# 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 qualityThe 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 *
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.