Nat. Hazards Earth Syst. Sci., 15, 627–636, 2015 www.nat-hazards-earth-syst-sci.net/15/627/2015/ doi:10.5194/nhess-15-627-2015 © Author(s) 2015. CC Attribution 3.0 License. Large-scale numerical modeling of hydro-acoustic waves generated by tsunamigenic earthquakes C. Cecioni1, A. Abdolali1,2, G. Bellotti1, and P. Sammarco3 1Roma Tre University, Engineering Department, Via Vito Volterra 62, 00146 Rome, Italy 2Department of Civil and Environmental Engineering, Center for Applied Coastal Research, University of Delaware, Newark, Delaware, USA 3University of Rome Tor Vergata, Civil Engineering Department, Via del Politecnico 1, 00133 Rome, Italy Correspondence to: C. Cecioni ([email protected]) Received: 26 May 2014 – Published in Nat. Hazards Earth Syst. Sci. Discuss.: 11 July 2014 Revised: – – Accepted: 9 March 2015 – Published: 24 March 2015 Abstract. Tsunamigenic fast movements of the seabed order effects of compressibility on the generation of sur- generate pressure waves in weakly compressible seawater, face (tsunami) and hydro-acoustic waves, and does not con- namely hydro-acoustic waves, which travel at the sound sider the secondary wave-to-wave interaction (e.g., pseudo- celerity in water (about 1500 m s−1). These waves travel Rayleigh and acoustic-gravity waves considered in the work much faster than the counterpart long free-surface gravity of Ardhuin and Herbers, 2013). waves and contain significant information on the source. Since the hydro-acoustic waves travel much faster than the Measurement of hydro-acoustic waves can therefore antici- surface waves, their real-time recording allows the antici- pate the tsunami arrival and significantly improve the capa- pation of the tsunami arrival. Moreover, the hydro-acoustic bility of tsunami early warning systems. In this paper a novel wave signals contain significant information on the tsunami- numerical model for reproduction of hydro-acoustic waves genic source (Cecioni et al., 2014; Chierici et al., 2010). is applied to analyze the generation and propagation in real Therefore the detection and the complete modeling of hydro- bathymetry of these pressure perturbations for two historical acoustic waves (speed around 1500 m s−1), together with catastrophic earthquake scenarios in Mediterranean Sea. The measurements of seismic waves (speed around 5000 m s−1), model is based on the solution of a depth-integrated equation, could in principle dramatically improve the effectiveness of and therefore results are computationally efficient in recon- tsunami early warning systems. structing the hydro-acoustic waves propagation scenarios. Earlier studies on tsunami evolution in weakly compress- ible water have been carried out by Miyoshi(1954), Sells (1965) and Yamamoto(1982). Later, analytical studies have solved the potential fluid problem in weakly compressible 1 Introduction water, with fast-rising motion of the seabed (Nosov, 1999; Stiassnie, 2010; Chierici et al., 2010). The analytical mod- Submarine earthquakes are the major cause of generation els, although extremely useful to investigate the features of of tsunami. A correct modeling of the wave field gener- hydro-acoustic wave generation and propagation processes, ated by seabed movement is mandatory to understand the are not suited for reproduction of such phenomena at real- physics of the tsunami and its propagation. Most of the geographical scale. The numerical solution of the 3-D prob- hydraulic tsunami models make use of the water incom- lem (Nosov and Kolesov, 2007; Bolshakova et al., 2011) is pressibility hypothesis. Nevertheless a sudden movement of straightforward to obtain but requires unacceptable compu- the seabed, triggered by underwater earthquake, compresses tational time when applied to large areas. A depth-integrated the water column and generates pressure waves (hydro- equation has therefore been proposed by Sammarco et al. acoustic waves) that propagate in the sea at the celerity of (2013), which reproduces the mechanics of propagation of sound in water. The present analysis involves only the first- Published by Copernicus Publications on behalf of the European Geosciences Union. 628 C. Cecioni et al.: Large-scale numerical modeling of hydro-acoustic waves low-frequency hydro-acoustic waves due to a sudden bottom seabed motion. In the framework of linearized theory the displacement associated with earthquakes. The wave simu- governing equation and boundary conditions for the fluid po- lation by means of this equation overcomes the computa- tential 8.x;y;z;t/ are tional difficulties of three-dimensional models and retains − 2r2 − 2 D all the physical features of the phenomena. The model has 8tt cs 8 cs 8zz 0 been applied by Abdolali et al.