The Multitaper Spectrum Analysis Package in Python

Abstract

Spectral analysis has been a fundamental tool in analyzing seismic signals for studying the earthquake source, propagation of seismic waveforms through the Earth, and even monitoring changes in Earth’s structure. I present an open-source Python package, multitaper, for spectral analysis using the multitaper algorithm. The package not only includes power spectral density estimation (with confidence intervals) but also includes bivariate problems such as coherence, dual-frequency correlations, and deconvolution estimation. Implementation of the sine and quadratic multitaper algorithms is also available. For the reader to quickly learn how to use the package, I briefly present several examples using earthquake records from the 2019 Mw 6.0 Mesetas, Colombia, earthquake and its aftershocks recorded at regional distances for estimating time–frequency spectrograms, spectral ratio and source time functions, and correlations between neighboring frequencies. Jupyter Notebooks are shared to reproduce the figures.

Interplate Slip Rate Variation Between Closely Spaced Earthquakes in Southern Mexico: The 2012 Ometepec and 2018 Pinotepa Nacional Thrust Events

“…$$m$$ is a factor that is applied in the frequency domain depending on whether the spectrum is on displacement ($$m=0$$), velocity ($$m=1$$), or acceleration ($$m=2$$), $${f}_{c}$$ is the corner frequency and $${{\Omega}}_{0}$$ is the flat level at low frequencies in the displacement spectrum. We used a multitaper spectrum library to estimate the spectrum as shown by Prieto (2022) and fit the resulting spectrum for all three possible combinations of spectra (displacement, velocity, and acceleration) for the vertical component. Then, we estimated the coefficient of determination, $${R}^{2}$$, and thus evaluated the goodness of the fitting.…”

Optimal Frequency-domain Analysis for Spacecraft Time Series: Introducing the Missing-data Multitaper Power Spectrum Estimator

“…The coupled Equations (11) and (12) are solved iteratively so as to produce estimates S f xx ˆ( ) that match within a user-defined tolerance. All functionality for calculating S f xx ˆ( ) according to Equations (11) and (12) is included in the Multitaper.jl software package (Haley & Geoga 2020a) used for this paper, as well as in the R multitaper package and the python package of Prieto (2022). Multitaper outperforms the Welch (1967) power spectrum estimator adapted for astronomical use 7 See Harris (1978) for a detailed discussion of the bandwidths of commonly used tapers (also called windows), such as the Hamming taper, the Hann taper, and the Blackman-Harris taper.…”

Examining Infrasound Propagation at High Spatial Resolution Using a Nodal Seismic Array

“…We used infresnel (v0.2.0; Toney, 2023a) to calculate direct and diffracted paths for our propagation analysis. The spectra in Figure S2e in Supporting Information S1 were produced using multitaper (Prieto, 2022). Figures were made with PyGMT (v0.9.0; Uieda et al., 2023; Wessel et al., 2019) and Matplotlib (Hunter, 2007).…”