Causal and Uncertainty-Aware Instrument Correction in Broadband Seismology: Minimum-Phase Inversion, Discretization Effects, and Self-Noise Performance Bounds
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ID: 320332
2026
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Abstract
Summary Instrument correction is a fundamental step in broadband seismology, yet it is commonly treated as a purely numerical operation stabilized by heuristic procedures. In practice, inverse filtering of instrumental responses is constrained by causality, stability, discretization, and uncertainty in instrument parameters, which jointly limit the recoverable frequency content and the physical interpretability of corrected ground motion. Here I present a unified framework for causal and uncertainty-aware instrument correction that explicitly formulates deconvolution as a constrained inverse problem in the digital domain. The proposed approach enforces causal realizability and bounded inverse behaviour while introducing regularization as a physically interpretable control of the bias–noise trade-off. Discretization effects arising from the mapping between continuous- and discrete-time responses are quantified and shown to induce systematic, frequency-dependent amplitude bias that interacts nonlinearly with regularization. I further extend the formulation to incorporate parametric uncertainty in the instrument response, propagating it through the inverse filter to derive confidence bounds on effective amplitude response and noise amplification. A set of diagnostic metrics is introduced to jointly characterize amplitude bias, noise amplification, effective bandwidth, and robustness under uncertainty. These diagnostics are combined into a data-driven decision framework that supports objective selection of the inverse filter and explicitly defines the frequency range over which instrument correction is reliable. Time-domain kernel diagnostics complement the frequency-domain analysis by ensuring causal behaviour and controlled temporal support. The framework is summarized in an end-to-end algorithmic workflow designed for reproducible application to broadband seismic data without reliance on ad hoc stabilization choices. By making physical constraints, trade-offs, and uncertainties explicit, the proposed methodology enhances the robustness and interpretability of instrument-corrected seismic waveforms and provides a principled foundation for downstream analyses in source studies, spectral characterization, and waveform-based investigations.
| Reference Key |
openalex_W7167853883
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|---|---|
| Authors | Antonino D’Alessandro |
| Journal | geophysical journal international |
| Year | 2026 |
| DOI |
10.1093/gji/ggag265
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| URL | |
| Keywords | Keywords not found |
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