Monitoring changes of seismic properties at depth can provide a first
order insight into Earth's dynamic evolution. Coda wave interferometry
is the primary tool for this purpose. This technique exploits small
changes of waveforms in the seismic coda and relates them to temporal
variations of attenuation or velocity at depth. While most existing
studies assume statistically homogeneous scattering strength in the
lithosphere, geological observations suggest that this hypothesis may
not be fulfilled in active tectonic or volcanic areas. In a numerical
study we explore the impact of a non-uniform distribution of scattering
strength on the spatio-temporal sensitivity of coda waves. Based on
Monte Carlo simulation of the radiative transfer process, we calculate
sensitivity kernels for three different observables, namely travel-time,
decorrelation and intensity. Our results demonstrate that laterally
varying scattering properties can have a profound impact on the
sensitivities of coda waves. Furthermore, we demonstrate that the
knowledge of the mean intensity, specific intensity and energy flux,
governed by spatial variation of scattering strength, is key to
understanding the decorrelation, travel-time and intensity kernels,
respectively. A number of previous works on coda wave sensitivity
kernels neglect the directivity of energy fluxes by employing formulas
extrapolated from the diffusion approximation. In this work, we
demonstrate and visually illustrate the importance of the use of
specific intensity for the travel-time and scattering kernels, in the
context of volcanic and fault zone setting models. Our results let us
foresee new applications of coda wave monitoring in environments of high
scattering contrast.