Microseismic Location Error Due to Eikonal Traveltime Calculation

Dmitry Alexandrov,Umair Bin Waheed,Leo Eisner

doi:10.3390/app11030982

Dmitry Alexandrov, Umair Bin Waheed + Show 1 more

Open Access

https://doi.org/10.3390/app11030982

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Abstract

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.

Highlights

Diffraction stacking is a recently developed method for locating microseismic events.The method utilizes hodographs from every grid point of a selected volume to build an image function through stacking recorded waveforms along this hodograph [1]
We compare the performance of regular fast sweeping method (FSM), factored FSM, and the physics-informed neural networks (PINNs) eikonal solver in microseismic source localization
We use a rather simple horizontally layered model in order to emphasize how numerical errors from traveltime computation propagate into the location error

Summary

Introduction

Diffraction stacking is a recently developed method for locating microseismic events. The method utilizes hodographs from every grid point of a selected volume to build an image function through stacking recorded waveforms along this hodograph [1]. The errors in traveltime computation will propagate into the stack and result in inaccurate event locations. One of the efficient and popular approaches of computing traveltimes is solving the eikonal equation using an iterative fast sweeping method (FSM) [4] or direct fast marching method (FMM) [5]. A simple discretization of the eikonal equation yields inaccurate solution due to the singularity at the point-source. Since the wavefront curvature around the point-source is extremely large, the finite-difference approximation results in large truncation errors that propagate into the entire computational domain [4]

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Conclusion