Mondaic
This tutorial is presented as Python code running inside a Jupyter Notebook, the recommended way to use Salvus. To run it yourself you can copy/type each individual cell or directly download the full notebook, including all required files.
The 1D model file format is adopted from AxiSEM and also used as a standard within the NASA Insight mission. It is based on
KEY VALUE pairs as follows:KEY VALUE definitions
The key value format can accomodate 3 different types of values: single values, list of values and tables,
all separated by white space. Keys are case sensitive and must not have leading white space. Comments
are indicated byt the # character. Continuation lines of tables are indented by at least one blank.
# single value KEY VALUE # list of values KEY VALUE1 VALUE2 VALUE3 # table KEY HEADER1 HEADER2 VALUE11 VALUE21 VALUE12 VALUE22
Available Keys for Salvus
For Salvus, the following keys can be used:
NAME Name of the model. type: string, default: filename without ending.DESCRIPTION Reference or verbal description of the model.ANISOTROPIC Whether the model is anisotropic. type: boolean, default: false.ANELASTIC Whether the model includes an attenuation model. type: boolean, default: false.REFERENCE_FREQUENCY Frequency at which the seismic velocities are defined in Hz. type: float, default:
1.0.UNITS Units used for density, seismic velocities and depth/radius, either m for SI units (m, m/s, kg/m 3 )
or km for (km, km/s, g/cm 3 ). type: string, default: m.COLUMNS Table containing the depth dependent model parameters. type: float.Depth dependent parameters
Discontinuities in the model (both first and second order) are detected based on repeated radius/depth values. In between these discontinuities, paramteres are assumed to be smooth and interpolated using splines (cubic by default). The table columns in the table
COLUMNS have no particular order, the rows can be sorted either from top to bottom or vice versa. The table needs to contain at least these colums:radius or depthrhovp and vs if ANISOTROPIC is false.vpv, vph, vsv, vsh and eta if ANISOTROPIC is true.QMU and QKAPPA if ANELASTIC is trueSample File 1: a local isotropic elastic model with 3 layers
A three layer 1D model where the seismic velocities have gradients in the upper 2 layers and constant below.
NAME true_model UNITS m COLUMNS depth rho vp vs 0.0 2384.4 3500.0 2020.0 2000.0 2441.9 3850.0 2223.0 2000.0 2570.1 4725.0 2728.0 7000.0 2780.8 6475.0 3738.0 7000.0 2835.5 7000.0 4041.0 10000.0 2835.5 7000.0 4041.0
Sample File 2: a global PREM model
some lines removed as indicated by
[...]:# Input file for Salvus NAME prem_ani ANELASTIC T ANISOTROPIC T UNITS m COLUMNS radius rho vpv vsv qka qmu vph vsh eta 6371000. 2600.00 5800.00 3200.00 57827.0 600.0 5800.00 3200.00 1.00000 6356000. 2600.00 5800.00 3200.00 57827.0 600.0 5800.00 3200.00 1.00000 # Discontinuity 1, depth: 15.00 km < this just a comment and ignored by the software 6356000. 2900.00 6800.00 3900.00 57827.0 600.0 6800.00 3900.00 1.00000 6346600. 2900.00 6800.00 3900.00 57827.0 600.0 6800.00 3900.00 1.00000 # Discontinuity 2, depth: 24.40 km 6346600. 3380.75 8190.32 4396.02 57827.0 600.0 8190.32 4611.80 0.90039 6335480. 3379.54 8182.26 4398.58 57827.0 600.0 8182.26 4601.82 0.90471 [...] 5771000. 3975.82 10157.83 5515.93 57827.0 143.0 10157.83 5515.93 1.00000 # Discontinuity 6, depth: 600.00 km > second order discontinuity 5771000. 3975.82 10157.76 5516.02 57827.0 143.0 10157.76 5516.02 1.00000 [... 3480000. 5566.46 13716.62 7264.65 57827.0 312.0 13716.62 7264.65 1.00000 # Discontinuity 10, depth: 2891.00 km > fluid by vs=0 3480000. 9903.44 8064.79 0.00 57827.0 0.0 8064.79 0.00 1.00000 [...] 1221500. 12166.33 10355.72 0.00 57827.0 0.0 10355.72 0.00 1.00000 # Discontinuity 11, depth: 5149.50 km 1221500. 12763.61 11028.26 3504.31 1327.7 84.6 11028.26 3504.31 1.00000 [...] 0. 13088.50 11262.20 3667.80 1327.7 84.6 11262.20 3667.80 1.00000
Salvus includes a number of popular 1D models that can directly be used for meshing.
