First-arrival tomography with fast sweeping method solving the factored eikonal equation

ABSTRACT

This paper presents a first-arrival tomography incorporating a fast sweeping method (FSM) solving the factored eikonal equation (factored FSM). The traveltime calculation method plays a significant role in velocity inversion. However, for a point source condition, all finite-difference based eikonal solvers suffer from the source singularity problem. Numerical error caused by source singularity will propagate from the source to all computational domains, and makes traveltimes inaccurate. A FSM solving the factored eikonal equation can deal with the source singularity problem very well. Therefore, a first-arrival tomography is developed by incorporating 2D and 3D factored FSMs to provide more accurate traveltimes in velocity inversion. For comparison, an open source package PStomo_eq is used to invert the same data set. It incorporates the traveltime calculation algorithms fdtime2d.c and fdtime3d.c. Traveltime accuracy tests show that factored FSM can generate more accurate traveltimes than FSM, fdtime2d.c and fdtime3d.c. Numerical and field data tests show that inversion with factored FSM can acquire much better tomograms than inversion with fdtime2d.c and fdtime3d.c. Therefore, it is worthwhile using a more accurate traveltime computation method in velocity inversion.

KEYWORDS:

• seismic tomography
• fast sweeping method
• factored eikonal equation

Acknowledgements

The authors greatly appreciate Dr. Jonathan B. Ajo-Franklin in Lawrence Berkeley National Laboratory kindly provided the first arrival data, and coordinates of shots and geophones in real data test.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is jointly supported by National Natural Science Foundation of China (41504095, 41764006), Foundation of Education Department in Jiangxi (GJJ160570), and China Scholarship Council. Dr Luo was partially supported by NSF Division of Mathematical Sciences 1418908 and 1719907.