Unusual travel-time grids

[SquirrelKnight]

Hi @bernard-giroux. Sorry for troubling you again. I have been making further progress in using the travel-time grids with my location algorithm, however I noticed that many of the events seemed to coalesce into extremely linear patterns. When compared to locations used with NonLinLoc and Stingray derived travel-time grids, I do not see such linear features. Further, I have compared the travel-time grids amongst these methods, and have found that the same linear features are reflected by the differential of the travel-times. I've attached several example figures to show this, and I have also tested using both DSPM and FSM methods. Please note that I did not create the Stingray travel-time grids, as they were provided to me by a colleague.

Here is an example comparing NonLinLoc to the DSPM output:

Here is an example comparing Stingray to the DSPM output:

Here is an example comparing NonLinLoc to the FSM output:

Here is an example comparing Stingray to the FSM output:

Finally, here is a comparison between the DSPM and FSM outputs:

I have also noted that changing the receiver seems to alter the travel-time grid as well (this is shown with the DSPM method):

[bernard-giroux]

Hi @SquirrelKnight

Thanks for sharing your observations. I'm not too surprised by these differences. Each method is based on some assumptions that inevitably introduce errors/differences in the results ("All models are wrong, some are useful", G. Box). The patterns are likely due to the grid-based nature of the SPM/DSPM schemes that discretize angular paths. The difference is rather small and the question is to determine if the difference is acceptable. Using more secondary nodes and/or smaller grids should reduce the error. For the latter case (moving rcv), I guess the difference is within some tolerance factor in the code, but confirming this would require some investigations...

Hope this helps

[SquirrelKnight]

Thanks @bernard-giroux, I will try DSPM with 4 secondary nodes (5 takes too much RAM for my computer to handle), as opposed to 2. Looking again at the shift in travel-times when changing the receiver location, it seems the change is pretty minimal, so it is pretty tolerable.

I've attached the earthquake locations derived from the original DSPM travel-time grids (set to 2 secondary and 2 tertiary nodes) for an ocean-bottom seismometer array at a spreading centre. The grid is located 21 degrees clockwise to translate from XYZ to geodetic coordinates. You can see the artificial lineations radiating from the centre.

The second image shows my solution when using Pykonal (an Eikonal Solver). There's still some seismicity in the regions with the lineations, but it aligns more with the bathymetric ridges.

[bernard-giroux]

Hi, what is the location algorithm?

[SquirrelKnight]

I am using an enhanced implementation of the Maximum-Intersection method (MAXI).

Font, Y., Kao, H., Lallemand, S., Liu, C. S., & Chiao, L. Y. (2004). Hypocentre determination offshore of eastern Taiwan using the Maximum Intersection method. Geophysical Journal International, 158(2), 655-675.

I am also meaning to test with NonLinLoc, but I need to write a few scripts to get everything in the right format.

I am currently using the assumption that my seismometers are at 0m depth, which is where the velocity model starts. Will this cause potential instabilities in calculating the travel-times?

[SquirrelKnight]

@bernard-giroux To test my last point, I added some additional velocity layers to the top of the model and it looks like the results are pretty much the same.

I've also included an image of the P-velocity grid (at 1 km depth). As you can see, it is quite heterogeneous.

[bernard-giroux]

@SquirrelKnight I would need to do some testing to see what could cause the difference, but my schedule is quite full at the moment. Some thoughts: Does the MAXI method restrict the final solution to a grid node? Are grid cells the same size for Pykonal & ttcrpy?

[SquirrelKnight]

@bernard-giroux The MAXI method uses the initial grid to determine a best location using a ranking system. From there, I refine the solution by interpolating the travel-time grids from neighbouring nodes with scipy.ndimage.zoom (it uses 3-dimensional spline interpolation). The grid cells are the same size between the two methods.

No worries about your schedule being busy. I appreciate you taking the time to respond and understand having a full schedule! If you find that you need some of my files, I am happy to share. I could load them onto a Google Drive for you to access.