# Generating synthetic stacks from Intercept and Gradient volumes

An overview of the workflow:

- Calculate reference angle stacks from the gathers (see
*Angle Stacks*). - Calculate intercept and gradient from the gathers (see
*Intercept/Gradient*). - Use Shuey's approximation to calculate the synthetic volume (see
*Volume Maths*). - (optional) Band-limit the synthetic to match the reference stack (see
*Band-pass Filter*). - Calculate the residual using Volume Maths.

## Setup

In this example, we prepared the following data:

For Angle Stacks

- Load gathers
- Load velocity model

- Draw a map polygon
- Create a window model to evaluate spectra at the target

For I/G calculation (from gathers)

- Define angle mutes
- Load gathers
- Load velocity model

Use this workflow. Repeat steps 3, 4 and 5 for additional angles.

The spectral analysis window is included as a reference.

- Yellow = Stack
- Orange = Synthetic
- Red = Filtered Synthetic
- Black = Residual

## Workflow

- Create angle stacks from the gathers. We will be using the average of the min and max stacking angle for Shuey's equation.

- Calculate Intercept and Gradient from the gathers. Use angle mutes to avoid including near-offset noise and NMO stretch.

- Use Volume Maths and Shuey's equation to calculate the amplitude using the Intercept and Gradient results for a specific angle. Note that the trigonometric functions expect radians as input (e.g. for 30 degrees).
- Formula: I + G * (sin(30*pi/180)^2)

- Depending on your data, the synthetic result may contain more high-frequencies than your angle stack, increasing the energy in the residual. By applying a bandpass filter, we can match the synthetic spectrum to the stack spectrum.