  We investigate the effect induced by variations in the density profile of the
Earth's interior using a long-baseline neutrino oscillation experiment.
  At first, we point out two facts. (i) The most essential part of the matter
profile is the first Fourier mode of the matter profile function; and (ii) The
Earth models based on the study of seismology include a large uncertainty for
the first Fourier mode.
  Next, we show that there is a strong correlation between the average density
value and the first Fourier coefficient in the analysis of oscillation
probability.
  This means that the matter profile effect induces added uncertainty for the
average matter parameter. %although the average density can be determined at a
few percent accuracy.
  Taking into account this extra uncertainty, we make numerical calculations
for the sensitivity to CP violation search and show that CP sensitivity is
impaired by this added uncertainty within a large $U_{e3}$ region.
