Mathematical And Statistical Analyses Of Acoustic Time Series To Quantify Trends And Events In Underwater Ocean Sounds

Abstract

This thesis aims to develop a robust mathematical framework to study underwater acoustics data in relation to climate change. The general question we want to answer is: Can we hear evidence for weather and climate change using underwater recordings and what do these measurements say? The project poses challenges in physics, statistics and mathematics, thus requiring a unifying language for the three disciplines.

The study of the oceans' properties starts with the sound recording by hydrophones. The Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) hydroacoustic network relies on the International Monitoring System (IMS) to provide a reliable dataset spanning over 20 years. In collaboration with the National Physical Laboratory (NPL, UK), we develop a robust algorithm to extract two metrics: Sound Pressure Levels (SPLs), yielding information about sound intensities and Hjorth's Mobility, giving information about the mean frequency contents of the acoustic signal.

The analysis of the Earth's climate is looked at first through studying the impact of typhoons on the Pacific Ocean soundscape. We show that SPLs increase significantly during typhoon events, particularly for lower frequency bands (1.25 – 15 Hz), and that individual typhoons can be detected up to 5838 km away.

Our global study of ocean soundscapes revealed a statistically significant decrease in time of sound pressure levels across major oceans, with the exception of a specific frequency band in the Pacific. Sea surface temperature (SST) alone cannot fully explain these changes, and CO₂ levels also play a crucial role in understanding changes in sound intensity.

The mathematical aspects of signal decomposition are investigated and a new perspective on signal decomposition is investigated. We show the equivalence of the Fast Iterative Filtering (FIF) method with iterative solvers used in numerical linear algebra. The connection between these branches of Mathematics could lead to improvement in both areas.

Date of Award	22 Jan 2025
Original language	English
Awarding Institution	University of Bath
Supervisor	Matthew Nunes (Supervisor), Chris Budd (Supervisor) & Philippe Blondel (Supervisor)