 m. Long-offset traces may suffer from anisotropy effects, stretch, or muting. Set this value to the maximum reliable offset in your dataset. Including offsets beyond the reliable range can bias the regression and produce an incorrect RMS velocity.
The offset sampling step (in m) for the regression. The default is 20 m. A finer step provides a denser sampling of the offset axis for the regression, which can improve accuracy when the offset coverage within the regression range is irregular. Coarser steps speed up the computation.
This group defines the spatial grid resolutions used internally for different stages of the Riccati computation. The module uses three separate grids: one for computing the RMS velocity, one for the velocity model itself, and one for ray tracing. Additionally, a variable grid and an aperture extension are defined. Coarser grids reduce memory requirements and run time; finer grids improve accuracy but require more resources.
The horizontal (X and Y) grid spacing (in m) used when computing the RMS velocity from the interval velocity model. The default is 200 m. This grid does not need to be as fine as the velocity model grid; a coarser value is usually sufficient and reduces computation time for the pre-processing stage.
The vertical (depth) grid spacing (in m) used for the RMS velocity calculation. The default is 200 m. Coarser values are generally acceptable here; the RMS velocity is a smoothly varying quantity and does not require fine vertical sampling.
The horizontal grid spacing (in m) for the velocity perturbation model computed by the Riccati solver. The default is 10 m. This is the primary resolution parameter for the output velocity update. Finer values produce a more detailed velocity update but significantly increase memory use and solver run time.
The vertical grid spacing (in m) for the velocity perturbation model. The default is 10 m. Match this to the depth resolution needed for the velocity update. Finer values are important in areas with rapid vertical velocity variation but increase solver cost.
The horizontal spacing (in m) of the grid used for ray tracing through the velocity model. The default is 200 m. Ray tracing is used to compute travel times and ray parameter fields required by the Riccati equations. A coarser ray grid speeds up this step but may reduce accuracy in areas of strong lateral velocity variation.
The vertical spacing (in m) of the ray tracing grid. The default is 200 m. As with the horizontal ray grid step, coarser values speed up the ray tracing at some cost to accuracy in depth.
The step size (in m) used when advancing along each ray during ray tracing. The default is 10 m. Smaller values produce more accurate ray paths through complex velocity structures but increase the number of integration steps and thus the computation time. Use smaller values when tracing rays through regions of high velocity gradient.
The horizontal spacing (in m) of the auxiliary variable grid used within the Riccati solver. The default is 200 m. This grid holds intermediate variables computed during the inversion. A coarser grid reduces memory use; a finer grid may improve stability of the solution in laterally complex areas.
The vertical spacing (in m) of the auxiliary variable grid. The default is 200 m. Keep this consistent with the horizontal variable grid step unless you have specific reasons to use anisotropic sampling in the vertical direction.
The lateral extension (in m) added around the velocity model boundaries during the computation. The default is 500 m. This aperture prevents edge effects from affecting the Riccati solution near the boundaries of the input velocity model. Increase this value if the area of interest extends close to the model edges.
The vertical extension (in m) added below the velocity model during computation. The default is 1000 m. This prevents boundary effects from propagating upward and contaminating the velocity update within the target depth interval.
This group contains parameters that control the iterative optimization solver used to find the velocity perturbation that best fits the DM picks. The solver combines a shrinkage scheme (for regularization) with a global/local iteration strategy, optional smoothing, and a convergence threshold.
The number of shrinkage iterations used to progressively reduce the solver step size during the inversion. The default is 3 (valid range: 1–6). More shrinkage iterations allow finer convergence but increase total computation time. This parameter controls the multi-resolution aspect of the solver: the step size is divided by the Shrinkage factor at each shrinkage iteration.
The factor by which the solver step size is reduced at each shrinkage iteration. The default is 1.5 (valid range: 1.01–2.0). A value of 1.5 means each successive shrinkage pass uses a step 1.5 times smaller than the previous one. Higher values produce a more aggressive step reduction, which can improve convergence stability at the cost of requiring more iterations.
