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1-D models

Jupyter Notebook

This page is automatically generated from a Jupyter Notebook.

Note that everything here is fully automatically tested against - and thus guaranteed to work - only for the latest versions of all the Salvus packages. So please update if anything works differently on your machine.

1D Model File Format

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 depth

rho

vp and vs if ANISOTROPIC is false.

vpv, vph, vsv, vsh and eta if ANISOTROPIC is true.

QMU and QKAPPA if ANELASTIC is true

Sample 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

Built-in Models

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.

Plotting 1D Models

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()

png

# plot vp vs only
mod = model.built_in('prem_iso')
mod.plot_vp_vs_profile()

png

# 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": "--"})

png

Derived Parameters

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()

png

mod.plot_gravity()

png