@article {Dagnino2014,
	title = {{Scale- and parameter-adaptive model-based gradient pre-conditioner for elastic full-waveform inversion}},
	journal = {Geophysical Journal International},
	volume = {198},
	number = {2},
	year = {2014},
	month = {jun},
	pages = {1130{\textendash}1142},
	publisher = {Oxford University Press},
	abstract = {We present a scale- and parameter-adaptive method to pre-condition the gradient of the parameters to be inverted in time-domain 2-D elastic full-waveform inversion (FWI). The proposed technique, which relies on a change of variables of the model parameters, allows to balance the value of the gradient of the Lam{\'e} parameters and density throughout the model in each step of the multiscale inversion. The main difference compared to existing gradient pre-conditioners is that the variables are automatically selected based on a least squares minimization criteria of the gradient weight, which corresponds to the product of the gradient by a power of the parameter to be inverted. Based on numerical tests made with (1) a modified version of the Marmousi-2 model, and (2) a high-velocity and density local anomaly model, we illustrate that the value of the power helps to balance the gradient throughout the model. In addition, we show that a particular value exists for each parameter that optimizes the inversion results in terms of accuracy and efficiency. For the two models, the optimal power is \~{}2.0-2.5 and and \~{}1.5 for the first and second Lam{\'e} parameters, respectively; and between 3 and 6, depending on the inverted frequency, for density. These power values provide the fastest and most accurate inversion results for the three parameters in the framework of multiscale and multishooting FWI using three different optimization schemes. {\textcopyright} The Authors 2014. Published by Oxford University Press on behalf of The Royal Astronomical Society.},
	keywords = {Computational seismology, Inverse theory, Numerical approximations and analysis, Seismic tomography},
	issn = {0956-540X},
	doi = {10.1093/gji/ggu175},
	url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-84903949166\&partnerID=tZOtx3y1},
	author = {Dagnino, D. and Sallar{\`e}s, V. and Ranero, C. R.}
}
@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}
}
