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The Dix - TV module converts RMS velocity (VRMS) data into interval velocity using a Total-Variation (TV) regularized inversion. Unlike the classical Dix formula, which differentiates VRMS with respect to time and is highly sensitive to noise, this module uses a Split-Bregman optimization solver that produces stable, physically plausible interval velocity models even when VRMS picks are noisy or spatially irregular.
The module supports three operating modes depending on what optional inputs are connected. When only the VRMS gather is provided, the inversion works sample-by-sample across the full time axis. When a correlation (semblance) gather is also connected, the module uses the correlation peaks to identify the most reliable VRMS picks within a search window, restricting the inversion to those high-confidence time samples. When time horizons are also provided, the module performs a layer-stripping inversion constrained to the reflector times, which is the most geologically consistent approach for layered models.
The output is delivered in two domains simultaneously: interval velocity as a function of two-way time, and interval velocity as a function of depth. The depth-domain result is obtained by converting the time-domain interval velocity using an average velocity integral, with the output grid defined by the number of samples and depth step parameters.
The input RMS velocity gather to be converted into interval velocity. This is a mandatory input. Connect the output of a velocity analysis module (such as a semblance-based velocity picker) or an existing VRMS model gather. The gather must contain bin picket coordinates so that the module can build the spatial grid for inversion. Each trace represents the VRMS function versus two-way time at one lateral position.
An optional semblance or correlation gather that indicates the quality (confidence) of the VRMS picks as a function of time. When connected, the module searches within a time window of width equal to the Correlation Window parameter around each candidate sample time to find the local semblance maximum. Only the VRMS values at these high-confidence times are used in the inversion. This allows the solver to focus on the most reliable portion of the velocity field and reject low-semblance noise between reflection events. If not connected, all time samples from the VRMS gather are used.
An optional set of interpreted time horizons (a GHorizonPickingItem). When connected and the item contains at least one non-empty layer, the module switches to horizon-constrained layer-stripping mode. In this mode, the inversion uses the horizon times as the natural layer boundaries, sampling the VRMS gather at each reflector position. If the correlation gather is also connected, the picked horizon time is refined within the Correlation Window to the nearest semblance peak. This mode produces the most geologically meaningful interval velocity model when reliable horizon interpretations are available.
The half-width of the time search window (in seconds) used to locate the semblance maximum near each candidate VRMS sample or horizon pick. Default: 0.05 s. This parameter is active only when the Input Correlation gather is connected. A wider window allows a larger time shift between the nominal sample time and the nearest semblance peak, which is useful when the velocity picks are coarsely sampled. A narrower window keeps the time correction small and is appropriate when the initial pick times are already well-aligned with reflectors. Set to zero to disable the correlation-based time refinement.
The near-surface replacement velocity (m/s) applied between the datum level and the shallowest reflection event. Default: 1500 m/s. All output interval velocity samples above the datum-to-surface travel time are filled with this constant value. Set V0 to the average velocity of the weathered layer or water column, as appropriate for your survey. For marine data, 1480 to 1520 m/s is typical. For land data with significant topography, use the near-surface velocity from refraction statics analysis.
The reference elevation (m) used as the top of the interval velocity model. Default: 0 m. Valid range: -1000 m to 100000 m. The datum must be at or above the elevation of every trace in the input VRMS gather; the module will report an error if any trace surface is below the datum. For surveys with variable surface topography, set the datum to the flat reference plane used during processing (typically the same value as in the statics workflow). For marine data, the datum is usually 0 m (sea surface).
The number of depth samples in the depth-domain output interval velocity gather. Default: 1000. The total depth extent of the output is Number of samples multiplied by the Output sample rate (depth step). Choose a value large enough to cover the target depth. For example, with a depth step of 5 m and 1000 samples, the output reaches 5000 m depth. This parameter does not affect the time-domain output, which always matches the input VRMS time axis.
The depth spacing (m) between consecutive samples in the depth-domain output interval velocity gather. Default: 5 m. Minimum: 1 m. A finer depth step preserves more vertical resolution in the depth-domain velocity model but results in a larger output file. Use a depth step consistent with the target depth resolution of your depth migration workflow.
When enabled, VRMS samples whose values fall outside the range defined by Min VRMS to consider and Max VRMS to consider are excluded from the inversion. Default: off. Enable this option when the input VRMS gather contains outlier velocities caused by noise, cycle-skipping, or water-bottom multiples. When enabled, the Min VRMS and Max VRMS parameters become active.
The lower velocity threshold (m/s) for VRMS outlier rejection. Default: 1500 m/s. Active only when Don't use bad Vrms values is enabled. Any VRMS sample with a value below this threshold is ignored during inversion. Set this to the minimum physically plausible velocity in the survey area — typically the velocity of water or the slowest unconsolidated sediment.
The upper velocity threshold (m/s) for VRMS outlier rejection. Default: 4500 m/s. Active only when Don't use bad Vrms values is enabled. VRMS samples above this value are excluded from the inversion. Adjust to the maximum velocity expected in your geological section. For shallow surveys or soft-sediment basins, a lower cap (for example 3500 m/s) prevents unrealistically high velocities from corrupting the model.
This group contains the core iteration and grid parameters for the Split-Bregman total-variation inversion solver. The solver minimizes the difference between the forward-modeled VRMS (computed from the interval velocity model) and the observed VRMS gather, subject to a smoothness penalty in both the lateral and vertical directions.
The number of outer (Bregman) iterations in the Split-Bregman solver. Default: 5. Minimum: 1. Each outer iteration updates the total-variation constraint variables before running the inner LSQR sub-problem. Increasing the number of global iterations improves convergence at the cost of longer computation time. For most VRMS datasets, 5 to 10 global iterations are sufficient. Use more iterations only if the interval velocity model shows residual artifacts or has not converged.
