# Time-Variant Amplitude Matching

In this workflow, we’ll use a combination of DUG-Insight processes to create a time-variant scaling function to better match volume amplitudes.

The workflow matches amplitudes by calculating the RMS over a sliding window and generating a single gain function as a trace. This function is extrapolated to cover the area of the volume to correct, then applied.

Example: The image below shows two volumes. The target volume on the left has amplitudes that we would like to match in our uncorrected volume. The volume on the right needs amplitude adjustment to match the target.

The output from this workflow:

## Workflow

1. Use Volume Resampling to regrid the target volume to the uncorrected volume grid.  a.   Choose the regridded target volume.
b.   Select RMS within a window.
c.   Enter a window length. Adjust the window length to increase or decrease the vertical resolution
of the scaling function.
d.   Use a 50% overlap.
e.   Set lateral smoothing radius to 0.

1. This creates two volumes:

a.   An AGC result (not used)
b.   A gain result - the gain applied when calculating the AGC

1. Create a second AGC process. a.   Select the uncorrected volume.
b.   Use the same AGC settings as applied previously to the target volume. The settings must match!
c.   Now you have an RMS scalars volume for both target and uncorrected volume.

1. Calculate the relative gain using Volume Math (simple). a.   Divide the Uncorrected Scalars by the Target Scalars
b.   The result is a relative gain, calculated spatially for the overlapping area of the two volumes.

1. Spatially smooth the relative gain to avoid trace-trace variation. a.   Use Volume Smoothing on the relative gain result.
b.   Set the vertical smoothing radius to zero
c.   Choose a large enough IL and CL direction to get a “background” trend.
d.   Use a larger radius if there are large spatial changes in amplitude.

Important: If the smoothing radius is not large enough, the result may be biased by local variation.

At this point, the smoothed relative gain volume varies by location and time (spatial and temporal). If the two volumes overlap completely and a spatial & temporal adjustment is required, then apply (multiply) this gain volume to the uncorrected data using Volume Math (simple). See the last steps of this workflow for an example.

1. Review the smoothed relative gain result and choose a location (IL/CL) which has a good matching function.

a.   Choose this location carefully! This gain function will be applied to the entire uncorrected volume.

1. Select the single gain trace at the chosen location from the smoothed relative gain using Volume Resampling. a.   Enter the IL/CL location in the output extents for both the minimum and maximum values.

1. Extrapolate the single trace to cover the area of the uncorrected volume using Volume Interpolate/Extrapolate. a.   The default parameters do not need changing.
b.   Make sure [ ] Extrapolate is checked.
c.   Select the survey of the uncorrected volume and update the extents.

1. Apply the extrapolated scaling function to the uncorrected volume using Volume Math (simple). a.   Select the uncorrected volume.
b.   Choose multiple (x volume).
c.   Select the extrapolated scaling function.

The result of this process is the amplitude scaled result. View and compare the results in an IL/CL View or an arbline.

To tune up or adjust the results, try changing:

1. The length of the AGC windows

a.   Smaller windows create a more detailed (higher resolution) gain function.
b.   Longer windows create a “background” amplitude trend.