Overview
MUSA is a Python framework for fractal and multifractal analysis of spatial data, with a primary workflow for geological lineament layers in GIS environments.
For lineament studies, MUSA measures the total line length intersected by each grid cell. This preserves structural intensity and avoids reducing the pattern to simple presence or absence.
Motivation and Context
Fractal and multifractal methods can describe spatial complexity in structural geology, but their use in applied interpretation often depends on fragile workflows, incomplete diagnostics, or poorly documented scale choices.
MUSA was developed to make that workflow explicit, reproducible, and inspectable. It combines global spectrum estimation, local mother-cell analysis, reliability flags, and GIS-ready outputs for structural interpretation.
Method
The current implementation uses the direct Chhabra-Jensen method for the singularity spectrum and reports generalized dimensions across the selected q range.
- Global analysis of generalized dimensions Dq, mass exponent tau(q), alpha, and f(alpha)
- Local mother-cell analysis with probability normalization inside each analysis window
- Explicit support for q values from negative to positive ranges, subject to quality filtering
- Regression quality control for Dq, alpha, and f(alpha)
- GIS input through lineament layers and boundary polygons in metric coordinate systems
Reliability Controls
MUSA includes a zeta reliability weight for local regression. Zeta combines coverage, relative mass, scale position, and effective occupied boxes to help identify mother cells where local estimates are better supported.
Zeta is treated as a reliability weighting and diagnostic layer, not as a replacement for the canonical multifractal estimator.
Additional robustness tools include optional bootstrap intervals, Theil-Sen slopes, jackknife sensitivity, leverage diagnostics, Cook distance, negative-q probability flooring, and reliability flags for local products.
Outputs
The framework exports tabular and visual products designed for GIS review and technical reporting:
- Global analysis report with accepted q values, Dq, tau, alpha, f(alpha), and fit quality
- Scale diagnostics for global and local regressions
- Mother-cell products for alpha, f(alpha), weighted alpha, weighted f(alpha), zeta, reliability, and structural intensity
- Maps for weighted alpha, zeta, density, dominant azimuth, and lineament measure
- Plots for multifractal spectra, Dq versus q, fit quality, and local weighted spectra
Evidence Status
The current evidence package uses the Broken Hill lineament case with a 4000 m mother cell, divisors 2, 4, 6, 8, and 16, q values from -4 to 4, and an R2 filter of 0.9.
That run accepted 9 of 9 q values, produced Dq values from 1.3029 to 1.5948, and generated 598 mother cells with local q=2 results. The q=2 reliable fraction was 0.5268, which supports using reliability filters instead of mapping every local estimate without qualification.
Synthetic validation currently covers 30 cases across six scenarios, including uniform 2D, clustered faults, anisotropy, power-law lengths, sparse mother cells, and crossing networks. The project remains in development, with geological validation against independent layers planned as the next methodological step.