Physics Models and Analysis Theory#
This page explains the advanced models and analytical theories implemented in gwexpy for handling specific physical phenomena and hardware responses.
Response and Coupling Functions#
Automatic Excitation Detection#
Extracts stable intervals for analysis from data containing injections (such as swept sine or stepped sine). By tracking power in specific frequency bands on a spectrogram, it identifies segments that exceed thresholds, eliminating the need for manual time-range specification.
Coupling Function (:term:Coupling Function; CF)#
Estimates coupling functions while accounting for background noise. By comparing power during injection and background periods for both the target and witness signals, it isolates the true coupling degree.
Variable |
Definition |
Physical Meaning |
|---|---|---|
\(f\) |
Frequency |
Frequency point for analysis |
\(P_{\text{tgt,inj}}(f)\) |
Target signal power (during injection) |
Power distribution of the main signal during excitation |
\(P_{\text{tgt,bkg}}(f)\) |
Target signal power (during background) |
Noise floor of the main signal without excitation |
\(P_{\text{wit,inj}}(f)\) |
Witness signal power (during injection) |
Power of the reference signal (e.g., environmental noise) |
\(P_{\text{wit,bkg}}(f)\) |
Witness signal power (during background) |
Noise floor of the reference signal without excitation |
Related API: Analysis (
gwexpy.analysis.coupling.estimate_coupling)
Coherence (:term:Coherence)#
TimeSeries.coherence(), TimeSeriesDict.coherence(), and the BruCo engine’s FastCoherenceEngine.compute_coherence() all return the magnitude-squared coherence \(\gamma^2(f)\), following the convention used by scipy.signal.coherence and gwpy:
Variable |
Definition |
|---|---|
\(S_{xy}(f)\) |
Cross spectral density between \(x\) and \(y\) |
\(S_{xx}(f)\), \(S_{yy}(f)\) |
Power spectral densities of \(x\) and \(y\) |
\(\gamma^2\) is bounded in \([0, 1]\): values near 1 indicate a strong linear relationship between the two channels at that frequency; values near 0 indicate no linear relationship (or a noise-dominated measurement).
Throughout the docs, “Coherence” refers to \(\gamma^2\) unless explicitly labeled otherwise. When a page needs the amplitude ratio (e.g. to scale an ASD by the coherent fraction, as in noise projection), it uses \(\sqrt{\gamma^2}\) explicitly and labels it accordingly (e.g. “Coherence Amplitude”).
Related API: Time Series (
TimeSeries.coherence), Analysis (gwexpy.analysis.bruco)
Built-in Noise Models#
Provides physically motivated noise generators for use as initial models in simulations or fitting.
1. Schumann Resonance (:term:Schumann Resonance)#
Models magnetic noise corresponding to the resonance modes of the Earth-ionosphere cavity. It reproduces the low-frequency magnetic background by superimposing multiple independent Lorentzian profiles.
Related API: Noise (
gwexpy.noise.magnetic.schumann_resonance)
2. Voigt Profile#
Generates peak shapes found in atomic physics or high-Q mechanical resonances, which combine Gaussian (Doppler broadening, etc.) and Lorentzian (collision/natural broadening, etc.) characteristics. It is calculated efficiently using the Faddeeva function.
Related API: Noise (
gwexpy.noise.peaks.voigt_line)
Advanced Analysis Engines and Algorithms#
1. Independent and Principal Component Analysis (ICA/PCA)#
The ICA/PCA implementation in gwexpy provides preprocessing and metadata behavior intended for physical-data workflows:
Unit Variance Standardization: Standardizes data to unit variance internally to improve convergence, then restores (re-scales) the original physical scale after computation.
Spatio-temporal Metadata Inheritance: Automatically inherits the GPS time conventions from the input data for each statistically extracted component.
Related API: Signal Processing (ICA, PCA)
2. Fast Correlation Engine (:term:Bruco)#
The FastCoherenceEngine supports batch coherence scans over auxiliary channels for a target signal.
FFT Caching: Reuses FFT results for a common target signal in memory.
Sparse-like Computation: Skips non-correlated channels early to focus resources on significant contributors.
Related API: Analysis (
gwexpy.analysis.bruco.FastCoherenceEngine)
3. Bayesian Inference and GLS Fitting#
Handles parameter estimation for multidimensional data with complex error structures.
GLS (Generalized Least Squares): Applies statistically justified weighting when bins at different frequencies have correlated (non-diagonal) covariance.
MCMC Integration: Uses
emceefor posterior sampling, enabling robust fitting even for non-linear physical models.Related API: Analysis