{"content":[{"text":"Onset of energy equipartition \n among surface and body \n waves \n L. Borcea1, J. Garnier2,3 and K. Sølna4 \n 1Department of Mathematics, University of Michigan, Ann Arbor, \n MI, 48109 USA \n 2CMAP, CNRS, Ecole polytechnique, Institut Polytechnique de Paris, \n 91128 Palaiseau Cedex, France \n 3INRIA, France \n 4Department of Mathematics, University of California at Irvine, \n Irvine, CA 92697, USA \n JG, 0000-0002-3518-4159","bbox":{"left":0.456157,"top":0.015005,"width":0.40965999999999997,"height":0.335724}},{"text":"royalsocietypublishing.org/journal/rspa","bbox":{"left":0.124757,"top":0.069366,"width":0.26769,"height":0.020234000000000002}},{"text":"Research \n Cite this article: Borcea L, Garnier J, Sï£¡lna \n K. 2021 Onset of energy equipartition among \n surface and body waves. Proc.R.Soc.A 477: \n 20200775. \n https://doi.org/10.1098/rspa.2020.0775","bbox":{"left":0.124757,"top":0.149139,"width":0.251232,"height":0.13991300000000004}},{"text":"Received: 25 September 2020 \n Accepted: 13 January 2021","bbox":{"left":0.124759,"top":0.313196,"width":0.16351,"height":0.03678500000000007}},{"text":"We derive a radiative transfer equation that accounts \n for coupling from surface waves to body waves and \n the other way around. The model is the acoustic \n wave equation in a two-dimensional waveguide \n with reﬂecting boundary. The waveguide has a thin, \n weakly randomly heterogeneous layer near the top \n surface, and a thick homogeneous layer beneath it. \n There are two types of modes that propagate along the \n axis of the waveguide: those that are almost trapped \n in the thin layer, and thus model surface waves, \n and those that penetrate deep in the waveguide, \n and thus model body waves. The remaining modes \n are evanescent waves. We introduce a mathematical \n theory of mode coupling induced by scattering in the \n thin layer, and derive a radiative transfer equation \n which quantiﬁes the mean mode power exchange. We \n study the solution of this equation in the asymptotic \n limit of inﬁnite width of the waveguide. The main \n result is a quantiﬁcation of the rate of convergence of \n the mean mode powers toward equipartition.","bbox":{"left":0.467203,"top":0.371601,"width":0.39430099999999996,"height":0.339929}},{"text":"Subject Areas: \n applied mathematics","bbox":{"left":0.124759,"top":0.381291,"width":0.118936,"height":0.03709900000000005}},{"text":"Keywords: \n random medium, surface wave, body wave, \n mode coupling, radiative transfer, \n equipartition","bbox":{"left":0.124759,"top":0.438209,"width":0.24494899999999997,"height":0.07694600000000001}},{"text":"Author for correspondence: \n J. Garnier \n e-mail: josselin.garnier@polytechnique.edu","bbox":{"left":0.124759,"top":0.537802,"width":0.246543,"height":0.05703500000000006}},{"text":"1. Introduction \n The description of energy transfer between surface waves \n and body waves is of interest in seismology [1,2], \n ultrasonic inspection [3], manipulation of waves [4] and \n the development of surface acoustic wave devices like \n ﬁlters, resonators and scanners [5]. Radiative transfer [6] \n has been used for more than 30 years to describe wave \n propagation in heterogeneous media like the Earth’s \n crust [1,7–9], biological tissue [10], the atmosphere and","bbox":{"left":0.456158,"top":0.745961,"width":0.41545499999999996,"height":0.17005099999999995}},{"text":"2021 The Author(s) Published by the Royal Society. All rights reserved.","bbox":{"left":0.484603,"top":0.937458,"width":0.35009999999999997,"height":0.01517500000000005}}],"images_bbox":[{"left":0.456158,"top":0.336314,"width":0.017966,"height":0.013711}],"images_bbox_not_text_overlap":[{"left":0.456158,"top":0.336314,"width":0.017966,"height":0.013711}]}