MomentTensors.jl

What is MomentTensors.jl?

A Julia package for dealing with seismic moment tensors.

It is currently very limited, and useful for three main things:

1. Calculating the radiation pattern for a moment tensor;
2. Decomposing tensors into their istropic, double-couple and CLVD components; and
3. Rotating moment tensors.

I wrote this module because these are by far the most common things I need to do in my day-to-day global seismologist life.

What it isn't

Currently, no plotting is performed, nor conversion between conventions.

The module internally assumes the Harvard/Global CMT convention (see the module interactive help for details), though nothing is stopping you using another convention with it as long as you remember which indices correspond to which directions.

Input/output is limited to reading the CMTSOLUTION format used by SPECFEM3D and the NDK format used by the GlobalCMT project.

How to install

MomentTensors.jl can be added to your Julia install like so:

julia julia> import Pkg; Pkg.add("MomentTensors")

How to use

MT type

MomentTensors.jl represents moment tensors using the MT type.

Construction

They can be constructed by: - passing a set of six moment tensor components, in the order M_rr, M_θθ, M_φφ, M_rθ, M_rφ, M_θφ), - a vector of length six containing these components, - a 3 × 3 matrix M_ij with i,j ∈ {r,θ,φ}, or - the strike, dip and rake (in Aki & Richards convention) plus a moment in N.m.

The element type of an MT{T} where T instance is determined automatically from the values supplied, or one can specify a desired element type explicitly with e.g. MT{Float32}(1, 2, 3, 4, 5, 6).

See the docstring for MT for more details of construction.

Indexing

To retrieve an individual component of the MT m, you can: - access the i,j component with m[i,j] where i,j ∈ {1,2,3}; - get the named components with m[:rθ] or equivalently m[:rt] (see the docstring for getindex); and - get the I^th component of the six-element vector with m[I].

Exported functions

• MT: Construct a new moment tensor.
• amplitude_v_azimuth: Compute the P, SV and SH amplitudes, and polarisation angle, for a particular takeoff angle at a range of azimuths.
• cmtsolution: Construct a new moment tensor from a string in the SPECFEM3D 'CMTSOLUTION' format
• decompose: Decompose a moment tensor into its isotropic, double-couple and CLVD components, and report the relative proportion of the isotropic, deviatoric and double-couple parts, plus their associated moments.
• eps_non_dc: Calculate the non-double-couple component of an MT as defined by Giardini.
• m0: Return the scalar moment, given a moment magnitude.
• mw: Return the moment magnitude, given a scalar moment.
• ndk: Construct a new moment tensor from a string in the 'NDK' format used by the Global CMT project.
• radiation_pattern: Compute the P, SV and SH amplitude, and S polarisation angle, along a specific takeoff angle and azimuth.
• rotate: Rotate an MT.

Getting help

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

```julia help?> MT search: MT mtime SymTridiagonal Meta Method match Matrix mktemp methods matchall

MT(rr, θθ, ϕϕ, rθ, rϕ, θϕ) -> ::MT MT(M::Vector(6)) -> ::MT MT(M::Array(3,3)) -> ::MT MT(strike, dip, rake, M0) -> ::MT

Construct a new MT (moment tensor) in the native frame used by MomentTensors:

•    Radial (r) upwards

•    Colatitude (θ or t) southwards

•    Longitude (ϕ or p) eastwards)

Several forms exist to construct a moment tensor:

•    Supply individual components as a list of arguments

•    Supply a 6-vector

•    Give a 3×3 matrix

•    Specify a strike, dip and rake in degrees, and scalar moment (N.m)

One may access the values of a moment tensor M in two ways:

1.   M[i,j] yields the elements of M.m as if they were a two-tensor

2.   M[::Symbol] yields the elements by name; see getindex(::MT) for details

```

Contributing

If you find a bug with MomentTensors or have suggestions for improvement, please open an issue giving as much information as possible on how to reproduce the bug or problem.

Pull requests to add new features are welcome and will be seriously considered. Please note that the package aims to be lightweight and rely on few external dependencies.