The number of outer (global) iterations of the Riccati solver. The default is 5. Each global iteration involves a full pass through all shrinkage levels. More global iterations allow the solver to progressively refine the velocity update when the DM residuals are large, but they increase the total solve time proportionally.
The maximum number of inner (local) iterations for the linear solver at each shrinkage level. The default is 500. This limits the number of conjugate-gradient steps used to solve the linear system at each inner level. Increasing this allows the inner solver more time to converge to an accurate solution, which is particularly important when the velocity model is complex or when the grid is very fine.
When enabled, a spatial smoothing operator is applied to the intermediate differential moveout (H) field computed during the inversion. This can stabilize the solver in the presence of noisy or sparse DM picks. The default is off. Enable this option if the resulting velocity update shows high-frequency noise or spatial artifacts.
The maximum lateral smoothing window (in m) applied to the H field when Smooth H is enabled. The default is 3500 m. A wider window produces a smoother, more laterally continuous DM field but may blur real lateral velocity variations. The module uses both a minimum and a maximum window to apply a depth-varying smoothing.
The vertical smoothing window (in m) applied to the H field when Smooth H is enabled. The default is 200 m. Vertical smoothing reduces rapid depth-alternating oscillations in the DM field. Adjust this relative to the expected vertical scale of the velocity anomalies.
When enabled, a spatial smoothing operator is applied to the computed velocity perturbation field before it is added back to the reference velocity model. The default is off. Enabling this produces a smoother, more geologically plausible velocity update and helps suppress high-frequency inversion artifacts.
The maximum lateral smoothing window (in m) applied to the velocity perturbation when Smooth V is enabled. The default is 3500 m. As with H smoothing, a larger window produces a smoother velocity update over a wider lateral area. Balance the smoothing width against the spatial scale of the expected velocity anomalies.
The vertical smoothing window (in m) applied to the velocity perturbation when Smooth V is enabled. The default is 200 m. This constrains the vertical resolution of the velocity update and prevents the solver from creating artificially sharp velocity boundaries that are not supported by the picks.
The maximum allowed velocity perturbation (in m/s) that the solver can apply at any single location. The default is 300 m/s. Velocity updates larger than this threshold are clipped to prevent physically unreasonable corrections. Increase this value if the DM analysis indicates that large velocity errors exist; decrease it to apply more conservative updates.
See the description under Grid params above. This entry in the Solver params group is the same lateral aperture extension applied when building the internal computation grids for the solver stage.
See the description under Grid params above. This entry in the Solver params group is the same vertical aperture extension applied during the solver computation to avoid boundary effects at depth.
This group controls the semblance panel that the user interacts with to pick DM corrections. The semblance is displayed in the velocity-versus-depth domain, and the picks are made by selecting the velocity perturbation value (delta V) that best flattens each reflector across offsets. The parameters here also control the automatic picking behavior.
The minimum velocity perturbation (in m/s) displayed on the semblance panel. The default is -500 m/s. Set this to the most negative velocity error you expect. If reflectors are under-migrated (too fast a velocity was used), the DM picks will fall at positive delta V values; if over-migrated (too slow a velocity), the picks will fall at negative values.
The maximum velocity perturbation (in m/s) displayed on the semblance panel. The default is +500 m/s. Set this to the maximum positive velocity error you expect. Increase the range if the velocity model errors are larger than ±500 m/s.
The velocity perturbation sampling step (in m/s) on the semblance panel. The default is 25 m/s. A smaller step gives a finer resolution semblance display, making it easier to identify and pick the exact velocity perturbation at the semblance peak, but increases the number of test velocities that must be computed.
The maximum offset (in m) to include when computing semblance. The default is 2000 m. Only offsets up to this value contribute to the semblance calculation. Limiting the offset range is useful when long-offset traces suffer from stretch, anisotropy, or noise that would degrade the quality of the semblance.
