Structured regularization based velocity structure estimation in local earthquake tomography for the adaptation to velocity discontinuities

Abstract

Abstract We propose a local earthquake tomography method that applies a structured regularization technique to determine sharp changes in Earth’s seismic velocity structure using arrival time data of direct waves. Our approach focuses on the ability to better image two common features that are observed in Earth’s seismic velocity structure: sharp changes in velocities that correspond to material boundaries, such as the Conrad and Moho discontinuities; and gradual changes in velocity that are associated with pressure and temperature distributions in the crust and mantle. We employ different penalty terms in the vertical and horizontal directions to refine the earthquake tomography. We utilize a vertical-direction (depth) penalty that takes the form of the $${l}_{1}$$ l 1 -sum of the $${l}_{2}$$ l 2 -norms of the second-order differences of the horizontal units in the vertical direction. This penalty is intended to represent sharp velocity changes caused by discontinuities by creating a piecewise linear depth profile of seismic velocity. We set a horizontal-direction penalty term on the basis of the $${l}_{2}$$ l 2 -norm to express gradual velocity tendencies in the horizontal direction, which has been often used in conventional tomography methods. We use a synthetic data set to demonstrate that our method provides significant improvements over velocity structures estimated using conventional methods by obtaining stable estimates of both steep and gradual changes in velocity. We also demonstrate that our proposed method is robust to variations in the amplitude of the velocity jump, the initial velocity model, and the number of observed arrival times, compared with conventional approaches, and verify the adaptability of the proposed method to dipping discontinuities. Furthermore, we apply our proposed method to real seismic data in central Japan and present the potential of our method for detecting velocity discontinuities using the observed arrival times from a small number of local earthquakes. Graphical Abstract

Keywords

• Local earthquake tomography
• Computational seismology
• Statistical methods
• Japan