Refraction 2D modeling

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Refraction 2D modeling

 

Description

The Refraction 2D Modeling module builds and refines a 2D depth-velocity model by performing refraction tomography on a preloaded depth velocity gather. It first computes synthetic first-break traveltimes using the fast-marching method (FMM), which traces wave propagation through the initial slowness model. The computed traveltimes are then compared with theoretical first-arrival times derived from the input velocity model, and the velocity model is updated iteratively using SIRT (Simultaneous Iterative Reconstruction Technique), SIRT2, or LSQR inversion. This cycle of forward modelling and inversion repeats for the specified number of iterations, progressively reducing the mismatch between modelled and reference traveltimes.

Use this module when you need to produce a near-surface velocity model for static corrections or depth imaging starting from an initial estimate. The module outputs both the smoothed initial model and the tomography-updated model, allowing you to compare them and assess the update quality. Multi-threaded and GPU-accelerated execution is supported for processing large 2D lines efficiently.

Input data

Depth refraction velocity

The starting depth-velocity model for the 2D refraction survey. This gather must be defined on a depth axis (Z axis in metres) and contains the initial velocity values at each model node. The module uses this input to generate the initial slowness grid and as the reference for computing traveltime residuals during tomographic inversion. The model is typically produced by a depth conversion or a previous velocity analysis step.

Parameters

Test

When enabled, the module runs in test mode, which executes the forward modelling and inversion pipeline with reduced computation to allow you to verify parameter settings quickly before a full production run. Use this flag when tuning grid spacing, smoothing, or iteration counts to avoid long processing times during experimentation.

Default: Enabled.

Constant model params

This parameter group controls the spatial sampling of the internal tomography grid and the degree of horizontal smoothing applied to the velocity model during inversion.

Delta X

The horizontal grid spacing of the internal slowness model in metres. Smaller values produce a finer model grid that can resolve shorter-wavelength lateral velocity variations but require more memory and computation time. Set this value to be comparable to the nominal shot or receiver spacing to avoid aliasing the model relative to the data sampling.

Default: 5 m.

Delta Z

The vertical grid spacing of the internal slowness model in metres. This controls the depth resolution of the tomographic update. Use a value consistent with the expected depth of the refractors you wish to image; for shallow refraction surveys targeting the weathering layer, values of 2–10 m are typical.

Default: 5 m.

Horizontal Smooth

The lateral smoothing length applied to the velocity model at each inversion iteration, in metres. Larger values produce a smoother, more geologically plausible model and help suppress noise-driven artefacts, but reduce the lateral resolution of the result. Smaller values allow the model to conform more closely to the data but may produce noisy updates in areas of poor ray coverage. A typical starting value is 50–200 m, depending on the survey scale.

Default: 100 m.

Detect topography

Controls how the module handles the near-surface air layer above the topography when constructing the slowness grid. Three options are available:

No topo — no topographic correction is applied; the grid surface is assumed flat.

By air velocity — the module fills the air cells above the topographic surface with the velocity specified in the Air velocity parameter. This is the recommended option when you have a known or estimated surface elevation profile.

By headers — elevation information is taken from the trace headers of the input data, allowing per-shot or per-receiver topography variation.

Default: By air velocity.

Air velocity

The velocity assigned to model cells that lie above the topographic surface (the air layer), in m/s. This parameter is active only when Detect topography is set to By air velocity. Setting this to the speed of sound in air (~330 m/s) or a very high value effectively prevents rays from propagating through the air cells. The default value of 310 m/s is appropriate for standard atmospheric conditions.

Default: 310 m/s.

Source step

The decimation interval for source positions when constructing the traveltime tables. A value of 1 uses every source; a value of 5 uses every fifth source. Increasing this value reduces computation time but may degrade the tomographic coverage in areas with sparse source spacing. Use a small value (1–2) for production runs and a larger value for quick parameter tests.

Default: 5.

Iters count

The number of tomographic inversion iterations. Each iteration recomputes traveltimes through the updated model and applies another SIRT/LSQR update step. More iterations generally improve convergence but increase run time. For well-constrained surveys, 3–10 iterations are typically sufficient; poorly constrained or complex geology may require more. Monitor the traveltime residual in the output to determine when additional iterations are no longer reducing the misfit.

Default: 5.

Receivers count

The number of synthetic receivers per source used when computing the forward traveltime model. This controls the density of the receiver array in the modelling step. A larger number provides denser ray coverage and potentially better model constraint but increases memory and computation time. Set this to match or exceed the actual receiver count in your survey template.