The time window (in seconds) over which semblance values are averaged for display. The default is 0.05 s. A wider smoothing window produces a more stable semblance image that is easier to pick visually, but reduces the temporal resolution and may merge nearby reflectors. Use a narrower window when reflectors are closely spaced.
The time window (in seconds) used for amplitude normalization before computing semblance. The default is 0.1 s. Normalization compensates for amplitude variations with depth so that shallow and deep reflectors contribute more equally to the semblance display. Increase this window if deep reflectors appear too dim on the semblance panel.
The depth (in m) at which the automatic semblance picker begins placing picks. The default is 400 m. The auto-picker skips the depth range above this value, which helps avoid shallow noise zones or the water-bottom multiple in marine data. Set this to the shallowest reliable reflector depth for your dataset.
The vertical spacing (in m) between successive auto-picks in the depth domain. The default is 400 m. A finer step produces a denser set of picks that captures more detail in the velocity update but takes longer to compute. Use a coarser step for a first-pass update and refine manually or with a finer step afterward.
The trace decimation step used when computing semblance for automatic picking. The default is 50 traces. A larger step skips more traces during the semblance stacking and speeds up the auto-picking; a smaller step uses more traces and may improve pick quality in areas with low fold or noisy data.
When enabled (default: on), the automatic picker searches for semblance peaks only within the corridor defined by the DM corridor picking item. This prevents spurious picks outside the expected velocity perturbation range and is especially useful in complex geological settings where multiple semblance peaks exist. Disable this option to allow unconstrained automatic picking across the full delta V range.
The half-width (in m/s) of the search corridor applied around the corridor picks when clicking to add a new auto-pick. The default is 50 m/s. When a user clicks on the semblance to define a corridor point, the auto-picker searches within ±this value from the clicked velocity. Larger values allow more freedom for the picker; smaller values constrain it more tightly to the clicked position.
When enabled, a smoothing filter is applied to the automatic picks after they are generated to reduce erratic pick jumps between adjacent depth levels. The default is off. Enable this when the semblance is noisy and the raw auto-picks show large depth-to-depth variations that are not physically reasonable.
The time window (in seconds) of the smoothing filter applied to the auto-picks when Use smooth for auto picking is enabled. The default is 0.05 s. A wider window produces smoother picks at the cost of suppressing real rapid velocity variations. Adjust to match the expected scale of velocity variation in your dataset.
The module produces the following output datasets. All depth-domain gathers can be viewed interactively in the linked visualization panels.
Updated depth velocity gather — The primary output: a depth velocity gather in which the interval velocities have been corrected by the Riccati solver based on the DM picks. This gather can be used directly as input to a subsequent depth migration module.
Inline V depth — A depth velocity cross-section extracted along the inline direction through the currently selected bin. This allows the user to inspect the velocity model along the inline before and after the update.
Crossline V depth — A depth velocity cross-section extracted along the crossline direction through the currently selected bin.
Vertical time tables inline / crossline — Depth-to-time conversion tables computed from the velocity model along the inline and crossline directions. These tables map each depth sample to its corresponding two-way time and are used internally when displaying the CIG in the time domain.
Selected CIG time / Selected CIG depth — The common image gather for the currently selected bin, shown in both the time domain and the depth domain for visual quality control. The time-domain CIG is used for semblance analysis; the depth-domain CIG shows the migrated result directly.
Removes all existing DM picks and corridor picks from the current session. Use this action when you want to start a fresh picking session without any previously stored corrections.
Saves the current DM picks and corridor picks to the connected picking storage items so they can be reused in a subsequent session or shared with other modules.
Loads previously saved DM picks and corridor picks from the connected picking storage items into the current session. Use this to resume picking from a prior session or to apply picks that were prepared in another context.
Triggers the Riccati-based velocity update using the current DM picks. The solver runs through all configured global and shrinkage iterations and writes the updated velocity model to the Updated depth velocity gather output. After the solve completes, the Misfit display shows the spatial distribution of the residual DM, allowing you to assess the quality of the update and identify areas that may need additional picking.