Hi everyone,
I am working on a 3D first-arrival traveltime tomography problem. As part of this, I have the data as first-arrival times (d, 205000), model parameters (m, 170000), and the length matrix (G, 205000 by 170000). The length matrix is generated based on tetrahedral meshes (0.5 km near the surface and 2.0 km in the deeper parts) because my initial model is complex. This matrix is very sparse, and I am trying to solve it using the LSMR and LSQR iterative schemes (https://docs.scipy.org/doc/scipy/reference/sparse.linalg.html). However, if the initial model (x0) is set to None, it generates incorrect results. How do I solve this problem?
Best regards,
Bhaskar
Hi Bhaskar,
It sounds like you're dealing with a complex inverse problem in traveltime tomography. The issue with the initial model 𝑥0
affecting your results could be due to several factors, including the initial guess, convergence criteria, or even the specifics of your data and model setup.
Hi,
a way to solve sparse matrices in tomography are SIRT or ART algorithms
Van Der Sluis, A., Van Der Vorst, H.A.
Numerical solution of large, sparse linear algebraic systems arising from tomographic problems.
(1987) Seismic tomography, pp. 49-83.
You can find applications also in the works of Aldo Vesnaver, Gualtiero Boehm and myself such as
doi: 10.1111/j.1365-246X.1996.tb05274.x
10.1111/j.1365-2478.2006.00563.x
10.3997/1873-0604.2017037
and references therein
Many wishes
Thank you very much Giuliana Rossi and Muhammad Abdullah Shahid
I am going through the above suggestions.
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