  Compton-to-peak analysis is a method for selecting coefficients for
converting count rates measured with in situ gamma ray spectrometry to
radioactivity concentrations of $^{134}$Cs and $^{137}$Cs in the environment.
Compton-to-peak analysis is based on the count rate ratio between the spectral
regions containing scattered gamma rays to the primary $^{134}$Cs and
$^{137}$Cs photopeaks (known as the Compton-to-peak ratio - RCP). RCP changes
with the vertical distribution of $^{134}$Cs and $^{137}$Cs within the ground.
Inferring this distribution enables the selection of appropriate count rate to
activity concentration conversion coefficients. Here PHITS was used to simulate
the dependency of RCP on different vertical distributions of $^{134}$Cs and
$^{137}$Cs within the ground. A model was created of a LaBr$_3$(Ce) detector
used in drone helicopter aerial surveys in Fukushima Prefecture. The model was
verified by comparing simulated gamma ray spectra to measurements from test
sources. Simulations were performed for the infinite half-space geometry to
calculate the dependency of RCP on the mass depth distribution (exponential or
uniform) of $^{134}$Cs and $^{137}$Cs within the ground, and on the altitude of
the detector above the ground. The calculations suggest that the sensitivity of
the Compton-to-peak method is greatest for the initial period following nuclear
fallout when $^{134}$Cs and $^{137}$Cs are located close to the ground surface,
and for aerial surveys conducted at low altitudes. This is because the relative
differences calculated between RCP with respect to changes in the mass depth
distribution were largest for these two cases. Data on the measurement height
above and on the $^{134}$Cs to $^{137}$Cs activity ratio is necessary for
applying the Compton-to-peak method to determine the distribution and
radioactivity concentration of $^{134}$Cs and $^{137}$Cs within the ground.
