  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 l1-sum
of the l2-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 l2-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.
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.
