Surface Waves

How fast do surface waves travel globally after any earthquake?
Do we get the same information from various measurement techniques?
Which features in the Earth are robust and can be resolved by a reference model?

Surface waves are the most prominent phases recorded at teleseismic distances at periods longer than 30 s, especially from shallow-focus earthquakes. Two types of surface waves are observed, distinguished by their polarization during propagation through the Earth: Love (SH) and Rayleigh (P–SV) waves, recorded on the transverse and vertical/longitudinal components, respectively. Surface wave arrivals are denoted by the orbit number (e.g. No = 1 for minor-arc L1 or R1 waves), a proxy for the number of times the wave circles around the Earth (Nc = [No – 1]/2 for odd No, No/2 otherwise). The wave trains excited by large mega-thrust earthquakes (Mw ≥ 7.5) circle the Earth multiple times (Nc ≥ 1) for many hours and manifest as discernible higher-orbit arrivals (e.g. L3–L5, R3–R5). Generation and propagation of surface waves can also be classified based on the properties of the corresponding normal modes. Fundamental-mode surface wave trains are excited more strongly by shallow and intermediate-depth earthquakes (h < 250 km) and appear well separated from other phases at teleseismic distances (> 30◦). Higher-mode or overtone vibrations are excited by deeper earthquakes and appear as faster propagating, compact wave packets that contribute to the long-period body waveforms. Characterizing surface waves and overtones is critical for the construction of elastic reference Earth models (see REM3D).

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Zenodo Repository

All the data and software can be downloaded from our Open Access Zenodo repository.


Please mail your inquiries to Raj Moulik ( at [email protected] 

Global reference seismological data sets: multimode surface wave dispersion

Reference data with uncertainties are useful for improving existing measurement techniques, validating models of interior structure, calculating teleseismic data corrections in local or multiscale investigations and developing a 3-D reference Earth model. This study was done in collaboration with 18 scientists from 16 institutions in 7 countries who actively participated in the REM3D project. The project assimilated, archived, reconciled and modeled big (>200 million measurements) and diverse surface-wave datasets for global subsurface structure.

The reference data set summarizes measurements of dispersion of fundamental-mode surface waves and up to six overtone branches from 44,871 earthquakes recorded on 12,222 globally distributed seismographic stations. Dispersion curves are specified at a set of reference periods between 25 and 250 s to determine propagation-phase anomalies with respect to a reference Earth model. Empirically determined observational uncertainties (1 sigma) for each wave type, branch number and period can be found in Table 3. 


[I] Reconciled large and diverse catalogues of Love-wave (49.65 million) and Rayleigh-wave dispersion (177.66 million) from eight groups worldwide.
[II] Retrieved missing station and earthquake metadata in several legacy compilations and codified scalable formats to facilitate reproducibility, easy storage and fast I/O on HPC systems.
[III] Systematic discrepancies between raw phase anomalies can be attributed to discrepant theoretical approximations, reference Earth models and processing schemes.
[IV] Phase-velocity variations yielded by the inversion of the summary data set are highly correlated (R ≥ 0.8) with those from the quality-controlled contributing data sets, especially for long-wavelength variations (up to degree ∼25) in fundamental-mode dispersion (50–100 s).
[IV] Only 2ζ azimuthal variations in phase velocity of fundamental-mode Rayleigh waves are required; maps of 2ζ azimuthal variations are highly consistent between catalogues ( R = 0.6–0.8).


Please cite the following work if you use this data or software.

  • Moulik, P. et al., (2022) Global reference seismological data sets: multimode surface wave dispersion. Geophys J Int 228, 1808–1849, doi: 10.1093/gji/ggab418pdf

You can also cite the dataset and software from this Zenodo page (Optional).

  • Moulik, P. (2022) Dataset for Global Reference Seismological Data Sets: Multimode Surface Wave Dispersion. In Geophys. J. Int. (v1.0, Vol. 228, pp. 1808–1849). Zenodo. doi: 10.5281/zenodo.8371228

Download data products:

All the following data and software can be downloaded from our Zenodo repository. Reference dataset of phase-anomaly observations from this work is available below. All ASCII files are gzipped. We recommend the use of the HDF5 container files for efficient storage.

HDF5 Container Format

Summary (reference) data between pairs of 2562 evenly-spaced with an average knot spacing 4.33◦. These files store the data in the RSDF HDF5 container format. These can be read using standard modules (e.g. h5py) or using AVNI. For example, to read the reference data for fundamental mode R1 waves at 100s into a Pandas Dataframe containing data (df['data']) and a dictionary with the metadata (df['metadata']), and thereafter write contents to an ASCII text file, enter the following in Python:

  • from import readSWhdf5,writeSWascii
  • df=readSWhdf5(query='0/100.0/R1/REM3D',hdffile='',datatype='summary')
  • writeSWascii(df,'test.txt')

ASCII (text) Format

These files contain the same reference data as the HDF5 files above but in gzipped ASCII files. The files are named according to the overtone branch, wave type and period as Summary.$overtone.$wave.$period.REM3D.gz. Table A1 from the paper describes the various columns in the surface-wave RSDF ASCII format files.

Other Data Products

  • ReferenceSW_Moulik2022_Figures(.zip or .pdf) - contains all figures from the paper in .png format
  • - contains scatter plots similar to Figure 5 in the paper, which compares measurements between two sets of techniques. The files with the suffix *raw.png are comparisons for original raw datasets, which those with the suffix *.clean.png are comparisons after the entire workflow is completed to create the clean datasets (e.g. Figure 13, bottom row).
  • and - contains list of source-station paths where discrepancies were found between pairs of techniques. Half (±0.9–1.1 · π ) or full-cycle discrepancies (±0.9–1.1 · 2π ) identified in Section 4.5 are used during outlier analysis (Section 5.3) to create the clean summary dataset. Half- and full-cycle discrepancies identified in these files indicate potential polarity reversals and cycle skips respectively. Note that all of these discrepancies have not been checked for specific causes manually. 
  • vflip-table.REM3D - an ASCII file containing station names and start/end times where cycle skipping issues have been confirmed through manual analysis. This is in contrast to the automated full-cycle discrepancies identified in above.
  • M1442 and B2562 - Files containing the knot locations of evenly-spaced points on the surface. B2562 has an average knot spacing of 4.33◦ and is used as the underlying grid for the homogenization process to get summary data (Section 5.1). In order to obtain 2-D variations in local phase slowness or velocity, we use 1442 splines with an average knot spacing of 5.77◦ (Section 6.1)
  • and - Clean homogenized data for each research group obtained at the end of our workflow (Figure 2). The ASCII files containing the same data are provided in and summary dataset listed earlier represents the reconciled measurements, and should be preferred over those of individual groups in most applications.
  • - Contains an example of a 2D slowness map inversion with 2ζ azimuthal variations using the reference summary dataset at 100s for fundamental-mode minor-arc Rayleigh waves (R1). Also provided are plots for anistropic variation (Anisotropy_Plots), spline coeffients of 1442 evenly-spaced spherical splines (Spline_Coefficients), and corresponding values at every 1X1 degree pixel in extended pixel format (Maps_epix). The aim of this study is to provide a dispersion measurements of surface-wave arrivals, not to provide detailed 2D phase velocity/slowness models. 

Note about Data Format

A file explaining the format of the data files can be retrieved from the reference seismic data format (RSDF) project. Table A1 from the paper describes the various columns in the surface-wave RSDF format file above, and is provided below for reference.