Computational Geosciences manuscript No. (will be inserted by the editor) Low dispersive modeling of Rayleigh waves on Partly-Staggered grids O. Rojas · B. Otero · J. E. Castillo · S. M. Day Received: date / Accepted: date Abstract In elastic media, finite difference (FD) im- plementations of free surface (FS) boundary conditions on Partly-Staggered Grids (PSG) use the highly dis- persive vacuum formulation (VPSG). The FS bound- ary is embedded into a “vacuum” grid layer (null Lame constants and negligible density values) where the dis- cretized equations of motion allow computing surface displacements. We place a new set of Compound (stress- displacement) nodes along a planar FS and use unilat- eral mimetic FD discretization of the zero-traction con- ditions for displacement computation (MPSG). At inte- rior nodes, MPSG reduces to standard VPSG methods and applies fourth-order centered FD along cell diago- nals for staggered differentiation combined with nodal second-order FD in time. We perform a dispersion anal- ysis of these methods on a Lamb’s problem and estimate dispersion curves from the phase difference of windowed numerical Rayleigh pulses at two FS receivers. For a given grid sampling criterion (e.g., 6 or 10 nodes per reference S wavelength λ S ), MPSG dispersion errors are O. Rojas Universidad Central de Venezuela, Caracas, Venezuela Tel.: +058-416-5380442 - +058-212-6051264 Fax: +058-212-6051131 E-mail: rojasotilio@gmail.com B. Otero Universitat Polit´ ecnica de Catalunya-TECH, Barcelona, Spain Tel.: +034-93-4054046 - +034-636557161 Fax: +034-93-4017055 E-mail: botero@ac.upc.edu J. E. Castillo San Diego State University, California, USA E-mail: jcastillo@sdsu.edu S. M. Day San Diego State University, California, USA E-mail: day@moho.sdsu.edu only a quarter of the VPSG method. We also quantify root-mean-square (RMS) misfits of numerical time se- ries relative to analytical waveforms. MPSG RMS mis- fits barely exceed 10% when 9 nodes sample the min- imum S wavelength λ S MIN in transit (along distances ∼ 145λ S MIN ). In same tests, VPSG RMS misfits exceed 70%. We additionally compare MPSG to a consistently fourth-order mimetic method designed on a Standard Staggered Grid. The latter equates former’s dispersion errors on grids twice denser, and shows higher RMS precision only on grids with 6 or less nodes per λ S MIN . Keywords Staggered grid · high-order modeling · finite difference · wave equation Mathematics Subject Classification (2000) 35A24 · 35L02 · 65L12 · 81T80 1 Introduction Modern finite differences (FD) methods in computa- tional seismology use a Cartesian Staggered Grid (SG) for domain and wavefield discretization. In a SG, ma- terial parameters are defined on individual rectangular meshes displaced by half of the grid spacing in one or more directions. Similar staggering distribution is used to locate each wavefield at the center of those it de- pends upon, and numerical differentiation gains accu- racy by halving the grid spacing. A widely used SG on elastic wave propagation collocates each displace- ment (or particle velocity) component and each shear stress at a distinct grid site. Only normal stresses are placed at the same grid location given its common de- pendency on all diagonal strain components. This grid has been referred as Standard Staggered Grid (SSG) by Moczo et al. [27] and Saenger et al. [36]. Pioneering