  Soils have been heralded as a hidden resource that can be leveraged to
mitigate and address some of the major global environmental challenges.
Specifically, the organic carbon stored in soils, called Soil Organic Carbon
(SOC), can, through proper soil management, help offset fuel emissions,
increase food productivity, and improve water quality. As collecting data on
SOC is costly and time consuming, not much data on SOC is available, although
understanding the spatial variability in SOC is of fundamental importance for
effective soil management.
  In this manuscript, we propose a modeling framework that can be used to gain
a better understanding of the dependence structure of a spatial process by
identifying regions within a spatial domain where the process displays the same
spatial correlation range. To achieve this goal, we propose a generalization of
the Multi-Resolution Approximation (M-RA) modeling framework of Katzfuss (2017)
originally introduced as a strategy to reduce the computational burden
encountered when analyzing massive spatial datasets.
  To allow for the possibility that the correlation of a spatial process might
be characterized by a different range in different subregions of a spatial
domain, we provide the M-RA basis functions weights with a two-component
mixture prior with one of the mixture components a shrinking prior. We call our
approach the mixture M-RA. Application of the mixture M-RA model to both
stationary and non-stationary data shows that the mixture M-RA model can handle
both types of data, can correctly establish the type of spatial dependence
structure in the data (e.g. stationary vs not), and can identify regions of
local stationarity.
