Calculating Angle of Incidence

Angle of incidence can be useful in analysis and in calculations. While angle-mutes, raytraced using a velocity model, are the most accurate means of displaying the intercept angle, they can be awkward to use analytically. The two methods shown here calculate an angle of incidence for use in other calculations.

Methods:

Approximate Method

This method finds the angle of incidence assuming a straight-ray cast from the offset to the calculated point. This flow creates gathers of incidence angle, from which you can extract amplitudes from as you would any other volume.

It requires:

  • Velocity Model
  • Gathers (to define the offset extents)
  1. To Calculate depth values sampled in time from the velocities, click Process tab >> add New Process >> Velocity Conversion.
  2. Add a name for this Velocity Conversion process and set the values below:
    • Input: Velocity Model
    • Output type: Depth values sampled in time (ZT)
  1. Calculate the angle of incidence at each offset. Go to Process tab >> add New Process >> Volume Maths
  2. Add a name for this Volume Maths process and set the values below:
    • Input: Gathers [v1]
    • Input: Velocity-DepthInTime ("Vels_ZT") [v2]
    • Formula: ( atan ( offset / ( 2 * v2 ) ) ) ( 360 / ( 2 * pi ) ) + ( v1 * 0 )
  3. Set the class of the "AngleOfIncidence" volume to a new class "Angle" and choose a useful colourbar (e.g. Banded-Decile-Light) with the range 0 to 100. Read Classes and Colourbars Overview.

Accurate Method

This method, derived from the NMO equation, finds a more accurate angle of incidence.

Given:

  • G0 : A volume of gathers, to define the offset extents (metres)
  • Vint : The velocity model, converted to interval velocity (m/s)
    • Use a Velocity Conversion process if necessary.
  • Vrms : The velocity model, converted to RMS velocity (m/s)
    • Use a Velocity Conversion process if necessary.

Create a volume maths process, using the above volumes as inputs:

  • Formula
asin(sqrt(
    (
        (offset*offset) * (Vint*Vint) 
    ) / (
        (Vrms * Vrms) * 
        (twt_ms/1000 * twt_ms/1000 * Vrms * Vrms + offset * offset)
    )
)) * (180/pi)

The process looks like:

And the result:

In this example, two mutes at 10 and 20 degrees are displayed over a group containing the angle of incidence (accurate method, in colour) over offset gathers (in grey). the mutes correspond to changes in angle using a banded colour bar and appropriate ranges.