(2015a) to reproduce the wave 8tt C g8z D 0 at z D 0 ; (1) field generated by the 2012 Haida Gwaii tsunamigenic earth- 8z C rh · r8 C ht D 0 at z D −h.x;y;t/ quake, and model results are compared with in situ wave 2 measurements. where r and r are respectively the gradient and the Lapla- In this paper the results and the physical implications cian in the horizontal plane x;y, while subscript with the of a large geographical scale application of the numerical independent variables denotes partial derivatives, cs is the model based on the depth-integrated equation of Sammarco celerity of sound in water, and g is the gravity acceleration. et al.(2013) are illustrated. The model is applied to simu- h is the water depth, given by the rest bottom topography late the hydro-acoustic wave propagation generated by two hb .x;y/ net of the earthquake bottom motion ζ .x;y;t/: main tsunamigenic destructive historical earthquakes that oc- D − curred in the Mediterranean Sea: the AD 365 Crete event h.x;y;t/ hb .x;y/ ζ .x;y;t/: (2) and the 1693 Sicily event. The depth-integrated model has From Eq. (2) h , the water depth time variation, is zero ev- been validated through comparison with the solution of the t erywhere except on the earthquake zone, full three-dimensional weakly compressible wave problem in real bathymetry, along vertical sections of the sea. The com- ζ h D −ζ D − 0 [H .t/ − H .t − τ/]; (3) parison allowed some computational parameters to be set up t t τ in order to optimize the depth-integrated model. The simulation of hydro-acoustic wave propagation in real where H is the Heaviside step function, ζ0 .x;y/ is the resid- bathymetry enables the investigation of the correlation be- ual displacement, τ is the duration of the seabed motion and tween the hydro-acoustic waves and the generation mech- the seabed velocity is assumed constant, as ζ0/τ. anism, the source location, the bottom topography and the The solution of Eq. (1) is given by an infinite sum of nat- depth of the pressure recording point. The model is based ural modes, n D 0, 1, ::: (Eyov et al., 2013). The first mode on the hypothesis of rigid seabed; however, it is worth cit- (n D 0) represents the gravity surface wave, i.e., the tsunami; ing Eyov et al.(2013), who study the effects of replacing the other modes (n ≥ 1), namely the hydro-acoustic modes, the rigid-bottom assumption by an elastic half-space solid are responsible for elastic oscillations of the water body. The medium on the properties of the acoustic-gravity waves. hydro-acoustic waves are characterized by a set of natural Chierici et al.(2010) investigated on the effect of a porous frequencies, namely cutoff frequencies: seabed, and more recently Abdolali et al.(2014) and Ab- .2n − 1/c dolali et al.(2015b) presented a depth-integrated equation f .n/ D s ; (4) to simulate gravity and hydro-acoustic waves over a viscous 4h compressible sedimentary layer underlying seawater. where n ≥ 1 is the indicator of the hydro-acoustic mode. In the portion of the Mediterranean Sea considered in Evanescent and progressive waves are associated respec- the present research, two deep-sea observatories are located tively with lower and higher frequencies than the cutoff ones off-shore of the eastern Sicilian coast. These observatories, (Eq.4). described later in more details, are equipped, among oth- Sammarco et al.(2013) via a proper application of the av- ers instruments, with low-frequency and large-bandwidth hy- eraging technique to the problem (Eq.1), in the hypothesis drophones. Therefore the numerically reproduced scenarios of constant cs and mild sloped seabed (rh kh), found a provide indications on the attended hydro-acoustic signals in depth-integrated equation, which in hyperbolic form reads the case of submarine earthquake occurrence. The paper is structured as follows: the next section deals C 1 !2 n C −r .C r /C −β2C Dh D ; (5) with the description of the numerical model; Sect. 3 describes ntt 2 n n n n n t n cs g g the large-scale numerical simulations of the two selected his- torical tsunamis; in Sect. 4 discussions and conclusions are where .x;y;t/ is the fluid velocity potential at the undis- given. turbed free surface. Equation (5) has been named a mild- slope equation in weakly compressible fluid (MSEWC). The subscript n indicates that Eq. (5) is valid for the 2 Description of the numerical model generic nth mode (hydro-acoustic and gravity). Superimpo- sition of the solutions of Eq. (5) for each mode will lead Consider the problem of wave propagation in weakly com- to complete modeling of the fluid potential, 8.x;y;z;t/ D P1 pressible inviscid fluid, where waves are generated by a nD0 n .x;y;t/fn .z/, generated by a fast seabed motion, Nat. Hazards Earth Syst. Sci., 15, 627–636, 2015 www.nat-hazards-earth-syst-sci.net/15/627/2015/ C. Cecioni et al.: Large-scale numerical modeling of hydro-acoustic waves 629 Table 1.