Frequency-dependent effects on travel times and waveforms of long-period S and SS waves

Abstract The spectral properties of upper-mantle velocity perturbations are dominantly determined from regional and global tomographic models. In this paper we study frequency-dependent effects of l3ng-period S and SS waves of SH-type through random upper-mantle models with specified spectral properties. In particular, we investigate the information content of the power spectra of travel time perturbations as a function of model spectrum and frequency band. Wave propagation is simulated by a finite-difference (FD) approximation to the axi-symmetric wave equation in spherical coordinates. For global models with cylindrical symmetry and constant angular increment Δθ, the use of spherical coordinates leads to an effective lateral grid spacing (arc length) decreasing with depth. This is contrary to the requirements of global models with low velocities at the top of the mantle, which necessitate a dense grid spacing at small depths and a wider grid spacing at the base of the mantle. We introduce a grid with depth-dependent lateral grid spacing to overcome this inconsistency. Our main findings are that (1) the properties of spatial power spectra of travel time fluctuations are frequency-dependent; (2) power spectra of models obtained from long-period tomography may underestimate the power at intermediate scales; (3) frequency-dependent effects on the waveform are sensitive to the scales and amplitudes of perturbations present in the upper mantle.

[1]  Olafur Gudmundsson,et al.  Spectra of mantle shear wave velocity structure , 1992 .

[2]  Jean Virieux,et al.  SH-wave propagation in heterogeneous media: velocity-stress finite-difference method , 1984 .

[3]  Heiner Igel,et al.  Anisotropic wave propagation through finite-difference grids , 1995 .

[4]  Olafur Gudmundsson,et al.  Stochastic analysis of global traveltime data: mantle heterogeneity and random errors in the ISC data , 1990 .

[5]  Jean-Paul Montagner,et al.  Can seismology tell us anything about convection in the mantle , 1994 .

[6]  Roel Snieder,et al.  On the presence of intermediate-scale heterogeneity in the upper mantle , 1995 .

[7]  Cord Jastram,et al.  Elastic modelling on a grid with vertically varying spacing1 , 1994 .

[8]  J. Virieux.  P-SV wave propagation in heterogeneous media: Velocity‐stress finite‐difference method , 1986 .

[9]  Jean-Paul Montagner,et al.  Global upper mantle tomography of seismic velocities and anisotropies , 1991 .

[10]  F. Pollitz.  Global tomography from Rayleigh and Love wave dispersion: effect of ray-path bending , 1994 .

[11]  Heiner Igel,et al.  SH-wave propagation in the whole mantle using high-order finite differences , 1995 .

[12]  G. Masters,et al.  Frequency-dependent polarization measurements of long-period surface waves and their implications for global phase-velocity maps , 1994 .

[13]  Eugene M. Lavely,et al.  Three‐dimensional seismic models of the Earth's mantle , 1995 .

[14]  Robert J. Geller,et al.  Computation of synthetic seismograms and their partial derivatives for heterogeneous media with arbitrary natural boundary conditions using the Direct Solution Method , 1994 .

[15]  Wei-jia Su,et al.  Predominance of long-wavelength heterogeneity in the mantle , 1991, Nature.

[16]  Heiner Igel,et al.  P‐SV wave propagation in the Earth's mantle using finite differences: Application to heterogeneous lowermost mantle structure , 1996 .

[17]  O. Witte,et al.  Ray tracing in random media , 1996 .

[18]  E. R. Lapwood,et al.  Free oscillations of the earth , 1981 .

[19]  T. Tanimoto,et al.  Global Love wave phase velocity variation and its significance to plate tectonics , 1991 .

[20]  Ó. Gudmundsson.  On the effect of diffraction on traveltime measurements , 1996 .

[21]  Olav Holberg,et al.  COMPUTATIONAL ASPECTS OF THE CHOICE OF OPERATOR AND SAMPLING INTERVAL FOR NUMERICAL DIFFERENTIATION IN LARGE-SCALE SIMULATION OF WAVE PHENOMENA* , 1987 .

[22]  Robert J. Geller,et al.  DSM complete synthetic seismograms : SH, spherically symmetric, case , 1994 .

[23]  Paul G. Richards,et al.  Pulse distortion and Hilbert transformation in multiply reflected and refracted body waves , 1975, Bulletin of the Seismological Society of America.

[24]  Wei-jia Su,et al.  On the scale of mantle heterogeneity , 1992 .

[25]  Roel Snieder,et al.  Large-scale waveform inversions of surface waves for lateral heterogeneity , 1988 .

[26]  Robert D. van der Hilst,et al.  Travel-time tomography of the European-Mediterranean mantle down to 1400 km , 1993 .

[27]  Toshiro Tanimoto,et al.  High-resolution global upper mantle structure and plate tectonics , 1993 .

[28]  D. L. Anderson,et al.  Preliminary reference earth model , 1981 .