Solve Integrated Statics

This standalone process uses a robust, damped least-squares algorithm to find static corrections with picked trim lags from either 3D Reflection Correlation Autostatics or External Model Correlation. If the newer Autostatics program is used, then the solver will also use multiple picks for each lag, with appropriate reweighting during convergence. All input picked lags and correlation/quality factors are read from the database, and all solutions are written to the database. Because it simultaneously optimizes all components, this method converges better and separates components more thoroughly than Gauss-Seidel.

Statics contributions can be decomposed for any combination of five database keys: source SIN, receiver SRF, offset bin OFB, channel number CHN, and a midpoint bin number CDP. All components can be initialized or constrained separately with previous solutions. Three keys are solved by default: the surface-consistent SIN and SRF components, and a structural term using CDP midpoint bin. Any can be omitted as well.

You may want to add channel number CHN for a marine survey with a cable-consistent distortion. Offset bin OFB is appropriate if a consistent residual moveout in your time window might corrupt the solution. Without such systematic distortions, these terms will not affect the solution significantly, but will increase the solution time slightly.

The CDP structural solution avoids the unnecessary modeling and removal of reflection structure. Trim static cross-correlations assume reflections to be relatively flat and can bias the solution toward flatness. A CDP term removes much of this bias. CDP structural terms are smoothed over the number of inline and crossline bins you choose. This smoothing suppresses short spatial incoherence in the CDP solution from insufficient fold. Smoothing also avoids distortions of structure when near-offsets are lost in zones with residual moveout, particularly at the tapered boundaries of the survey.

When solving very noisy picks, you may need to increase the "Minimum fold to estimate a static" from the default value of 1. A static value will be set to zero if fewer than this number of picked lags contribute to the estimation of the static value. This fold constraint affects all SIN, SRF, OFB, CHN, and CDP static values. Usually the smoothness of the CDP solution makes this option unnecessary as a constraint on CDP alone.

Rather than use an alpha-trim mean like Gauss-Seidel to suppress picked lags with large inconsistent errors, this solver uses iteratively reweighted least-squares to approximate a least-median (L1) solution. Noise, the difference between modeled and picked lags, is assumed to have a Poisson rather than Gaussian distribution. Large isolated wild picks will receive very low weights and will not corrupt the estimated statics of corresponding keys. Iterative reweighting is applied only to errors larger than your "Expected error in fitting trim picked lags". Otherwise, weights decrease as the reciprocal of increasing errors.

Damping is important to suppress unnecessary complexity in the solution due to non-uniqueness. With a full optimization it is possible to find large perturbations of the static solution which make a small but negligible improvement to fitting the picked lags. Damping allows only perturbations that have a statistically significant effect on fitting the data. Methods such as Gauss-Seidel damp the solution by converging only partially toward a solution, with the risk of losing useful detail as well.

The damped least-squares algorithm balances a penalty for increasing the error in fitting picked lags with a penalty for increasing the magnitude of the solved static shifts. To control this damping, you specify two parameters: the "Expected error in fitting trim picked lags" (i.e. the expected magnitude of noise) and the "Expected magnitude of estimated static shifts." These are are soft constraints that express a relative bias to fit the data with smaller statics and more noise, or with larger statics and less noise. If the ratio of these two numbers (i.e. the signal-to-noise ratio) is plausible to within two orders of magnitude, you will see reasonable and consistent results.

If your solutions appear suspiciously small compared to your picked lags, then try decreasing the "Expected error in fitting trim picked lags" or increasing the "Expected magnitude of estimated static shifts." It may also be that you have given too many degrees of freedom to the solution, and that one of your components is being modeled by another. For example, OFB and CHN might coincide. Very low-fold might allow surface-consistent changes to be modeled by a rough CDP component.

If your solutions appear wild and poorly constrained, then first try increasing the "Minimum fold to estimate a static." If that is insufficient, then then try increasing the "Expected error in fitting trim picked lags" or reducing the "Expected magnitude of estimated static shifts."

You can also clip solved static values explicitly by specifying maximum magnitudes for each key, such as "Maximum magnitude for source SIN statics". Any solved value that falls outside of this range is set to NULL before writing to the output database. An excessive magnitude is assumed to be unreliable and no better than a zero value. Clipping is not applied during optimization to avoid distributing an unreliable shift over a larger number of samples. Be careful not to overlook important anomalies by routine use of small clip values. Editing of the output database values may be preferable.

§ Database entries:

If requested, this solver will look for the following database entries from 3D Reflection Correlation Autostatics. You specify the four character ID xxxx as a parameter. iiii is an automatic index for multiple picks.

      order  info      name     explanation
      ---    ----      ----     -----------
      TRC  TRMLxxxx  LAG_iiii   Trim static lag in ms
      TRC  TRMQxxxx  QLT_iiii   Correlation coefficient (optional)

Alternatively, this solver will look for the following database entries from External Model Correlation. You specify the four character ID xxxx as a parameter.

      order  info      name       explanation
      ---    ----      ----       -----------
      TRC    STATICS   TRM_xxxx   Trim static lag in ms 
      TRC    STATICS   QLT_xxxx   Correlation quality
      SIN    QC_ESTIM  X_QCxxxx   Average quality for picks (optional)
      SRF    QC_ESTIM  X_QCxxxx   Average quality for picks (optional)
      OFB    QC_ESTIM  X_QCxxxx   Average quality for picks (optional)
      CDP    QC_ESTIM  X_QCxxxx   Average quality for picks (optional)

