To date, the majority of microseisms studies carried out with beamforming analysis make use of the most basic algorithm, the frequency wavenumber beamforming. The robustness and simplicity of fk beamforming make it a appealing approach for estimating the ambient noise wavefield, but it is subject to limited resolution. Hence fk beamforming as implemented to date can be used to estimate only the strongest signals within the wavefield. When the interest is only the strongest
source in the wavefield, little benefit is gained by using higher resolution beamformers as the estimation of the strongest signal between fk and Capon beamforming is comparable (e.g. Koper et al., 2010). The true benefit of higher resolution beamforming approaches becomes evident when weaker or multiple sources are of interest, as the array response is more strongly suppressed. In the case of conventional fk beamforming, weak sources can be overshadowed by strong sources and remain undetected.
Ideally, one is interested in removing the effect of the ARF completely, which would allow accurate estimation of the directional energy present in the wavefield. A potential way of removing the ARF is to use deconvolution to remove the array pattern from the power spectrum. Such tech- niques have been popular in other fields of research, such as Astronomy (e.g. Richardson, 1972; Lucy, 1974; Högbom, 1974), and acoustic beamforming (e.g. Dougherty and Stoker, 1998; Wang et al., 2004; Brooks and Humphreys, 2006b,a; Sijtsma, 2007; Yardibi et al., 2008). To date, no use has been made of deconvolution to improve beamforming power spectra with the sole exception of Nishida et al. (2008a), who implemented the Richardson-Lucy deconvolution to reduce beam sidelobe contributions.
The aim of this thesis, is to design aand implement beamforming framework tailored to the optimal processing of the microseismic wavefield for the purpose of extracting novel information from the ambient noise wavefield.
The thesis is structured as follows: • Chapter 1: Introduction
The introduction chapter is divided into two parts. In the first part, the focus is to familiarize the reader with the properties of the microseismic wavefield and the conventional ways of observing/analyzing it. The microseisms spectrum and the processes that drive the genera- tion of ambient noise vibration, the distribution of energy varying with frequency, seasonal patterns and regional and global differences in the observed wavefield are discussed. The commonly used methods to observe the wavefield are summarized. In the second part of this chapter, the focus is directed at array beamforming techniques which are utilised to study microseisms. The signal model, which is used to describe the wavefield, is introduced fol- lowed by the fk and Capon beamformer. Multiple ways to extend narrowband beamforming to broadband are discussed and an introduction to three component beamforming is given. • Chapter 2: Optimal Beamforming Framework for the Analysis of Microseisms
Given the existing beamforming methods, a framework is developed to for an optimal anal- ysis of microseisms. The goal is to accurately estimate multiple arrivals from a variety of directions simultaneously. Procedures such as tapering, averaging over frequency and time, the use of the coherence matrix, diagonal loading for the Capon beamformer and how these procedures affect the beamforming result are discussed. The framework is tested on multiple arrays to display its performances under different conditions. As this paper was published (relatively) early in the PhD candidature, the notation used in this chapter follows the notation used by Capon (1969).
To analyse weak energy present in the microseisms wavefield, it is necessary to remove the beam sidelobe contribution from strong sources. One promising option is the process of deconvolution, where the the wavefield is decomposed into its most fundamental con- tributions. An overview of potential deconvolution techniques that can be used to remove the ARF from the power estimates and hence decompose the power spectrum into its most fundamental components is given. The specific focus is the CLEAN algorithm (Schmidt, 1986) developed in radio astronomy, which iteratively removes the ARF to reduce side- lobe contributions. The performance of this algorithm in combination with fk and Capon beamforming is analysed and an extension to three component array beamforming is pre- sented. Capabilities of the novel algorithm are compared to the conventional beamformers on multiple arrays for single and three component arrays.
• Chapter 4: Long duration ambient study of the Southern Oceans
In this chapter, the short-period microseisms wavefield over a two decade time span is in- vestigated. Of interest is the temporal variability of the microseisms wavefield, which is directly linked to the ocean wave climate and storm patterns. With an array study over the course of 2 decades, the changes in the generation location of microseisms are studied. The study is performed with the single component Warramunga Array located in North Australia which was originally deployed for nuclear explosion monitoring. The IAS-Capon method introduced in chapter 2 is used, which extracts multiple arrivals estimated from each 1 hour beamforming result. The frequency dependence, temporal variability and locations of gen- erations are studied over the course of 1991-2012.
• Chapter 5: Full Wavefield decomposition by means of deconvolution enhance beamforming The full short period microseismic wavefield is decomposed into its separable energy con- tributions by means of the CLEAN-3C (chapter 3). For this task, the Pilbara Array located in north west of Australia is used. The array is composed of 13 three component stations arranged in a spiral shape, which is ideal for a omnidirectional microseismic wavefield esti- mation. One year (2013) is analysed with CLEAN-3C and decomposed into its elementary energy contributions. The study focuses on surface waves, and estimates the mean power of Rayleigh, Love and Lg waves for the period of the full year. Generation locations, de-
pendence on frequency and backazimuth of each surface phase and potential generation mechanisms of Love waves are discussed.
• Chapter 6: Presents an overall discussion and synthesis of main findings. • Chapter 7: Summary.
Improved implementation of the fk and Capon
methods for array analysis of seismic noise
Published in Geophysical Journal International, year 2014, vol. 198, no. 2, pp 1045-1054(This paper uses the original Capon notation (Capon, 1969) in contrast from prescending and subsequent chapters)
2.1 Abstract
The frequency-wavenumber (fk) and Capon methods are widely used in seismic array studies of background or ambient noise to infer the backazimuth and slowness of microseismic sources. We present an implementation of these techniques for the analysis of microseisms (0.05 - 2 Hz) which draws on array signal processing literature from a range of disciplines. The presented techniques avoid frequency mixing in the cross-power spectral density and therefore yield an accurate slow- ness vector estimation of the incoming seismic waves. Using synthetic data, we show explicitly how the frequency averaged broadband approach can result in a slowness-shifted spectrum. The presented implementation performs the slowness estimations individually for each frequency bin and sums the resulting slowness spectra over a specific frequency range. This may be termed an Incoherently Averaged Signal, or IAS, approach. We further modify the method through diag- onal loading to ensure a robust solution. The synthetic data show good agreement between the analytically derived and inferred error in slowness. Results for real (observed) data are compared between the approximate and IAS methods for two different seismic arrays. The IAS method re- sults in the improved resolution of features, particularly for the Capon spectrum, and enables, for instance, Rg and Lg arrivals from similar backazimuths to be separated in the case of real data.