Negative observation weights

[CedricDM]

Hi Anthony,

I am using NonLinLoc to get locations for extensive earthquake catalogues in a remote region in New Zealand. When running NLLoc I am getting the following errors for some of my stations.

• NLLoc: ERROR" negative observation weight
• NLLoc: Gaussian model error (see LOCGAU) may be too large relative to obs uncertainty (see LOCQUAL2ERR, or NLL-Phase format ErrMag)

My current input file setup is as follows:

LOCGAU 0.2 40.0
LOCGAU2 0.01 0.05 0.5

LOCQUAL2ERR 0.05 0.1 0.2 0.6 99999.9 99999.9 99999.9 99999.9 99999.9 99999.9

As I am using automated phase detection algorithms to produce extensive earthquake catalogues, I have currently set the ErrMag for every pick to 0.1s as manually evaluating them will take too much time.

While this error is produced, the stations in question still are used by NLLoc as the picks both appear in the list of used picks and in the output file with an assigned time residual and weight. I was wondering what produces these negative observation weights and what their consequences on the final results are? Also, do you have any recommendations to resolve this error?

Kind regards,

Cedric

[alomax]

Hello Cedric,

I think the problem is (but am not sure, I would have to check carefully the code and underlying algorithms):
The model error values go into a covariance matrix of observations which is inverted before use in location (following Tarantola and Valette, 1982). So if the off-diagonal terms, which are scaled by correlation length, are too large, the inverse has negative elements.

So I think your large correlation length of 40.0 km needs to be reduced.

But in general, with LOCMETH EDT* I use correlation length = 0.0, since the EDT formulation considers pairs of observations in accumulating the misfit, which diverges from the original Tarantola and Valette, 1982 formulation which only accumulates over individual observations. Thus off-diagonal terms in the covariance matrix are different entities in EDT vs the original formulation.

Typically, for a local-regional scale study, I use settings like:

LOCGAU 0.05 0.0
LOCGAU2 0.02 0.02 1.0

Best regards,

Anthony

Tarantola and Valette, (1982), "Inverse Problems = Quest for Information", J Geophys 50, 159-170.