Check comparisons with prop8 paper

[valentineap]

Comment from @hemmelig in openjournals/joss-reviews#4217:

I ran the provided script for re-producing the figures presented in O’Toole & Woodhouse (2011) and O’Toole et al. (2012). Critically, these only run if the user installs matplotlib, which is not addressed anywhere in the documentation. Where possible, I tried to ensure I was comparing the figures at a similar scale/aspect ratio. By eye, the figures were largely identical. I note, however, some differences:

2011, Fig 1 – vertical traces show a slight concave deflection after the primary peak (strongest in proximal traces). There also appear to be a number of deflections later in the prop8 time series that are absent in the pyprop8 figures - e.g., using the notation “r2” to represent the nth trace (from top to bottom) of the radial component: r2, r4, r5, r10, t2, t6, v3, v7) 2011, Fig 5 – pyprop8 figure seems significantly smoother than that presented in the the original paper 2012, Fig 1 – a number of pyprop8 the GPS excitation kernels in pyprop8 do not appear to meet the reference line as they do in the original paper figure – e.g. Mr,theta East/Vertical, etc. This may well just be a scaling/reference point issue, but would be good to get some clarity. 2012, Fig 2 – a much clearer example of what I noted for Fig 1. Depth, zc East component intersects with the reference line, but the pyprop8 example does not. Time, tc North component looks quite different, too. Latitude North/Vertical, same note.

Also deal with matplotlib dependency.

[valentineap]

Unfortunately, but perhaps inevitably, there are various details that are not fully and unambiguously described in the papers. For example, the source-time function used in Fig. 1 of O'Toole & Woodhouse (2011) is described as a 'symmetrical cosine tapered boxcar', but no explicit formula is given, and I do not seem to have any scripts/code that can confirm precisely what was done. It would seem some information is missing, regarding the length of taper applied to the boxcar. [In fact the pyprop8 version was using a trapezoidal source time-function here, but changing this does not seem to resolve the issue.]

For that Fig.1, specifically, it seems to me that there are artefacts present in the traces shown in the paper: there are acausal long-period features that I suspect are 'edge effects' from some aspect of the processing. This is most evident in trace r17 (per @hemmelig's notation) where there is a clear downwards deflection in the first 30s of the trace, before the arrival of the main wavefront. Other traces including r2, r5 and r10 show something similar towards the end of the time series, as noted by the reviewer. Given that these do not display any 'move-out' or other coherent behaviour across traces, and have no obvious explanation within the simple physics of the setup here, I am comfortable not to be reproducing these in our new version.

[valentineap]

For Fig. 5 (2011), I again think the issue is with the source time-function. The paper seems to indicate that a cosine-tapered boxcar and another, untapered boxcar are both convolved with the traces. I have tried various combinations of possibilities here and have not hit on anything that matches the paper precisely.

For the 2012 paper it seems the traces are filtered but not otherwise convolved with a source time function - I think I can now reproduce these and address the issues noted by the reviewer.

[valentineap]

I think these comparisons are as close as they're going to get, and the differences are explainable. I have clarified this within the relevant scripts. I am therefore closing this issue, but please reopen if you still have concerns.