The number of inner LSQR iterations performed within each global Bregman iteration. Default: 15. Minimum: 1. Each local iteration refines the interval velocity model by solving the least-squares sub-problem one step further. More local iterations lead to a more accurate solution within each outer loop but also increase runtime. A value of 10 to 20 is appropriate for typical problems. Reduce to 5 to 10 for a faster, approximate result when processing large 3D datasets.
The convergence tolerance for the inner LSQR solver. Default: 1e-6. The inner solver stops early when the relative residual norm falls below this value. A smaller tolerance enforces stricter convergence but increases computation time. The default value is appropriate for most applications. Increase to 1e-4 or 1e-3 for faster approximate results on large problems.
The lateral grid step (m) in the inline (X) direction used to build the internal calculation grid from the scattered VRMS bin positions. Default: 50 m. Minimum: 1 m. The module maps the irregular VRMS bin locations onto a regular grid with this spacing before running the inversion. A smaller step results in a finer lateral resolution but a larger system to solve. Set this value to approximately match the CMP spacing or the natural lateral spacing of the input velocity analysis locations.
The lateral grid step (m) in the crossline (Y) direction used to build the internal calculation grid. Default: 50 m. Minimum: 1 m. For 2D data, set Calc step Y to any positive value (it has no effect if only one crossline is present). For 3D data, match this value to the crossline CMP spacing or the spacing of velocity analysis panels in the crossline direction.
A mandatory collection of time-velocity constraint rows that define the physically acceptable range of interval velocities at each depth level. Each row specifies a Time start (s), a Min Velocity (m/s, default 1500, minimum 110), and a Max Velocity (m/s, default 7000, minimum 110). The table must have at least one row. Rows must be ordered by increasing time, and each row's Min Velocity must be strictly less than its Max Velocity. The solver uses these bounds as hard constraints to prevent the inversion from producing physically impossible interval velocities. For example, add a row at time 0 s with Min 1400 m/s and Max 2000 m/s to restrict near-surface velocities, and another at 2 s with Min 2000 m/s and Max 5000 m/s for deeper layers.
When enabled, the solver applies an additional constraint that limits how much the interval velocity is allowed to decrease from one time sample to the next. Default: on. This prevents the inversion from producing unrealistic velocity inversions (low-velocity zones caused by numerical instability rather than geology). When enabled, the Fraction of decrease parameter becomes active. Disable this option only if your geological model genuinely contains significant low-velocity zones that must be resolved.
Controls the maximum permitted fractional decrease of interval velocity from one time sample to the next. Default: 0.99. Valid range: 0.01 to 1. Active only when Limit decrease of VINT is enabled. A value close to 1 (for example 0.99) allows only a very small decrease per sample, effectively enforcing a near-monotone velocity profile. A lower value (for example 0.8) permits larger decreases between samples. In practice, the default of 0.99 is appropriate for most datasets and prevents oscillatory instabilities in the inversion result.
This group contains low-level parameters of the Split-Bregman solver that control the regularization strength and the numerical step sizes of the optimization algorithm. In most cases, the default values work well and do not need to be changed. Adjust these parameters only when the standard solver settings produce unsatisfactory results, such as excessive smoothing or oscillatory artifacts.
The regularization weight applied in the lateral (inline) direction by the total-variation penalty term. Default: 2. A larger value enforces stronger lateral smoothness of the interval velocity model, reducing lateral variability at the cost of potentially blurring genuine lateral velocity contrasts. Reduce this value if lateral velocity gradients are expected and should be preserved, for example in areas of salt flanks or steep dip.
The regularization weight applied in the vertical (time) direction by the total-variation penalty term. Default: 2. A larger value enforces stronger vertical smoothness, producing a gradual velocity profile with fewer abrupt changes between time samples. Reduce this value to allow sharper vertical velocity contrasts, for example when thin high-velocity layers are expected. Increasing this value is an effective way to suppress numerical noise in the inverted interval velocity if the result shows high-frequency oscillations with depth.
The augmented Lagrangian penalty parameter (mu) of the Split-Bregman algorithm. Default: 1.5. This parameter controls the coupling between the data fidelity term and the regularization constraint in the outer Bregman loop. Larger values of Mu increase the weight of the constraint enforcement and can speed up convergence but may also make the solver less stable. The default value is appropriate for typical VRMS inversion problems. Change this parameter only if the solver is not converging or is producing strongly oscillatory results.
The step-size scaling factor for the Bregman update in the outer loop. Default: 1. Valid range: 0.9 to 1.1. Values slightly above 1 can accelerate convergence in some cases, while values slightly below 1 can improve stability. In practice, the default of 1 is suitable for the vast majority of VRMS inversion problems and should only be adjusted as a last resort when the solver exhibits instability.
The inverted interval velocity model expressed as a function of two-way time. This gather has the same time axis (number of samples and sample rate) as the input VRMS gather. Each trace represents the interval velocity versus time at one lateral position. Samples above the datum level are filled with the V0 constant velocity. This output is suitable for NMO-based workflows, for further velocity manipulation in the time domain, or as a quality control display to compare against the input VRMS.
The inverted interval velocity model expressed as a function of depth. The depth axis is defined by the Number of samples in output and Output sample rate parameters. The conversion from the time-domain interval velocity to depth is performed by integrating the interval velocity to compute the average velocity function, then resampling the interval velocity onto the depth axis. This output is ready for use as input to depth migration workflows or for direct comparison with well log velocities.