Elastic systems driven by intermittent energy release generate non-Gaussian transients across domains such as brittle fracture, seismicity, rotating machinery and interferometric instrumentation. These signals often contain bursts, ringdowns, ridges and clustered energy packets, but it remains unclear whether such motifs define a measurable morphology comparable across physical systems. Here we use a frozen convolutional encoder trained on transient-rich interferometric noise as a fixed probe of non-Gaussian elastic morphology. The encoder is not fine-tuned, retrained or recalibrated on any target domain. Signals are mapped to a common time-frequency representation and compared through latent geometry and perturbation response rather than task-specific classification. In granite acoustic-emission experiments, L2-normalized embeddings define trajectories on a latent hypersphere. The cumulative angular path provides a derivative-free observable of morphological reorganization. This geometry distinguishes two fracture organizations: a more distributed damage evolution and a more localized rupture regime. The localized regime accumulates a larger angular path and degrades more strongly under phase randomization and temporal-order perturbation, consistent with a more phase-sensitive and sequence-dependent rupture morphology. Synthetic controls and seismic morphology-destruction experiments indicate that the response is not explained by marginal spectral energy alone, while random-weight attribution controls show that visual localization is insufficient without quantitative perturbation tests. These results support frozen transient-rich representations as fixed measurement probes for comparing non-Gaussian elastic morphology across heterogeneous physical systems.