ravn: Two Dimensional Scaling

Introduction

Many attempts have been made, in the past, to provide a range variant scaling routine that compensated for decay due to geometric spreading [spherical divergence] while preserving relative amplitude information. Most were flawed in that they estimated the decay surface of a given endpoint record through two dimensional sampling in time then independently in space. This resulted in a gain surface that could only fit some average of the spatial decay function over a given record. ravn however, uses a full three dimensional algorithm to fit the decay surface of a seismic record concurrently in space and time, thus having the capability of fully preserving relative amplitude information while correcting for the effects of spherical divergence.

The Decay Surface

An estimate of the gain surface required to correct for the amplitude decay of an input record (Fig. 1) is calculated using a median agc operator. This surface (Fig. 2) is too rugose to accurately compensate for amplitude decay and if applied to the data would make impossible the resolution of relative amplitude variations with offset. The ravn algorithm is capable of calculating a robust fit to this surface, resulting in an optimum order gain correction which when applied to the data preserves relative amplitude information (Fig. 3).

The Algorithm

The principal algorithm consists of the following logic:
1. compute, using a median agc operator, a gain surface to scale the input record.
2. sample this surface as defined by command lineinput parameters for trace and sample decimation.
3. calculate [with a user defined number of iterations of re-weighted least squares] the coefficients describing a best fit of order N to the agc gain surface.
4. calculate a regression coefficient and F-test value for statistical significance at this order.
5. repeat steps 3 and 4 over a program determined range of orders.
6. determine which of the orders of fit tested provides the optimum, statistically significant fit with respect to the input data.

Once the optimum order of fit has been determined, that order along with the coefficients required to construct the surface are recorded.

At this point the following addition to the algorithm is optional:

1. for each individual trace, the median of the residuals between the agc gain surface and that calculated by the above algorithm is computed.
2. the agc gain surface is then adjusted to compensate for this residual.
3. the modified agc gain surface is again passed through the principal algorithm yielding an updated surface and corresponding set of coefficients.
4. this process is iterated a user defined number of times.

This enhancement allows ravn to compensate for those traces that have anomalous amplitude relationships with respect to the rest of the record as would occur due to instrumentation difficulties and/or coupling variations.

At this point the calculated gain surface is applied to the data (Fig. 4). Contrast this result with that obtained using an agc alone (Fig. 5). The latter suffers from the usual shortcomings associated with the agc process, washed out [low amplitude] zones near high amplitude events and a bright [high amplitude] onset to the data due to the algorithm used to scale samples within the first half window length of the agc operator.

Consider a data example where trace to trace variations are severe (Fig. 6). The amplitude decay due to spherical divergence is complicated by the differences in channel amplification imparting a striped texture to the record. Using ravn to scale this data, executing only the principal part of the algorithm [no median trace amplitude adjustment], results in a correction for spherical divergence but leaves the striped texture which is particularly obvious over the last hundred or so traces of the record (Fig. 7). To reduce this striping ravn was rerun utilizing the median trace amplitude adjustment option. The resulting record (Fig. 8) displays an improved continuity over the zone of interest [2.0 to 2.8 seconds] but a totally unsatisfactory result shallow. Which result is preferable is a function of the goal of the processing.

Post Ravn Scaling

Since ravn is a record constant process any record to record amplitude variations [due to source coupling for instance] will be preserved in the output. It is advisable to run a record constant median gasp after the ravn to compensate for these variations.

Coefficients Files

ravn creates the coefficients file RavnCoefs each time it is run. This file contains information concerning the polynomial order of the gain surface and any median trace adjustment scalars for each input record. This file may be accessed by a future ravn run to remove or re-apply the gain calculated by the first iteration of the program without having to go through the surface generation routine [thus reducing run time]. The gain may be applied/removed either with or without the median amplitude adjustment.

Program gasp, when run in the record constant mode, also generates a coefficients file entitled GaspCoef which may be used to remove or reapply the gasp scaling. The GaspCoef file may be plotted using xgraph to give you a quick graphical look at the record to record variations across your dataset.

ravn [In Practice]

The following is an example of the command line entries used and coefficients file output examined in a ravn application.

Prior to running the routine it is mandatory that an onset mute be applied to the data.

editt -N raw -R 025 |
bdmute -P mutePicks -M on -O rawMute

The program recognizes the start of your data as the first non-zero sample in the trace time series. If your data does not have hard zeroes prior to the onset of real data and you do not mute prior to running ravn, very disastrous results are likely to occur as ravn will treat the garbage amplitudes above your data as contributing to the overall decay surface of your record.

