  To strike a balance between modeling accuracy and computational efficiency
for simulations of ultrasound waves in soft tissues, we derive a
pseudodifferential factorization of the wave operator with fractional
attenuation. This factorization allows us to approximately solve the Helmholtz
equation via one-way (transmission) or two-way (transmission and reflection)
sweeping schemes tailored to high-frequency wave fields. We provide explicitly
the three highest order terms of the pseudodifferential expansion to
incorporate the well-known square-root first order symbol for wave propagation,
the zeroth order symbol for amplitude modulation due to changes in wave speed
and damping, and the next symbol to model fractional attenuation. We also
propose wide-angle Pade approximations for the pseudodifferential operators
corresponding to these three highest order symbols. Our analysis provides
insights regarding the role played by the frequency and the Pade approximations
in the estimation of error bounds. We also provide a proof-of-concept numerical
implementation of the proposed method and test the error estimates numerically.
