  Time-distance helioseismology uses cross-covariances of wave motions on the
solar surface to determine the travel times of wave packets moving from one
surface location to another. We review the methodology to interpret travel-time
measurements in terms of small, localized perturbations to a horizontally
homogeneous reference solar model. Using the first Born approximation, we
derive and compute 3D travel-time sensitivity (Fr\'echet) kernels for
perturbations in sound-speed, density, pressure, and vector flows. While
kernels for sound speed and flows had been computed previously, here we extend
the calculation to kernels for density and pressure, hence providing a complete
description of the effects of solar dynamics and structure on travel times. We
treat three thermodynamic quantities as independent and do not assume
hydrostatic equilibrium. We present a convenient approach to computing damped
Green's functions using a normal-mode summation. The Green's function must be
computed on a wavenumber grid that has sufficient resolution to resolve the
longest lived modes. The typical kernel calculations used in this paper are
computer intensive and require on the order of 600 CPU hours per kernel.
Kernels are validated by computing the travel-time perturbation that results
from horizontally-invariant perturbations using two independent approaches. At
fixed sound-speed, the density and pressure kernels are approximately related
through a negative multiplicative factor, therefore implying that perturbations
in density and pressure are difficult to disentangle. Mean travel-times are not
only sensitive to sound-speed, density and pressure perturbations, but also to
flows, especially vertical flows. Accurate sensitivity kernels are needed to
interpret complex flow patterns such as convection.
