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# Time Depth Conversion using a Volume Polynomial Function

 TIPS & TRICKS Time Depth Conversion using a Volume Polynomial Function

Derive a third order polynomial function to define the interval velocity at any time value in the project area. A third order polynomial has the following structure where A, B, C, and D are constants.

Velocity = A*twt_ms^3 + B*twt_ms^2 + C*twt_ms + D

Note: A third order polynomial is a complex function but it is also possible to define velocity as a less complex second order polynomial, a first order linear regression, or even a constant value.

In the following example, the interval velocity function has been calculated as a function of time as follows:

Velocityint = (-1.02*(twt_ms/1000)^3) + (30.2*(twt_ms/1000)^2) + (995.2*(twt_ms/1000)) + 1150

Where twt_ms is the two-way-time (twt in milliseconds) of any location in the project area.

## Part 1: Create a velocity volume from Velocity function and set it as active

1. In the Process Tab, click the Create (+) button, and add a new Volume Maths process.
2. Provide a name for the velocity model. An example is Velocity-polynomial.
3. In the Input Volumes section, select the seismic volume for your area. This expedites the definition of X, Y, and Z extents of the output.
4. Input the formula in the Formula field. Mistakes will be highlighted for you to correct.
5. Adjust the Output Extents to have an increment of 100m x 100m x 24ms, which should be adequate sampling for most datasets, whilst providing high performance.
1. Next, open the Volume tab. The volume is defined with the same class as the seismic selected as an input to the formula. Change the Class to Velocity (Interval).
2. Set the min/max values in the Range fields to a sensible range for your project area.
1. QC your volume in a section view. Check the velocity at the top of the section and the base to make sure they are sensible values.

Note: The velocity in this example only uses twt_ms as an input variable and so has a horizontal layered appearance that cuts across structure. To have function that also follows structure, you would need to add one or more horizons into the formula.

1. Finally, set the velocity model in the Configure Time/Depth Conversion window.

Optionally, export velocity volumes to the disk (fixed). Exporting the velocity volume to a disk file will speed up the performance of time depth calculations because the calculation from time to depth is done once during export and then read from disk for future conversion. The system load is transferred from the CPU to the disk & network.

To do this, navigate to the Volume tab, right click on the Velocity volume > Export.

Be sure to select the Add to session when export completes option.

Finally, update the velocity selection to your new disk volume in the  Configure Time/Depth Conversion window.

### Part 2: Time Depth convert sections (on the fly)

1. In the section, view flip the Domain value in the top left corner of the window to TVDSS to see all the section data (seismic, horizons, faults, wells) in TVDSS.

You can also export the seismic traces to disk to speed up the performance of depth displays by reading the depth from the disk instead of calculating it each time. The system load is transferred from the CPU to the disk & network.

To do this, follow the steps below:

1. In the Volume tab, right-click on the seismic volume, and select Export.
2. In the Vertical Extents section, select the Override option, and set the domain to TVDSS (m).
3. Set an appropriate TVDSS range for your project area.
4. Select the Add to session when export completes option.
5. Click OK.

Remember to change the volume selection to the new disk volume in the section view.

## Part 3: Time Depth convert horizons (on the fly)

In the map view, there are two places to perform time depth conversion.

Option 1: The Domain value on the top left controls the time-depth conversion of volumes and slice-based data such as fault intersections. Change the domain to TVDSS to dynamically convert from time to depth.

Option 2: The Horizon display has its own independent time-depth conversion controlled by the horizon property, set the property to TVDSS to dynamically convert the horizon to depth.

You can also export the depth horizon to the disk to speed up the performance of depth displays by reading the depth from the disk instead of calculating it each time. The system load is transferred from the CPU to the disk and network.

There are three methods to do this:

• After displaying the horizon in-depth, right-click the horizon, and select Save horizon as a custom property. Select the custom property for display instead of the dynamically converted version.
• In the Operations tab, use the Horizon Maths operation to calculate the TVDSSS property and output it to a new horizon or property.
• Right-click and export the horizon from the control panel. Select the custom export and choose TVDSS as the Z value. Import the file as a new TVDSS horizon.