Microseismic Location Error Due to Eikonal Traveltime Calculation

The accuracy of computed traveltimes in a velocity model plays a crucial role in localization of microseismic events. The conventional approach usually utilizes robust fast sweeping or fast marching methods to solve the eikonal equation numerically with a finite-difference scheme. These methods introduce traveltime errors that strongly depend on the direction of wave propagation. Such error results in moveout changes of the computed traveltimes and introduces significant location bias. The issue can be addressed by using a finite-difference scheme to solve the factored eikonal equation. This equation yields significantly more accurate traveltimes and therefore reduces location error, though the traveltimes computed with the factored eikonal equation still contain small errors with systematic bias. Alternatively, the traveltimes can be computed using a physics-informed neural network solver, which yields more randomized traveltimes and resulting location errors.