EarthModels.jl

Deprecation notice

EarthModels.jl is wholly replaced by SeisModels.jl.

EarthModels.jl will continue to work, but will not be updated in the future.

Previous README file

What is EarthModels.jl?

A Julia package for dealing with models of the Earth's (and other quasi-1D planets') seismic properties.

Currently, only three kinds of one-dimensional models are supported, but all model parameterisations and models are acceptable for inclusion. Contributions are welcome.

Built in models are PREM and AK135.

How to install

Although not registered as an official package, EarthModels.jl can be added to your Julia install like so:

julia> import Pkg; Pkg.add("https://github.com/anowacki/EarthModels.jl")

(On version 0.6 of Julia, instead use the command Pkg.clone("https://github.com/anowacki/EarthModels.jl").)

How to use

Model types

The module defines the EarthModel type and subtypes of this specify the kind of model (i.e., symmetry, nature of basis function, etc.).

julia> using EarthModels

julia> subtypes(EarthModel)
1-element Array{Any,1}:
 EarthModel1D

julia> subtypes(EarthModel1D)
3-element Array{Any,1}:
 LinearLayeredModel
 PREMPolyModel
 SteppedLayeredModel

So, there are currently three types of models implemented, all 1D models, with polynomial, linear or constant basis within each layer.

Calculating properties

You can either create your own models by creating a new instance of one of the immutable types, or use the inbuilt models. For instance, for PREM, one can evaluate at an arbitrary radius:

• V_P
• V_S
• density ρ
• anisotropic parameters V_PH, V_PV, V_SH, V_SV and η

Calculate these by calling the function with the model as the first argument:

julia> vp(PREM, 3500)
13.71171655163979

julia> Qκ(PREM, 1000)
1327.7

julia> density(AK135, radius(AK135, 20))
2.449

In the last example, we used the radius function to convert depth in the AK135 model to radius and calculate the density at 20 km depth. Some functions also accept the depth keyword argument to instead evaluate properties at a point below the surface:

julia> density(AK135, radius(AK135, 20)) == density(AK135, 20, depth=true)
true

You can also evaluate values programmatically (i.e., where the parameter of interest is a variable) by using the exported evaluate function, and broadcast the call to get multiple values:

julia> evaluate(AK135, :vp, 3580)
13.653094354838709

julia> parameters = (:vp, :vs, :density);

julia> evaluate.(AK135, parameters, 3680)
(13.591187999999999, 7.226264, 5.4003499999999995)

Model input and output

Support for reading and writing model files is currently limited. However, EarthModels does support reading and writing of Mineos-format ‘tabular’ models (i.e., SteppedLayeredModels) via the read_mineos and write_mineos functions.

Reference

Exported types

• EarthModel: Abstract supertype of all models
  • EarthModel1D: Abstract supertype of 1D models
    • LinearLayeredModel: 1D model with linearly-varying properties between node points
    • PREMPolyModel: 1D model defined by PREM-style polynomials (of arbitrary degree)
    • SteppedLayeredModel: 1D model with constant properties between node points

Exported model instances

• AK135
• PREM

Exported functions

Model properties

• depth: Return depth in km given a radius and model
• hasattenuation: Whether a model includes attenuation
• isanisotropic: Whether a model is anisotropic
• radius: Return radius in km given a depth and model
• surface_radius: Radius in km of planet

Evaluation functions

• evaluate: Evaluate a given field for a model at any radius
• vp: P-wave velocity in km/s
• vs: S-wave velocity in km/s
• density: Density in g/cm^3
• vph: Horizontal P-wave velocity in km/s
• vpv: Vertical (radial) P-wave velocity in km/s
• vsh: Horizontally-polarised S-wave velocity in km/s
• vsv: Vertically-polarised S-wave velocity in km/s
• eta: Anisotropic parameter
• Qμ, Qmu: Shear quality factor
• Qκ, Qkappa: Bulk quality factor

Derived properties

• bulk_modulus: Bulk modulus (K) in Pa
• gravity: Acceleration due to gravity in m/s^2 at a given radius
• mass: Mass in kg from centre of model to a given radius
• moment_of_inertia: MOI in kg m^2
• poissons_ratio: Poisson's ratio
• pressure: Pressure in Pa
• shear_modulus: Shear modulus (G) in Pa
• surface_mass: Mass between two radii
• youngs_modulus: Young's modulus in Pa

IO

• read_mineos: Read Mineos tabular-format file
• write_mineos: Write Mineos tabular-format file

Getting help

Types and methods are documented, so at the REPL type ? to get a help?> prompt, and type the name of the function:

help?> PREMPolyModel
search: PREMPolyModel

  PREMPolyModel <: EarthModel1D

  Type describing the Earth as a set of layers within which properties vary according to a set of
  polynomials.

  Physical parameters are represented by arrays of size (order+1,n), where n is the number of
  layers, and order is the order of polynomial which is used to represent the parameter. Hence a
  constant layer has size (1,n), and to compute the value of x in layer i, for an Earth radius of
  a km, at a radius of r km, the expression is:

  val_x = x[i,1] + (r/a)*x[i,2] + (r/a)^2*x[i,3] ... (r/a)^order*x[i,order+1]