ccrook
commented
1 year ago Followed up with Matt on these comments
Thank you so much for your comments on the deformation model specification proposal. I won't address in detail now, but of course I am especially grateful for your spotting on the cyclic time function. It has been a source of concern to me that no-one else has properly looked at the formulae in this proposal, so this is a great relief to me.
It looks like your comment on the hyperbolic tangent function is truncated, so feel free to elaborate further on that
Re hyperbolic, I was just wondering if the /2 in the hyperbolic is necessary in that it just makes the equation more complex and hence prone to error and just means the scale factor is x2.
The hyperbolic time function was proposed by a geophysicist in the group (Jeff Freymueller) as a model used for slow slip events. The origin of the time function is in the middle of the event.
It is considered as starting some time before that when the tanh function is approximately -1 and finishing some time after when it is approximately 1. The scaling and offset applied to tanh in the deformation model is to provide time function that is (more or less) 0 at the beginning of the event, and 1 at the end of the event. The spatial function represents the magnitude of the event. I am not sure it will be used as I suspect that the time evolution of slow slip events will tend to be more complex spatially than allowed for by a simple time function times a spatial function. However it allows at least a first order approximation.
To date we have not modelled slow slip events in the NZ deformation model - they are averaged into the national velocity model. However, I can imagine that it is something that there will be an increasing need in the future for as we move to more real time maintenance of the deformation model based on observation techniques such as InSAR, and as the dependence on accurate transformations from ITRF grows due to the use of technologies such as SBAS.
To cover some of your other points:
Error of the time function.
You are correct - it is considered error free. Or to put it another way, the error is all placed in the spatial function. This means the total error from a component is proportional to the time function, which is I think a reasonable first order approximation.
In practice the error is at best indicative in any case. Formal error estimation carried though the derivation of the model is unlikely to be realistic, even if it is practical. Projecting the error into the future is also not very realistic with the possibility of earthquakes or other deformation events.
To my mind the much bigger flaw in the model is that it doesn't represent the covariance of the displacements between grid nodes, so any calculation of the error of a vector (the commonest use case) is completely unrealistic. Possibly some distance based covariance function might be a good alternative?
Despite these shortcomings there was a strong desire in the project team to at least provide some representation of the error of the model, and the proposed approach was adopted. There is a body of discussion on this buried in the github issues for the project.
Time-varying cyclic to reflect modulation of amplitude or shifting phase over time as occurs with seasonal signals cf pure annual.
An interest potential future option and not one that came up at all in our discussions of time functions. Thank you for raising it.
Helpful replies and I am content with that, and it is a good start to build on. Good point on the covariances.
PART B