A more advanced synthetic velocity model features Multiple layers with a linear increase in velocity as a function of depth, often referred to as V0-K velocity modelling.
The layers can be created using constant Time or depth Z values, or horizons.
Open the process tab and create a new volume maths process.
The name that you give the process will become the name of the velocity volume you create.
Select a seismic volume.
Although this is not required for 3D data,
the input volume IL/CL range can be used to quickly define the output volume range, even though the amplitude values are not part of the process.
Let's assume that velocity increases as a linear function of time,
increasing from an initial V0 of 1500 meters per second by a gradient K of 0.5 times the current timevalue.
In the Formula box type 1500 + twt_ms * 0.5.
Set the output geometry to be at least 100m by 100m in the X/Y axis and 24ms in the Z axis to keep processing time efficient.
You need to set the volume class to Interval Velocity for it to display correctly.
Set the min and max range to match the class settings.
QC the model using a section view.
Let's make the formula more complex by introducing a constant layer.
Assume that sea bed is a constant 250 milliseconds and that velocity changes at the sea bed.
In this example use the if command to compare the twt in milliseconds to a cut-off of 250.
If less than 250, set the output velocity value to 1500 meters per second,
else if more than 250, set the output velocity value to the previous linear function.
For additional layers, continue to build a nested structure where the second variable becomes a new if statement.
The updated model will display in section view if you have the syntax correct.
You can add as many nested layers to the formula as required.
To make the model more structurally variable, swap the constants for Horizons.
Enable the horizons and display in map view and section view to check they are suitable for inclusion in the model.
Add the horizons to the process variables and assign the horizon names.
Change the constant time values to the horizon variable symbols.
The model updates using the horizons as boundaries.
The same models can be used in 2D as in 3D.
Use the same procedure but select your 2D volume as the input to define the matching output geometry.
Display the 2D line with the 2d velocity for Quality Control.
Linear models can be referenced SubSea (datum 0) or can be referenced to mudline (sea bed), or any other horizon.
The current example is referenced to sea level.
To change the reference to a horizon, the datum horizon must be subtracted from the time (or depth) variable.
The equation now becomes the modified one shown in the formula box.
Because the datum has changed, the equation would need to be recalculated.
I will update the equations with newly calculated constant V0 to reflect this change.
See how the new velocity gradient follows the horizons where the previous gradient was horizontal.
Isn't it great to have such flexibility when constructing models?