from salvus.mesh.models_1D import model
for mname in sorted(model.get_builtin_models()):
mod = model.built_in(mname)
print("\033[1m" + mod.name + "\033[0m")
print(mod.description + "\n")Moon Weber Weber, Renee C., Pei Ying Lin, Edward J. Garnero, Quentin Williams, and Philippe Lognonné. 2011. “Seismic Detection of the Lunar Core.” Science 331 (6015): 309–12. doi:10.1126/science.1199375. VPREMOON Velocity model for the moon according to Garcia, Raphaël F., Jeannine Gagnepain-Beyneix, Sébastien Chevrot, and Philippe Lognonné. 2011. “Very Preliminary Reference Moon Model.” Physics of the Earth and Planetary Interiors 188 (1-2) (September): 96–113. doi:10.1016/j.pepi.2011.06.015. VPREMOON_noLVL Velocity model for the moon according to Garcia, Raphaël F., Jeannine Gagnepain-Beyneix, Sébastien Chevrot, and Philippe Lognonné. 2011. “Very Preliminary Reference Moon Model.” Physics of the Earth and Planetary Interiors 188 (1-2) (September): 96–113. doi:10.1016/j.pepi.2011.06.015. Shallow low velocity layer removed. ak135 Kennett, Brian L.N., E Robert Engdahl, and Ray Buland. 1995. “Constraints on Seismic Velocities in the Earth from Traveltimes.” Geophysical Journal International 122: 108–24. Q from PREM. ak135f Montagner, Jean Paul, and Brian L.N. Kennett. 1996. “How to Reconcile Body-Wave and Normal-Mode Reference Earth Models.” Geophysical Journal International 125: 229–48. doi:10.1111/j.1365-246X.1996.tb06548.x. csem Fichtner, Andreas, Dirk-Philip van Herwaarden, Michael Afanasiev, Saule Simute, Lion Krischer, Yesim Cubuk-Sabuncu, Tuncay Taymaz, Lorenzo Colli, Erdinc Saygin, Antonio Villasenor, Jeannot Trampert, Paul Cupillard, Hans-Peter Bunge, and Heiner Igel. 2018. "The Collaborative Seismic Earth Model: Generation 1." Geophysical Research Letters 45(9): 4007-4016. iasp91 Kennett, Brian L.N., and E Robert Engdahl. 1991. “Traveltimes for Global Earthquake Location and Phase Identification.” Geophysical Journal International 105 (2): 429–65. doi:10.1111/j.1365-246X.1991.tb06724.x. Density and Q from PREM. mars_sohl Sohl, Frank, and Tilman Spohn. 1997. “The Interior Structure of Mars: Implications from SNC Meteorites.” Journal of Geophysical Research: Planets 102 (E1): 1613–35. doi:10.1029/96JE03419. Model A. prem_ani Dziewonski, A.M., and Don L. Anderson. 1981. “Preliminary Reference Earth Model.” Physics of the Earth and Planetary Interiors 25 (4): 297–356. doi:10.1016/0031-9201(81)90046-7. No ocean layer. prem_ani_no_crust Dziewonski, A.M., and Don L. Anderson. 1981. “Preliminary Reference Earth Model.” Physics of the Earth and Planetary Interiors 25 (4): 297–356. doi:10.1016/0031-9201(81)90046-7. Crust replaced by upper mantle material. prem_ani_ocean Dziewonski, A.M., and Don L. Anderson. 1981. “Preliminary Reference Earth Model.” Physics of the Earth and Planetary Interiors 25 (4): 297–356. doi:10.1016/0031-9201(81)90046-7. prem_ani_one_crust Dziewonski, A.M., and Don L. Anderson. 1981. “Preliminary Reference Earth Model.” Physics of the Earth and Planetary Interiors 25 (4): 297–356. doi:10.1016/0031-9201(81)90046-7. Upper crustal layer replaced by lower crustal material. prem_crust20_cont Dziewonski, A.M., and Don L. Anderson. 1981. “Preliminary Reference Earth Model.” Physics of the Earth and Planetary Interiors 25 (4): 297–356. doi:10.1016/0031-9201(81)90046-7. Crust replaced by crust 2.0 continental average model. prem_crust20_global Dziewonski, A.M., and Don L. Anderson. 1981. “Preliminary Reference Earth Model.” Physics of the Earth and Planetary Interiors 25 (4): 297–356. doi:10.1016/0031-9201(81)90046-7. Crust replaced by crust 2.0 global average model. prem_crust20_ocean Dziewonski, A.M., and Don L. Anderson. 1981. “Preliminary Reference Earth Model.” Physics of the Earth and Planetary Interiors 25 (4): 297–356. doi:10.1016/0031-9201(81)90046-7. Crust replaced by crust 2.0 oceanic average model. prem_iso Dziewonski, A.M., and Don L. Anderson. 1981. “Preliminary Reference Earth Model.” Physics of the Earth and Planetary Interiors 25 (4): 297–356. doi:10.1016/0031-9201(81)90046-7. No ocean layer. prem_iso_no_crust Dziewonski, A.M., and Don L. Anderson. 1981. “Preliminary Reference Earth Model.” Physics of the Earth and Planetary Interiors 25 (4): 297–356. doi:10.1016/0031-9201(81)90046-7. Crust replaced by upper mantle material. prem_iso_one_crust Dziewonski, A.M., and Don L. Anderson. 1981. “Preliminary Reference Earth Model.” Physics of the Earth and Planetary Interiors 25 (4): 297–356. doi:10.1016/0031-9201(81)90046-7. Upper crustal layer replaced by lower crustal material.
Salvus' 1D model class includes funcionality to plot 1D models in a number of different ways.
# plot all model parameters
mod = model.built_in("prem_ani")
mod.plot()
# plot vp vs only
mod = model.built_in("prem_iso")
mod.plot_vp_vs_profile()
# compare 2 models
mod1 = model.built_in("prem_iso")
mod2 = model.built_in("ak135f")
figure = mod1.plot_vp_vs_profile(show=False)
figure = mod2.plot_vp_vs_profile(
show=True, figure=figure, linestylemap={"VP": "--", "VS": "--"}
)
Salvus' model class can also compute quantities that derive from the 1D parameters, in particular ellipticity as a function of depth by solving Clairaut's equation and the gravity potential and force by solving Poisson's equation:
mod = model.built_in("prem_ani")
mod.plot_ellipticity()
mod.plot_gravity()
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