# Solve Integrated Statics
This standalone process uses a robust, damped leastsquares
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 GaussSeidel.
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 surfaceconsistent 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 cableconsistent 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
crosscorrelations 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
nearoffsets 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 alphatrim mean like GaussSeidel to
suppress picked lags with large inconsistent errors, this
solver uses iteratively reweighted leastsquares to
approximate a leastmedian (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 nonuniqueness. 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 GaussSeidel
damp the solution by converging only partially toward a
solution, with the risk of losing useful detail as well.
The damped leastsquares 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
signaltonoise 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
lowfold might allow surfaceconsistent 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 (alphanumeric)
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 reoptimize 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 residualmoveout 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 cableconsistent 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)

The absolute value of estimated static values cannot exceed this value.
Values that would be larger will be set to NULL. Default: 100 ms.
 Maximum magnitude for receiver SRF statics (ms)

The absolute value of estimated static values cannot exceed this value.
Values that would be larger will be set to NULL. Default: 100 ms.
 Maximum magnitude for offset OFB statics (ms)

The absolute value of estimated static values cannot exceed this value.
Values that would be larger will be set to NULL. Default: 100 ms.
 Maximum magnitude for channel CHN statics (ms)

The absolute value of estimated static values cannot exceed this value.
Values that would be larger will be set to NULL. Default: 100 ms.
 Maximum magnitude for structural CDP statics (ms)

The absolute value of estimated static values cannot exceed this value.
Values that would be larger will be set to NULL. Default: 100 ms.
 Min trace offset MAGNITUDE for inclusion in analysis

Do not include offsets with absolute values less than this value.
Default: 0.
 Max trace offset MAGNITUDE for inclusion in analysis

Do not include offsets with absolute values larger than this value.
Default: 999999.
 Minimum fold to estimate a static

No static value will be estimated for a key that has fewer
contributing input lags than specified here. Increase the default
of 1 for noisy data that is producing unreliable estimates.
Fold for a component key is calculated by adding adding together
the normalized correlation coefficients of all picks that share
this static contribution. See fuller explanation above.
 Number of inline samples to smooth CDP structure term

The estimated CDP static structural term will be smoothed by
a filter with this halfwidth in the inline direction.
See fuller explanation above. Default: 15.
 Number of crossline samples to smooth CDP structure term

The estimated CDP static structural term will be smoothed by
a filter with this halfwidth in the crossline direction.
See fuller explanation above. Default: 15.
Bill Harlan, 1999