@article {Mel{\'e}ndez2013243,
	title = {{Origin of water layer multiple phases with anomalously high amplitude in near-seafloor wide-angle seismic recordings}},
	journal = {Geophysical Journal International},
	volume = {196},
	number = {1},
	year = {2013},
	pages = {243{\textendash}252},
	abstract = {Water layer multiple seismic phases are recorded at ocean bottom seismometers and hydrophones as arrivals that correspond to the reflection of the primary phases at the sea-free air interface. In regions of low to moderate seabed relief, the shape of these phases mimics that of the primary phases with a traveltime delay that depends on the water layer thickness at the receiver location. Given their longer travel paths, multiple phases should have smaller amplitudes than their corresponding primary phases. However, depending on the geological context it can be relatively common to observe the opposite, which results in the identification of the multiple phases at longer offsets than the primary events. In this paper, we examine the origin of this apparently paradoxical phenomenon by analysing the combined effect of the major factors potentially involved: the source frequency content, the subsurface velocity distribution, the receiver-seafloor distance, the geometrical spreading and attenuation of sound waves and the ambient noise level.We use synthetic modelling to show that for certain combinations of these factors, the interference between the multiple and its reflection at the seafloor is constructive and has a higher amplitude than the primary wave. Our analysis indicates that in the most favourable cases the phases resulting from this interference can be observed at offsets some tens of kilometres longer than their corresponding primary phases, and thus they can provide useful information for velocity modelling. {\textcopyright} The Authors 2013. Published by Oxford University Press on behalf of The Royal Astronomical Society.},
	keywords = {ambient noise, Controlled source seismology, Controlled-source seismologies, Earthquake effects, Geometrical spread, hydrophone, Numerical approximations and analysis, numerical method, ocea, Seismology, Site effects, Wave propagation},
	issn = {0956540X},
	doi = {10.1093/gji/ggt391},
	url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-84890885715\&partnerID=tZOtx3y1 http://www.scopus.com/inward/record.url?eid=2-s2.0-84890885715\&partnerID=40\&md5=a3729b5c20fafb9373a2a82c94b34990},
	author = {Mel{\'e}ndez, A.a and Sallar{\`e}s, V.a and Ranero, C.R.b R. and Kormann, J.c and Mel{\'e}ndez, A. and Sallar{\`e}s, V.}
}
@article {Santos2011,
	title = {{Compression and shear-wave velocities in discrete particle simulations of quartz granular packings: Improved Hertz-Mindlin contact model}},
	journal = {GEOPHYSICS},
	volume = {76},
	number = {5},
	year = {2011},
	month = {sep},
	pages = {E165{\textendash}E174},
	abstract = {The Hertz-Mindlin (HM) contact model has been a cornerstone for the development of several effective medium theories (EMTs) aimed at describing the mesoscopic and macroscopic mechanical behavior of granular materials like unconsolidated sands. In addition, this model is at the core of most of the discrete particle method designs used to numerically solve for the responses of these heterogeneous materials to external perturbations, like acoustic and stress-strain experiments. However, this model has shown shortcomings in the description of the shear response characterization of granular materials, partly due to the non-affine motions experienced by the grains. We have developed a correction of the model based on a detailed calibration of our acoustic numerical results with previous empirical data. Using a microscopic approach to the grain-grain contact surfaces, the nature of the corrections found appear to be related to the shear resistant asperities and the smaller scale of the grain-grain contact areas compared to the total area assumed by the HM model. An improved HM model characterized by a tangential stiffness weakening is based on these surface corrections. Using this observation an enhanced EMT theory emerges based not only on the tangential stiffness modification but also on the velocity-pressure dependence obtained during the calibration of our numerical model. {\textcopyright} 2011 Society of Exploration Geophysicists.},
	keywords = {3D, Compression wave (P-wave), Rock physics, Shear-wave (S-wave), Wave propagation},
	issn = {0016-8033},
	doi = {10.1190/geo2010-0376.1},
	url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-84857461284\&partnerID=tZOtx3y1},
	author = {Santos, Carlos and Urdaneta, Vanessa and Garcia, Xavier and Medina, Ernesto}
}
@article {Kaser2008,
	title = {{Quantitative accuracy analysis of the discontinuous Galerkin method for seismic wave propagation}},
	journal = {Geophysical Journal International},
	volume = {173},
	number = {3},
	year = {2008},
	month = {jun},
	pages = {990{\textendash}999},
	abstract = {We present a quantitative accuracy analysis of the Discontinuous Galerkin Finite-Element method for the simulation of seismic wave propagation on tetrahedral meshes. Several parameters are responsible for the accuracy of results, such as the chosen approximation order, the spatial discretization, that is, number of elements per wavelength, and the propagation distance of the waves due to numerical dispersion and dissipation. As error norm we choose the time-frequency representation of the envelope and phase misfit of seismograms to assess the accuracy of the resulting seismograms since this provides the time evolution of the spectral content and allows for the clear separation of amplitude and phase errors obtained by the numerical method. Our results can be directly used to set up the necessary modelling parameters for practical applications, such as the minimum approximation order for a given mesh spacing to reach a desired accuracy. Finally, we apply our results to the well-acknowledged LOH.1 and LOH.3 problems of the SPICE Code Validation project, including heterogeneous material and the free surface boundary condition, and compare our solutions with those of other methods. In general, we want to stress the increasing importance of certain standard procedures to facilitate future code validations and comparisons of results in the community of numerical seismology. {\textcopyright} 2008 The Authors Journal compilation {\textcopyright} 2008 RAS.},
	keywords = {Computational seismology, Numerical approximations and analysis, Numerical solutions, Time series analysis, Wave propagation, Wavelet transform},
	issn = {0956540X},
	doi = {10.1111/j.1365-246X.2008.03781.x},
	url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-43749087643\&partnerID=tZOtx3y1},
	author = {K{\"a}ser, Martin and Hermann, Verena and de la Puente, Josep}
}
