Observing and Modeling the Spectrum of a Slow Slip Event

Abstract

We estimate and model the normalized moment rate power spectrum of large slow slip events in Cascadia. We estimate the spectrum using data from GPS-derived slip inversions, borehole strain records, and beamforming-based tremor amplitudes. The normalized power spectrum initially decreases with frequency but then may flatten at periods of 1 to 10 days before decaying as frequency −n m at higher frequencies, where n m is between 1.1 and 1.4 when estimated from tremor and between 0.4 and 1.5 when estimated from strain. We explore one way to understand the observed spectrum: by modeling a month-long slow slip event as the sum of a steady background moment rate and a population of subevents. The subevents represent the wide variety of observed slow earthquakes, ranging from 0.5-s-long tremor to 3-hr-long rapid tremor reversals. We parameterize the subevents' magnitude distribution and moment-duration scaling, and we examine how the subevent population determines the slow slip spectrum. There are not enough data to rigorously test the subevent model, but we show that the data are consistent with a single continuum of slow earthquakes whose moments scale linearly with their duration, as has been proposed previously. Ide et al. (2007) proposed that all these bursts of slip, from LFEs to RTRs to large slow slip events, are components of a single slow earthquake family. Most well-observed slow earthquakes have roughly the same moment to duration ratio, or average moment rate (e.g., Ide et al. A Single Slow Earthquake Family, With One Moment-Duration Scaling?

The Transient and Intermittent Nature of Slow Slip

“…The size distribution of these events likely also follows a power law distribution, and, similarly, a continuous distribution of slip rates could be established. This is consistent with a composite moment rate power spectrum of slow slip, which shows a roughly decaying amplitude as a function of frequency (Hawthorne & Bartlow, ). Such a decaying spectrum suggests energy is released at all temporal scales, confirming the transient nature of slow events.…”

Detection of Low‐Frequency Earthquakes in Broadband Random Time Sequences: Are They Independent Events?

“…While the BSE model presented here assumes a homogeneous Gaussian fluctuation, other types of randomness obeying power law distributions also provides essentially the same results at lower frequencies due to the central limit theorem and might better explain the impulsive nature of LFE signals (Ide & Maury, ). Such a non‐Gaussian distribution function may be more consistent with the spatial inhomogeneity or localization of the observed LFE and tremor sources (Chestler & Creager, ; Ohta & Ide, ; Rubin & Armbruster, ; Hawthorne & Bartlow, ) suggested that the BSE model is not completely consistent with very broadband observations. While the BSE model only considers the nearest‐neighbor interaction, the long‐range interaction of elasticity has to be considered to produce a more realistic physical model (Aso et al, ; Ben‐Zion, ).…”

“…How are high‐frequency signals of LFEs and tremors related to low‐frequency VLF signals, as broadband slow earthquakes? Several ideas have been proposed to explain this relationship (Gomberg et al, ; Hawthorne & Bartlow, ; Ide, , ). Here we focus on a Brownian slow earthquake (BSE) model (Ide, , ) because of its simplicity and broad applicability.…”

Repeating VLFEs During ETS Events in Cascadia Track Slow Slip and Continue Throughout Inter‐ETS Period

“…Previously, it was only possible to make broad inferences about the relationship between VLFE, tremor, and SSEs in Cascadia due to the small handful of VLFEs detected through grid‐search centroid moment tensor inversion. Further, more recent studies, such as that of Hawthorne and Bartlow () further suggest that VLFEs are an inherent part of SSEs due to their moment scaling relationships. Fortunately, as a result of this research thousands of events detected through matched filtering make it possible to more deeply examine the role of VLFEs in ETS cycling.…”

“…It is largely thought that VLFEs, tremor, and slow slip are all manifestations of a greater, quasi‐periodic shearing activity that occurs on the plate interface that obey a unique linear moment scaling relationship (Ide et al, 2008; Shelly et al, ). More recently, Hawthorne and Bartlow () estimate the spectral distribution of moment rates in Cascadia for large SSEs using the sums of other types of slow earthquakes as subevents in the moment rate distribution. The findings of this study further support the findings of the linear moment scaling relationship of slow earthquakes and an interconnectedness of events.…”