V021

[paudetseis]

This PR is a major effort towards aligning the tilt calculation to Bell et al (2015) and allowing the calculation of the tilt angle (measured down from the vertical axis) in addition to the tilt direction (measured CW from H1). In-depth analysis of stations 7D.G03A and 7D.M03A uncovered inconsistencies in the analysis of Bell et al. (2015) and code improvement suggestions for the MATLAB ATaCR code.

• In Bell et al., the rotation of the horizontal components is counterclockwise in the calculation of the tilt direction, and the coherence is calculated between the rotated H2 (as opposed to H1) and the vertical HZ (example shown for 7D.G03A).
• In the MATLAB ATaCR, the rotation is also counterclockwise but correctly rotates H1 and not H2, and the frequency band used to calculate the tilt direction (example shown for 7D.M03A) is outside the band of high coherence, which biases the calculation. Also, a linear mean is used for the mean phase calculation; a circular mean gives much improved results in the selection of the correct azimuth for the double-peaked coherence.

To-do:

• Update the documentation for the example shown (7D.M03A) - explain why this differs from the MATLAB ATaCR
• Add example of the --figTilt to show the components of the transfer function, and the selection of frequency band (--tilt-freqs)
• Regenerate the scripts documentation and check all the tutorials.
• Calculate robust tilt measurements (remove outliers) and uncertainty
• Make sure to use only gooddays in the tilt vs time figure.
• Allow for left-handedness (check standard definitions) (Will require more investigation - many possible component definitions in this case)
• Add figure showing tilt as vector in polar projection (relative to H1, as in Bell et al., 2015)
• Add twin axis on admittance panel for daily Tilt figure showing tilt angle
• Add DataStream object for tilt+compliance removal, in addition to EventStream, which only corrects windows containing earthquake signals. This will allow rebuilding a waveform archive with corrected vertical components (e.g., for noise correlations, etc.). (Next version)
• Write a new script to remove noise from continuous waveforms (i.e., using a DayStream object) (Next version)
• Add stationXML support for scripts - see corresponding revisions to StDb