Acoustic–gravity waves from multi-fault rupture

Abstract

Abstract

On the propagation of acoustic–gravity waves due to a slender rupture in an elastic seabed

“…6.1. Acoustic-gravity waves Figure 13 compares the first acoustic mode for the elastic case (3.92) and rigid case ((3.22) of Williams et al (2021)). As in Eyov et al (2013) the values used for ρ l , ρ s , C l , C s and C p are average values taken from Dziewonshi & Anderson (1981).…”

“…Surface waves Consider now the surface waves generated by the single slender fault with parameters as per table 2. The equations generating the surface waves are (3.93) for the elastic case and (3.23) of Williams et al (2021) for the rigid case. At a depth of h = 4000 m there is little difference between elastic and rigid cases (figure 17a), but at a depth of h = 1000 m differences are more apparent (figure 17b).…”

“…The theory developed in this paper leading to the equations for pressure (3.92) and surface elevation (3.93) is linear. Therefore, as in Williams et al (2021), more complicated multi-fault scenarios can be constructed from single slender fault solutions by linear superposition, given that the parameters for each individual fault are known. To contrast the case of an elastic seabed with that of a rigid seabed we revisit the Sumatra 2004 earthquake discussed in § 5.1.2 of Williams et al (2021).…”

“…However, for those cases where the shape of the rupture can be modelled as a rectangular slender body (table 1 of Mei & Kadri 2018) multiple-scales analysis can be applied to take advantage of the differing length scales of the fault. Within Mei & Kadri (2018) the primary focus was on pure acoustic waves, ignoring gravitational effects, whereas a later work (Williams, Kadri & Abdolali 2021) extended the derivations to include gravity and therefore captured the behaviour of the surface-gravity waves in addition to the acoustic-gravity waves. Moreover, the slender-fault model was applied to more complex, multi-fault scenarios, such as the 2016 Kaikoura earthquake (Hamling et al 2016), via linear superposition -but still with a rigid seabed.…”

Earthquake source characterization by machine learning algorithms applied to acoustic signals

“…A semi-analytical inverse approach is employed assuming the fault is single (A similar solution can be derived for multi-fault rupture based on Williams et al 2021 49 ), slender and uniform, and the seabed is flat, which allows the calculation of the effective fault characteristics in almost real-time from the pressure acoustic signature. The three-dimensional wave equation governs the propagation of acoustic waves in slightly compressible fluids 50 : where is the velocity potential, the velocity field is defined by .…”