4D PWD Interpolation1877 ProMAX¨ Reference

4D PWD Interpolation

4D PWD (Plane Wave Destruction) Interpolation interpolates aliased data to a finer non-aliased grid using plane-wave estimates.

Theory

Spatially aliased data present problems for dip-estimation based algorithms such as those found in many interpolation and regridding tools. Because of aliasing, a unique dip cannot be determined. This problem is addressed by interpolating data to a finer spatial grid where the data are no longer aliased. There are two steps in this process: • dip estimation • interpolation

Dip Estimation

The dip estimation uses a combination of linear and nonlinear least-squares iterations to estimate the correct dip. It simultaneously maximizes plane-wave energy fit and the spatial smoothness of dip estimates. Simultaneously maximizing both plane-wave energy fit and spatial smoothness of dip estimates tends to favor the true dips over their aliased counterparts.

Interpolation

Once the dip has been computed, the interpolation step uses plane-wave destruction to interpolate data along the estimated dips. You can choose between several plane-wave destruction operator lengths. 4D PWD Interpolation operates on overlapping 3D data "bricks" or subsets of the entire dataset. The dip is estimated at each point within each data brick, using the data from the entire brick. There is a tradeoff in choosing the brick size. A large brick size means more data contributes to the dip estimate at each point, reducing the chance that aliased dips will be selected. A large brick size also costs less since fewer least-squares dip estimation problems need to be solved. However, if dips vary across a brick (if there is event

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curvature) then dip estimates will be less accurate. A smaller brick size increases the accuracy of local dip estimates. However it costs more and also means that less data is going into the dip estimation at each point, increasing the chance that aliased dips will be selected. A general rule of thumb is to make the brick size as large as possible, but not so large that there is significant event curvature within a brick.

Input Sort Requirements

To correctly sort your data for this process, these parameters in Disk Data Input should have the following entries:

Select primary trace header entry ILINE_NO Select secondary trace header entry XLINE_NO Select tertiary trace header entry NONE Sort order for dataset *:*/ However, the 4D Input Macro* simplifies the input sort requirements. Insert 4D Input Macro* before 4D PWD Interpolation and select 1 Input, ILINE_NO:XLINE_NO order for Sort Order.

Usage

If aliased energy is present, run this process prior to aligning the two datasets with the 3D Poststack Regrid, or before other ProMAX® 4D processing steps if regridding is not needed.

Parameters

Number of input inlines

Enter the number of ILINE_NO gathers in the input dataset.

Grid compression factor, Inline direction

Enter a value for decreasing output crossline spacing. Enter 1 for no change.

Grid compression factor, Crossline direction

Enter a value for decreasing inline spacing. Enter 1 for no change.

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Number of nonlinear iterations for slope estimation

Enter the number of nonlinear iterations used for slope estimation.

Number of linear iterations for slope estimation

Enter the number of linear iterations used for slope estimation.

Number of iterations for interpolation

Enter the number of iterations for interpolation. Enter 0 for the number of iterations to be 4 * Grid compression factor, Inline direction * Grid compression factor, Crossline direction.

Slope smoothness

Enter a slope smoothness value. This parameter is used with the slope estimation parameters. Increasing this value decreases the slope estimate of every sample in the window. You would use it with noisy data. For example, noisy data can give a different epsilon at every sample. Therefore, you want to increase this value for more smoothing.

Accuracy level for plane wave destruction

Select an accuracy level for plane wave destruction from the following choices; • Level 1 is the lowest accuracy level for aliased plane- wave destruction. • Level 2 is the intermediate accuracy level for aliased plane-wave destruction. • Level 3 is the highest accuracy level for aliased plane- wave destruction. This parameter solves for filter coefficients when creating a plane wave. A planar event does not need a lot of coefficients. Also, with diffraction data, you do not want a lot of filter coefficients because the higher levels will try to fit a plane to a curve. Landmark suggests using a lower level.

Window size, Time direction

Enter the window size in samples along the time axis.

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Window size, Inline direction

Enter the window size in traces along the axis in which XLINE_NO changes.

Window size, Crossline direction

Enter the window size in traces along the axis in which ILINE_NO changes.

Replace interpolated traces?

Select Yes to replace interpolated traces with original traces when they have identical locations.

First output XLINE_NO

This appears if Grid compression factor, Inline direction > 1. XLINE_NO values are reset for output traces. Enter the XLINE_NO value for the first trace in each output ensemble. If Grid compression factor, Inline direction = 1, the first output XLINE_NO is always 1.

First output ILINE_NO

This appears if Grid compression factor, Crossline direction > 1. ILINE_NO values are reset for output traces. Enter the ILINE_NO value for the first output ensemble. If Grid compression factor, Crossline direction = 1, the first output ILINE_NO is always 1.

First output CDP

This appears if Grid compression factor, Inline direction > 1 or Grid compression factor, Crossline direction > 1. CDP values are reset for output traces. Enter the CDP value for the first trace of the first output ensemble. If Grid compression factor, Inline direction = 1 and Grid compression factor, Crossline direction = 1, the first output CDP is always 1.

Output expanded diagnostics?

Select Yes to write detailed diagnostic output.

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