Default: 100.

Receivers step

The decimation step applied to receivers when building the traveltime tables, analogous to Source step. A value of 1 uses every receiver; higher values thin the receiver sampling to reduce processing time at the cost of ray coverage density.

Default: 1.

Padding size

The number of grid cells added as a border around the active model grid to prevent boundary reflections from contaminating the traveltime computation. The padding cells are filled with a constant velocity so that waves can exit the model cleanly. Larger values provide better boundary absorption but increase memory usage. The default value of 20 cells is adequate for most models; increase it if you observe edge effects in the output velocity model.

Default: 20.

angles size

The number of angular segments used in the fast-marching traveltime computation. The FMM algorithm discretises the propagation front into angular sectors; more sectors improves the angular accuracy of the wavefront expansion but increases computation time. The default value of 20 is appropriate for most surveys.

Default: 20.

Frequency

The dominant frequency of the first-break wavelet used internally when modelling synthetic traveltimes, in Hz. This value is used to define the Fresnel zone radius for the ray-path weighting during tomographic update. Set it to the approximate dominant frequency of the recorded first arrivals in your data.

Default: 20 Hz.

Velocity 0

The reference starting velocity for the initial constant velocity model, in m/s. When no input depth-velocity gather is available or when the initial model needs to be overridden with a homogeneous starting model, this value is used to fill the entire model grid. Set it to the average near-surface P-wave velocity for your area.

Default: 2700 m/s.

Velocity min

The lower bound on velocity values allowed during the tomographic update, in m/s. After each SIRT or LSQR iteration, any cell whose updated velocity falls below this threshold is clipped to this value. This prevents physically unreasonable low-velocity anomalies from developing in poorly constrained areas. Set this to the minimum realistic P-wave velocity for your near-surface geology.

Default: 2500 m/s.

Velocity max

The upper bound on velocity values allowed during the tomographic update, in m/s. Cells whose updated velocity exceeds this limit are clipped to this value. This prevents the inversion from producing unrealistically fast anomalies that could arise from noise or poor ray coverage. Set this to the maximum plausible velocity in the refraction layer you are imaging.

Default: 3000 m/s.

Offset max

The maximum source-receiver offset used when selecting first-break picks for the tomographic inversion, in metres. Traces at offsets greater than this value are excluded from the update. This allows you to restrict the inversion to first arrivals that are reliably refracted from shallow horizons and avoids including diving waves or reflections from deeper structures. Set this to the maximum offset at which your first-break picks are reliable.

Default: 5000 m.

Soft Treshold

A soft-thresholding factor applied to the traveltime residuals before the inversion update, expressed as a fraction (0–1). Residuals smaller than this threshold multiplied by the maximum residual are zeroed out, which suppresses small noisy contributions from poor picks without completely discarding them. Increase this value to make the inversion more robust against outlier picks; decrease it to allow all residuals to contribute to the update. A value of 0 disables soft-thresholding.

Default: 0.05 (5%).

Method

The tomographic inversion algorithm used to update the slowness model. Three options are available:

SIRT — Simultaneous Iterative Reconstruction Technique; robust and well-suited for underdetermined problems with uneven ray coverage.

SIRT2 — a modified SIRT variant with alternative weighting; may converge faster for certain model geometries.

LSQR — Least Squares QR decomposition; produces a minimum-norm solution and can converge in fewer iterations than SIRT for well-constrained problems.

Default: SIRT.

Time step

The temporal sampling interval used for the synthetic seismogram output, in seconds. This determines the time resolution of any modelled trace output produced alongside the velocity model. Set this to match the sample rate of your field data (e.g. 0.002 s for 2 ms data).

Default: 0.004 s (4 ms).

Samples count

The total number of time samples in the synthetic seismogram output. Together with Time step, this defines the total recording time (Total time = Samples count × Time step). Set this so that the total recording length covers the maximum expected first-break arrival time across all offsets.

Default: 100.

Output data

Initial velocity model

The depth-velocity model as it existed before tomographic updating — the input model resampled and smoothed to the internal grid spacing. This output allows you to compare the starting model against the final tomographic result and to quantify the magnitude of velocity updates applied during inversion.

Tomographic velocity model

The depth-velocity model produced after all tomographic inversion iterations have been completed. This is the primary result of the module and should be used as the near-surface velocity model for subsequent static corrections or depth imaging. Inspect this model for lateral velocity continuity and ensure that velocity values remain within geologically plausible bounds.