ArchGEM: Gravitational Wave Noise Analysis

• ArchGEM is a specialized software framework that characterizes non-Gaussian noise, specifically scattered light glitches, in gravitational wave strain data.
• It employs Q-transform derived time-frequency representations along with peak-finding and Gaussian mixture model clustering to extract physically interpretable parameters.
• Its output metrics, including scattering recurrence frequency and surface displacement, enhance signal discrimination and support improved detector performance.

ArchGEM is a software framework developed for the characterization of non-Gaussian noise artifacts in gravitational wave (GW) strain data, with particular emphasis on identifying and extracting physically interpretable parameters associated with scattered light glitches. In the analysis of GW231123—a "lite" intermediate mass black hole (IMBH) merger—ArchGEM played a critical role in disentangling instrumental noise from astrophysical signals by implementing advanced density estimation and clustering techniques.

1. Purpose and Context in Gravitational Wave Data Analysis

ArchGEM addresses the challenge of diagnosing non-Gaussian noise artifacts that can obscure or distort gravitational wave signals in interferometric detectors such as LIGO and Virgo. Specifically, scattered light glitches—arch-like features below 40 Hz in time–frequency representations—pose significant obstacles to accurate event identification and waveform reconstruction. In the analysis of GW231123, an event marked by high total mass (∼190–265 M⊙) and complex detector environment, ArchGEM facilitated robust noise characterization and contributed to the validation of the event’s astrophysical nature (Chatterjee et al., 11 Sep 2025).

2. Workflow: Time–Frequency Representation and Feature Extraction

The analytical pipeline for ArchGEM commences with the transformation of GW strain data into a time–frequency spectrogram via a Q-transform. This produces two-dimensional representations where scattered light glitches manifest as distinct arches in the sub-40 Hz frequency domain. Within an 18-second window surrounding the GW event, ArchGEM applies two principal feature extraction methods:

• Peak-Finding Algorithm: Extracts local maxima in frequency as a function of time. These detected peaks serve as initial candidates for clustering.
• Gaussian Mixture Model (GMM) Clustering: Operates directly on the set of time–frequency–energy points extracted from the spectrogram.

3. Gaussian Mixture Model–Based Soft Clustering

The heart of ArchGEM is a soft clustering methodology using Gaussian mixture models (GMMs). The probability density function over a $d$-dimensional point $x$ is modeled as:

$$p(x) = \sum_{k=1}^{K} \pi_k \, N(x | \mu_k, \Sigma_k)$$

where $\pi_k$ is the weight of the $k$-th Gaussian component, $\mu_k$ its mean, and $\Sigma_k$ its covariance matrix. In the GW231123 application, $K=9$ was selected for tractable representation of scattering features. The soft assignment approach allows each data point to belong probabilistically to multiple clusters, which is essential for representing the overlapping nature of arch-like glitches. The clustering output revealed centroids concentrated at lower frequencies, with an average maximum arch frequency $f_{\text{max,avg}} \approx 11.13$ Hz, affirming the identification of the scattered light feature.

4. Density Approximation and Extraction of Physical Parameters

Leveraging the clustered time–frequency maxima, ArchGEM computes physically interpretable parameters from the glitch population:

• Scattering Recurrence Frequency: Calculated from the peak timing distribution, found to be $f_{\text{scat}} \approx 0.19$ Hz.
• Surface Displacement: Derived from $f_{\text{scat}}$, yielding $x_{\text{surf}} \approx 0.11$ μm.
• Average Surface Velocity: Estimated as $v_{\text{surf,avg}} \approx 0.41$ μm/s.

These metrics provide unique insight into the mechanical and environmental state of the interferometer optics, directly informing commissioning and mitigation strategies.

5. Integration with Machine Learning Analysis Pipelines

ArchGEM was incorporated into a broader machine learning pipeline alongside GW-Whisper and AWaRe. GW-Whisper, an adaptation of OpenAI's audio transformer, autonomously classified data segments as containing a GW signal or noise. AWaRe, a probabilistic convolutional autoencoder, reconstructed the background-subtracted waveform for robust signal inference. ArchGEM’s clustering and parameter extraction were essential in distinguishing true GW features from noise-induced artifacts, and its outputs corroborated the astrophysical origin of the signal segment identified with >70% confidence.

Table: ArchGEM in the GW231123 Pipeline

Tool	Function	Output Type
ArchGEM	Soft clustering of glitch features, physical metrics	$f_{\text{max,avg}}$, $f_{\text{scat}}$, $x_{\text{surf}}$, $v_{\text{surf,avg}}$
GW-Whisper	Segment classification (GW/no noise)	Segment labels
AWaRe	Waveform reconstruction	Reconstructed strains

6. Astrophysical and Instrumental Significance

The implementation of ArchGEM enhances the reliability of GW event confirmation, particularly in noisy, high-mass merger scenarios. The provision of physically interpretable glitch parameters enables direct feedback for interferometer characterization and cleaning, which is critical for future IMBH studies. The approach supports the extraction of finer astrophysical details by improving signal-to-noise discrimination and by facilitating waveform reconstruction that potentially reveals physics beyond current model families (e.g., non-circular orbits, environmental effects). This suggests that integrated clustering and density approximation frameworks such as ArchGEM may become standard in next-generation GW data analysis streams.

7. Limitations and Future Directions

ArchGEM fundamentally relies on the quality and architecture of the chosen GMM for clustering spectrogram features, and its accuracy is bounded by the resolution and completeness of input spectral data. The current framework is most effective for well-localized, arch-like glitches at low frequency; generalization to other artifact types would require further methodological extension. A plausible implication is that future iterations could incorporate time-series priors or physics-informed constraints to enhance interpretability and reduce false positive assignments, thereby aiding the pipeline’s application to more varied GW noise environments.