Anisotropy Thomson Parameter Estimation

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Anisotropy Thomson Parameter Estimation

 

Description

Estimates the Thomsen anisotropy parameters delta (δ) and epsilon (ε) from depth-migrated seismic gathers. These two parameters describe the degree and nature of vertical transverse isotropy (VTI) in a layered earth model, which is the most common form of seismic anisotropy encountered in sedimentary basins.

For each subsurface location, the module computes the local incidence angle of each ray using a supplied interval velocity model, then fits the Thomsen NMO equation to the residual moveout observed in the migrated gathers. The fitting is performed using a least-squares SVD method, which simultaneously solves for the delta and epsilon values that best explain the observed residual moveout at every depth sample.

Use this module after depth migration when residual moveout is visible on common image point (CIP) gathers and you suspect the cause is anisotropy rather than a velocity error. The output delta and epsilon gathers can be used to update the anisotropic velocity model for a subsequent migration pass, improving image focus and amplitude fidelity.

 

Input data

The SEG-Y file handle pointing to the depth-domain seismic dataset (common image point gathers after depth migration). The data must be in the depth domain on a constant datum. This connection provides the seismic amplitudes analysed for residual moveout.

Input data trace headers

The trace header geometry object associated with the input SEG-Y data. Supplies source/receiver positions, offset values, and bin assignments for every trace. The datum elevation must be consistent for all traces; the module reports an error if source and receiver datums differ or if the data datum does not match the velocity model datum.

Depth velocity gather

An interval velocity model stored as a depth gather, with one velocity trace per spatial bin. Used to compute ray angles from the surface to every depth sample and to convert depth samples to two-way travel time for the residual moveout calculation. The datum of this model must match the input seismic data exactly.

Residual velocity model DM1 (second-order)

The second-order residual moveout (RMO) picking result expressed as a velocity model. This captures the offset-squared component of residual moveout and is used to separate the contribution of velocity errors from anisotropy when estimating Thomsen parameters.

Residual velocity model DM2 (fourth-order)

The fourth-order residual moveout picking result expressed as a velocity model. This higher-order term is sensitive to the anellipticity of the wavefront and provides additional constraint for separating the delta and epsilon Thomsen parameters. Both DM1 and DM2 should be derived from a consistent residual moveout analysis performed prior to running this module.

Parameters

V0

The near-surface reference velocity (m/s) used as the starting slowness for ray-parameter computation when tracing rays through the velocity model. Default: 1800 m/s. Set this to the velocity of the shallowest layer in your interval velocity model — typically the replacement velocity or the velocity immediately below the datum surface. Using an incorrect V0 will systematically shift all computed incidence angles and lead to errors in the estimated Thomsen parameters.

Min lambda

The lower bound of the search range for the Thomsen delta (δ) parameter (labelled "lambda" in the interface). Default: -0.1. Valid range: -1 to 1. For most sedimentary rocks, delta ranges from approximately -0.1 to +0.3. Set slightly below the minimum delta expected in your area. Widening the range allows the solver to handle highly anisotropic lithologies.

Max lambda

The upper bound of the search range for the Thomsen delta (δ) parameter. Default: 0.1. Valid range: -1 to 1. Must be greater than Min lambda. A typical starting range of -0.1 to +0.3 covers most clastic sedimentary sequences. If the output delta gather shows values consistently at the upper bound, increase Max lambda.

Step lambda

The increment used to step through the delta (δ) search range. Default: 0.01. Valid range: 0 to 1. A finer step produces a denser candidate grid and more accurate estimation. Use 0.05 for a quick quality-control run and 0.005 for a final high-resolution pass.

Min epsilon

The lower bound of the search range for the Thomsen epsilon (ε) parameter. Default: -0.1. Valid range: -1 to 1. Epsilon represents the fractional difference between horizontal and vertical P-wave velocities and typically ranges from 0 to 0.4 in sedimentary sequences. Negative values are rare but possible; set a small negative lower bound unless there is a specific geological reason to expect anomalous anisotropy.

Max epsilon

The upper bound of the search range for the Thomsen epsilon (ε) parameter. Default: 0.1. Valid range: -1 to 1. Must be greater than Min epsilon. For shale-dominated sequences, epsilon can exceed 0.3. If the output epsilon gather shows values at the upper bound, increase Max epsilon accordingly.

Step epsilon

The increment used to step through the epsilon (ε) search range. Default: 0.01. Valid range: 0 to 1. Has the same role as Step lambda. The total candidate grid density is proportional to (range / step) for both delta and epsilon; halving both step sizes roughly quadruples the grid density and computation time.

Max distance

The maximum lateral distance (m) used to search for a matching velocity model bin when associating input seismic traces with velocity values. Default: 100 m. Set to at least half the bin spacing of your seismic dataset. Increase if you see gaps in the output where data should exist, but avoid making it so large that velocity traces from distant bins are incorrectly used.

Max offset

The maximum source-to-receiver offset (m) to include in the Thomsen parameter estimation. Default: 10,000 m. Also serves as a normalisation factor in the residual moveout equation. Set to the actual maximum usable offset in your dataset. Reducing Max offset to exclude noisy far-offset traces can improve stability of the parameter estimation.

Angle smooth window length

The half-length of the depth smoothing window applied to the computed incidence angle gather before parameter estimation (m). Default: 50 m. Smoothing reduces sensitivity to rapid velocity fluctuations that can produce noisy or unstable angle values. Set to zero to disable. Increase in areas with high-frequency velocity noise; decrease where sharp velocity boundaries must be preserved.

Semblance smooth window length

The half-length of a depth smoothing window applied to intermediate coherence computations during the parameter search (m). Default: 50 m. Smoothing the coherence panel in the depth direction suppresses noise and produces a more continuous Thomsen parameter result. Set to zero to disable. If the output delta and epsilon gathers appear noisy or laterally inconsistent, try increasing this value.