This process will create the following database entries for components which you optimized or initialized. You can view and edit these values with DBTools. Statics are applied with Apply Residual Statics. You specify the four character ID xxxx as a parameter.

    opf  info      name      explanation
    ---  ----      ----      -----------
    SIN  STATICS   SSISxxxx  Shot static (ms)
    SIN  STATICS   QSISxxxx  Shot static quality
    SRF  STATICS   SSISxxxx  Receiver static (ms)
    SRF  STATICS   QSISxxxx  Receiver static quality
    OFB  STATICS   SSISxxxx  OFB residual moveout (ms)
    OFB  STATICS   QSISxxxx  OFB residual moveout quality
    CHN  STATICS   SSISxxxx  CHN cable correction
    CHN  STATICS   QSISxxxx  CHN cable correction quality
    CDP  STATICS   SSISxxxx  CDP structure (ms)
    CDP  STATICS   QSISxxxx  CDP structure quality

The following standard database entries are expected to exist:

    opf  info      name      explanation
    ---  ----      ----      -----------
    TRC  Geometry  SIN       Source index for each TRC
    TRC  Geometry  SRF       Receiver index for each TRC
    TRC  Geometry  OFB       Offset bin index for each TRC
    TRC  Geometry  CHN       Channel number for each TRC
    TRC  Geometry  CDP       CDP index for each TRC
    CDP  Geometry  ILINE     Inline index for each CDP
    CDP  Geometry  XLINE     Crossline index for each CDP
    SIN                      Must have a meaningful dimension defined.
    SRF                      Must have a meaningful dimension defined.
    OFB                      Must have a meaningful dimension defined.
    CHN                      Must have a meaningful dimension defined.

§ Parameters

Use internal or external model trim picks?

Choose "internal" (default) if your picks were prepared by 3D Reflection Correlation Autostatics. Choose "external" if your picks were prepared by External Model Correlation.

4 character ID for internal model trim lag picks (or none)

These four characters are the same as the unique string you supplied to 3D Reflection Correlation Autostatics. The corresponding database entries are not required to exist at the time that this flow is created, so correlations and static solution can be placed in the same flow. Existence will be checked at run time only.

4 character ID for input external model picks (or none)

These four numbers are the same as the default 0000 or whatever unique number you supplied to External Model Correlation. The corresponding database entries are not required to exist at the time that this flow is created, so that correlations and static solution can be placed in the same flow. Existence will be checked at run time only.

4 character ID for output statics database

Specify a four character string (alpha-numeric) to specify uniquely the output database names.

Do you want to provide initial values for statics?

Select "yes" if you want use previous solutions (perhaps after editing) from a previous run of this solver. You can initialize any subset of your static components and re-optimize any other subset. Default: no.

4 character ID to initialize SIN statics (or none)

Select the four characters that uniquely specify the SIN solution written to the database previously by this solver. Default: none.

4 character ID to initialize SRF statics (or none)

Select the four characters that uniquely specify the SRF solution written to the database previously by this solver. Default: none.

4 character ID to initialize OFB statics (or none)

Select the four characters that uniquely specify the OFB solution written to the database previously by this solver.

4 character ID to initialize CHN statics (or none)

Select the four characters that uniquely specify the CHN solution written to the database previously by this solver. Default: none.

4 character ID to initialize CDP statics (or none)

Select the four characters that uniquely specify the CDP solution written to the database previously by this solver. Default: none.

Do you want to (re)estimate source statics for SIN?

Choose whether this component should be included in the optimization. If not, then the values will be assumed zero, or left at the input initialized values. Default: yes.

(Re)estimate receiver statics for SRF?

Choose whether this component should be included in the optimization. If not, then the values will be assumed zero, or left at the input initialized values. Default: yes.

(Re)estimate residual-moveout offset statics for OFB?

Choose whether this component should be included in the optimization. If not, then the values will be assumed zero, or left at the input initialized values. Default: no.

(Re)estimate cable-consistent channel statics for CHN?

Choose whether this component should be included in the optimization. If not, then the values will be assumed zero, or left at the input initialized values. Default: no.

(Re)estimate structural statics over CDP?

Choose whether this component should be included in the optimization. If not, then the values will be assumed zero, or left at the input initialized values. Default: yes.

Robust iterative reweighting for L1 statistics?

If "yes" (default), then data errors larger than the expected error in fitting trim picked lags will be given less weight. This option approximates a median fit to the data. Reweighting doubles the run time.

Weight data with correlation coefficients?

If "yes" (default), then input correlation coefficients will be used to weight data misfits. If "no," then all input picks will be given equal weight. NULL picks are ignored either way.

Expected error in fitting trim picked lags (ms) for damping

Specify a reasonable magnitude for the noise corrupting input picks. A smaller value encourages more precision in fitting input lags and less damping of the static solution. See the fuller explanation above. Default: 4 ms.

Expected magnitude of estimated static shifts (ms)

Specify a reasonable magnitude for the estimated statics. A smaller value increases the damping of the statics solution, and increases the error in fitting input lags. See the fuller explanation above. Default: 100 ms.

Maximum magnitude for source SIN statics (ms)