A typical flow for parameter testing would be:

ravn -N rawMute|
gasp -rec -med -O testRavn

This will generate an output dataset which has been scaled, had median trace amplitude adjustment applied [the default] and had record to record median amplitude variations compensated for. The output coefficients files should now be renamed prior to any further testing or risk being overwritten on subsequent executions of the routines.

mv RavnCoefs RavnCoefsDefaults
mv GaspCoefs GaspCoefsDefaults

To view the results without trace to trace median amplitude adjustment run:

ravn -N rawMute -C RavnCoefsDefaults -coef |
gasp -rec -med -O testRavnNoMed

To view the gain surface generated with median trace amplitude adjustment run:

ravn -N rawMute -C RavnCoefsDefaults -G -coefmed -O rawRavnGain

or without median trace adjustment:

ravn -N rawMute -C RavnCoefsDefaults -G -coef -O rawRavnNoMedianGain

To remove the previously applied gain function run:

ravn -N testRavn -C RavnCoefsDefaults -coefmed -R |
gasp -C GaspCoefsDefaults -R -O rawGainRemoved

The above functionality allows one to apply gain, perform some type of processing [perhaps filter out direct arrivals or some problem noise event] then remove the gain. At this point the data could again be input to ravn for scaling with the deleterious effects of the above noise events removed.

ravn may be applied to any type of data to do amplitude balancing. If applying the process to post-stack data be certain to adjust the line header so that the data appears as one multi-trace record [this can be done using utop].

The program may even be run on map data, for example:

xyz2sis -N input |
ravn |
xyz2sis -R -O inputScaled

Again, be careful to rename the output coefficients file if you anticipate the need to re-use the result.

Runtime Considerations

There are several command line options that have a significant affect on the program runtime and should be thoroughly tested prior to processing your entire dataset. These are:

-iter the number of iterations used in median amplitude adjustment.

-sstep the sample step size [in milliseconds] used in decimating the agc gain surface. The smaller the number, the more data values will be gleaned from the surface for input to the robust fit algorithm.

-tstep the trace step size [in traces] used in decimating the agc gain surface. The smaller the number, the greater the number of data values will be passed to the robust fit algorithm.

-ilim the number of iterations to use in the weighted least squares fit of each order tested.

-ord the maximum order of fit to test.

These entries have a major effect on program run time. For instance, a 240 trace record of 2000 samples per trace requires about 40 seconds for execution [sparc 10, 40 series] using the default parameters. By halving the sstep and tstep entries the run time balloons to 5 minutes. By also boosting the iter and ilim parameters, run times in excess of 15 minutes are possible.

Hints For Run Time Minimization

Once you have finished parameter testing [especially on the above parameters] and are ready to process your entire dataset take a last look in the test coefficients file and make a note of the highest order of fit utilized. The following is an example of a coefficients file generated from a run on a record containing 120 traces:

1 3 10
2.7504248280674
2.1760460401234
5.5287304063947D-02
2.4995855927238D-02
-7.0404613392863D-03
-4.6123484337024D-05
-2.4520132377755D-05
-2.1881179727191D-05
5.6300200407620D-06
1.0192583114423D-07
1 -8.8198670655956
2 -4.4478562175573
3 -1.0434968292528
4 -2.8540453478965
5 2.9751945117894
6 4.8856963471932
7 -7.7204010086053
8 -12.226606111248
9 1.7779303540078
.
.
.
120 58.382315275584

The first line of the file contains the [record number, fit order, number of coefficients] for the gain surface used for this record. This is followed by the actual coefficients required to construct the gain surface. Finally are 120 lines, each of which contains a pair of numbers representing the [trace number, median adjustment scalar] for the record.

Use a -ord of the largest order of fit encountered. By default the program will look at several orders above this value. If you do not require median trace adjustment enter -iter0 and -coef which will prevent these calculations from be carried out.

Pitfalls

One major pitfall to avoid is undersampling the gain surface, during trace and sample decimation, prior to the calculation of the robust fit. This may occur, for instance, if:
1. the input dataset has a large number of dead traces per record. Undersampling may result as Ravn both recognizes and ignores these traces during the trace and sample decimation. Care taken during derivation of the tstep and tstart parameters should help avoid this problem.

2. your input dataset has live traces containing data which extends over a temporal interval less than the agc window length. No samples with be gleaned from these traces for input to the robust surface fit. This may occur on data having very long offsets and either a coarse sample interval or a relatively short trace length.

Adequate parameter testing prior to your actual processing run should help you avoid the above. However, as this algorithm is in it's formative stages there may exist other pitfalls which have not made themselves known as of yet. Should you encounter a new one please give one of us a call.

Track Record

To date, ravn has been run on data from the North Sea, Gulf of Mexico, China Sea, Canadian Foothills, Gulf of Suez and data from multi-component shear recording Mid Continent USA. In all cases the output provided correction for spherical divergence and increased resolution of spatial amplitude variations. In some cases the median trace adjustment was useful, in others it was dangerous so tests should be run both with it turned on and off. Please give this code a workout in your processing and call us if you run into trouble or just wish to talk.

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