🌊 Binary Tree Sampling for Seismic Data

Seismic Data Context

Imagine you have 64 seismic slices from a 3D cube. Instead of taking consecutive slices (which might miss geological features), binary tree sampling ensures good spatial coverage:

Selected slices (red) are distributed across the entire volume

Dataset Size: 20

Sample Size: 7

Dataset Visualization

Red lines show selected sample positions in the dataset

Binary Tree Structure

Each level shows how the algorithm recursively divides the range and selects samples

Algorithm Steps:

Step 1: Find midpoint of range [start, end] and select it

Step 2: Calculate remaining budget (size - 1)

Step 3: Split remaining budget between left and right halves using ceil/floor

Step 4: Recursively sample left half [start, midpoint) and right half (midpoint, end]

Step 5: Combine all samples and optionally sort them

Why This Works for Seismic Data:

Spatial Coverage: Samples are distributed across the entire dataset range
Hierarchical Structure: Ensures representation at multiple scales
Balanced Sampling: Avoids clustering samples in one region
Geological Relevance: Captures features across different depths/positions