Rayleigh-wave equivalent spheroidal modes nSl (P-SV motion) and Love-wave equivalent toroidal modes nTl (SH motion) with radial order n and angular order l provide depth-integrated constraints on Earth structure (e.g. sensitivity kernels above that are calculated from REM1D). Body waves can be understood as the time domain manifestations of the superposition and interactions of the overtones of spheroidal (P-SV phases; e.g., PKP) and toroidal modes (SH phases; e.g. ScS). In addition to identifying the arrivals of body/surface waves in time domain seismograms, measuring the eigenfrequencies and amplitude decay (e.g., quality factor Q) of the corresponding normal modes in the frequency domain is crucial for understanding interior structure. Substantial coupling can occur between different modes and their 2l+1 singlets are found to be split in the 'real’ Earth seismogram spectra due to rotation, ellipticity and heterogeneity. Our work has included complex splitting coefficients that provide information on both bulk structure (c00+id00) and lateral heterogeneity (e.g. cst, s>0).
Reference Eigenfrequencies and Quality Factors
A new reference dataset is created by reconciling a large dataset of normal modes available from the literature. These observations were obtained using five techniques: single station analysis, iterative spectral fitting (ISF), singlet stripping (SS), multiplet stripping (MS), and regionalized multiple stripping (RMS). For more details, the reader is referred to Section 2.2 of the reference below.
Reference:
Please cite the following work if you use this data.
- Moulik P. & G. Ekström (2025) Radial Structure of the Earth: (I) Model Concepts and Data, Phys. Earth Planet. Inter. doi:10.1016/j.pepi.2025.107319
You can also cite the dataset and software from this Zenodo page (Optional).
- Moulik, P. (2025) Dataset and Software for the Radial Reference Earth Model REM1D. In Phys. Earth Planet. Inter. (v1.0). Zenodo. doi: 10.5281/zenodo.8407693
Data Products
All links below point to a permanently archived data repository on Zenodo (10.5281/zenodo.8407693). Other REM1D model files are also available on Zenodo.
- Reference Normal Mode/Surface Wave Data
- Reference datasets of phase-velocity perturbations w.r.t. PREM predictions between 4-40 mHz
- Love waves (avgdcbyc_Love.ref)
- Rayleigh Waves (avgdcbyc_Rayleigh.ref)
- Reference normal mode datasets
- Radial Modes - Eigenfrequencies (RADIAL_F.ref), Quality Factors (RADIAL_Q.ref)
- Spheroidal Fundamental Modes - Eigenfrequencies (SFUND_F.ref), Quality Factors (SFUND_Q.ref)
- Spheroidal Overtones - Eigenfrequencies (SOVER_F.ref), Quality Factors (SOVER_Q.ref)
- Toroidal Fundamental Modes - Eigenfrequencies (TFUND_F.ref), Quality Factors (TFUND_Q.ref)
- Toroidal Overtones - Eigenfrequencies (TOVER_F.ref), Quality Factors (TOVER_Q.ref)
- Reference datasets of phase-velocity perturbations w.r.t. PREM predictions between 4-40 mHz
- REM1D Data Fits and Predictions
- Fits to reference datasets
- Radial Modes (FITS_RADIAL.txt)
- Spheroidal Fundamental Modes, including Rayleigh waves (FITS_SFUND.txt)
- Spheroidal Overtones (FITS_SOVER.txt)
- Toroidal Fundamental Modes, including Love waves (FITS_TFUND.txt)
- Toroidal Overtones (FITS_TOVER.txt)
- Normal mode catalogs for periods down to 24 seconds in binary (REM1D_024.rts) and HDF formats (REM1D_024.h5). These calculations use the new reference astronomic-geodetic constants (e.g. revised Gravitational constant G) from Paper I. These can be read using standard HDF5 modules (e.g. h5py) or the open-source AVNI package. Conversion from the binary file was done using the following commands:
- from avni.data import NM
- NM.write_modes_hdf( 'REM1D_024.rts', 'REM1D_024.h5')
- Non-linear crustal corrections derived from REM1D overlain with CRUST2.0 heterogeneity for Love (nonlinear_CRUST2_Love.csv) and Rayleigh waves (nonlinear_CRUST2_Rayl.csv). These files contain domega and dc/c that need to be added to the eigenfrequency and dispersion predictions from REM1D, respectively, following equations 13 and 14 in Paper I.
- Fits to reference datasets