  Here we propose a local earthquake tomography method that applies a
structured regularization technique to determine sharp changes in the Earth's
seismic velocity structure with travel time data of direct waves. Our approach
focuses on the ability to better image two common features that are observed
the Earth's seismic velocity structure: velocity jumps that correspond to
material boundaries, such as the Conrad and Moho discontinuities, and gradual
velocity changes that are associated with the pressure and temperature
distributions in the crust and mantle. We employ different penalty terms in the
vertical and horizontal directions to refine the imaging process. We utilize a
vertical-direction (depth) penalty term that takes the form of the l1-sum of
the l2-norm of the second-order differences of the horizontal units in the
vertical direction. This penalty is intended to represent sharp velocity jumps
due to discontinuities by creating a piecewise linear depth profile of the
average velocity structure. We set a horizontal-direction penalty term on the
basis of the l2-norm to express gradual velocity tendencies in the horizontal
direction. We use a synthetic dataset to demonstrate that our method provides
significant improvements over the estimated velocity structures from
conventional methods by obtaining stable estimates of both the velocity jumps
and gradual velocity changes. We also demonstrate that our proposed method is
relatively robust against variations in the amplitude of the velocity jump,
initial velocity model, and the number of observed travel times. Furthermore,
we present a considerable potential for detecting a velocity discontinuity
using the observed travel times from only a small number of direct-wave
observations.
