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.
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.
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.
Bill Harlan, 1999
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