https://github.com/anowacki/seissplit.jl

Seismic shear wave splitting analysis in Julia

https://github.com/anowacki/seissplit.jl

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Seismic shear wave splitting analysis in Julia

https://github.com/anowacki/SeisSplit.jl/blob/master/

# SeisSplit

SeisSplit is a package for measuring shear wave splitting using the
minimum eigenvalue method of Silver & Chan (1991), as modified by
Walsh et al. (2013).

It uses the [Seis.jl](https://github.com/anowacki/Seis.jl) package which
provides fast, flexible seismic analysis.

Computation of splitting using the rotation-correlation method
(e.g., Bowman & Ando, 1987) is also possible.  This is computed
automatically by the main `splitting` function for quality control
purposes.

## Installing

```julia
julia> ] # Press ']' to get to package mode

(@v1.5) pkg> add https://github.com/anowacki/Geodesics.jl https://github.com/anowacki/Seis.jl https://github.com/anowacki/SeisSplit.jl
```

## Using

The `splitting` function performs shear wave splitting analysis and returns a `SeisSplit.Result`
type containing information about the analysis.  Provide two `Seis.Trace`s, and
optionally specify the maximum delay time and number of fast orientation and delay
time analysis points.

We can show an example of using SeisSplit on some synthetic test data,
where the signal has had splitting of 1.4 s applied with a fast shear
wave orientation of 40.  Looking at the result `s`, the values of `s.phi_best`
and `s.dt_best` show have recovered the expected splitting parameters:

```julia
julia> using Seis, SeisSplit

julia> data_dir = joinpath(dirname(pathof(SeisSplit)), "..", "test", "data");

julia> n, e = Seis.read_sac.(joinpath(data_dir, "wave.BH") .* ("N", "E"))
(Seis.Trace(.SWAV..BHN: delta=0.05, b=0.0, nsamples=1999), Seis.Trace(.SWAV..BHE: delta=0.05, b=0.0, nsamples=1999))

julia> s = splitting(n, e, 15, 35)
SeisSplit.Result{Float32,Array{Float32,1}}:
           phi: -90.0:1.0:90.0
            dt: 0.0:0.1:4.0
          lam1: 18141 Array{Float32,2}: [68.06532, ..., 68.06532]
          lam2: 18141 Array{Float32,2}: [40.643196, ..., 40.643196]
      phi_best: 40.0 
          dphi: 0.5 
       dt_best: 1.4 s
           ddt: 0.025 s
          spol: 10.00806 
         dspol: 0.22093524 
        trace1: Seis.Trace(.SWAV..BHN: delta=0.05, b=0.0, nsamples=1999)
        trace2: Seis.Trace(.SWAV..BHE: delta=0.05, b=0.0, nsamples=1999)
  window_start: 15 s
    window_end: 35 s
           ndf: 302
     xcorr_phi: 90 Array{Float64,1}: [-90.0, ..., -88.0]
      xcorr_dt: 81 Array{Float32,1}: [0.0, ..., 0.05]
     xcorr_map: 8190 Array{Float32,2}: [0.48693663, ..., 0.5155819]
xcorr_phi_best: 42.0 
 xcorr_dt_best: 1.35 s
```

The following is the docstring for the `splitting` function:

```
    splitting(t1, t2, window_start=starttime(t1), window_end=endtime(t1); nphi=181, ndt=41, dt_max=4, xcorr=true) -> results

Perform a search over a pair of Seis traces, `t1` and `t2`, for the smallest value of the
minimum eigenvalue of the covariance matrix between the traces, for a set of `nphi``ndt`
shear wave splitting operators, up to `dt_max` s.

 ## Output

`results` is a `SeisSplit.Result` containing:

- `phi`: The set of fast shear wave orientations in 
- `dt`: The set of delays times in s
- `lam1`: The larger eigenvalues at each [phi,dt] point
- `lam2`: The smaller eigenvalues at each point
- `phi_best` and `dphi`: The best  and its 1 uncertainty.   is measured
  clockwise from local north (towards east) in .
- `dt_best` and `ddt`: The best t and its 1 uncertainty, in s
- `spol` and `dspol`: The source polarisation and an estimate of its uncertainty for the
  best-fitting  and t.  `spol` is given in  clockwise of local north.
- `trace1` and `trace2`, the original input traces, where `trace2` is clockwise of `trace1`
- `window_start`, `window_end`, the analysis time window end points.
- `ndf`, the number of degrees of freedom in the signal.

If `xcorr` is `true`, then the rotation correlation map for the pair
of traces is also computed and the following additional fields are
present in `results`:

- `xcorr_phi`: Angles over which rotation correlation was calculated ()
- `xcorr_dt`: Delay times over which rotation correlation was calculated (s)
- `xcorr_map`: Cross correlation at each [phi,dt] point
- `xcorr_phi_best`: Fast orientation of maximum cross correlation ()
- `xcorr_dt_best`: Delay time of maximum cross correlation (s)
```

### Plotting results

You can create a diagnostic plot of a `SeisSplit.Result` by loading
[`Plots.jl`](https://github.com/JuliaPlots/Plots.jl) and calling `plot()` on the result:

```julia
julia> using Plots

julia> plot(s)
```

![Example of a SeisSplit diagnostic plot](docs/images/diagnostic_plot_example.svg)

(Note that Plots.jl must be included in the current environment; if it
is not, then simply do `import Pkg; Pkg.add("Plots")` first.)


## Contributing

To report a bug, please
[open an issue](https://github.com/anowacki/SeisSplit.jl/issues/new) and
provide as much detail as possible to reproduce the bug.  Ideally this
should be in the form of some code representing a
minimal non-working example ([MWE](https://stackoverflow.com/help/minimal-reproducible-example)), but all reports are welcome.  I will
try and fix any bugs that are reported, but please note that this may
not be very quickly, depending on my other commitments.

Pull requests (especially if they implement bug fixes) are very welcome.
Feature requests will be seriously considered.  Please make sure that
new code comes with tests, and that all tests pass with your addition.


## References

- Bowman, J. R., Ando, M., 1987. Shear-wave splitting in the
  upper-mantle wedge above the Tonga subduction zone.  Geophys J R
  Astr Soc 88, 2541.
  doi:[10.1111/j.1365-246X.1987.tb01367.x](https://doi.org/10.1111/j.1365-246X.1987.tb01367.x)
- Silver, P.G., Chan, W.W., 1991. Shear-wave splitting and subcontinental mantle
  deformation. J Geophys Res-Sol Ea 96, 1642916454.
  doi:[10.1029/91JB00899](https://doi.org/10.1029/91JB00899)
- Walsh, E., Arnold, R., Savage, M.K., 2013. Silver and Chan revisited.
  Journal of Geophysical Research: Solid Earth 118, 55005515.
  doi:[10.1002/jgrb.50386](https://doi.org/10.1002/jgrb.50386)

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