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picture very complicated and does not change our qualitative conclusion. 

In this configuration, there are three slabs, I, II and III. Ea ch of them is assumed to possess a uniform matter density and can be treated with an R -matrix [22]. 

The elements of the R -matrix are determined by the mass- squared difference Δ m 2 $_{M}$, neutrino energy E$_{ν}$ and antineu- trino path length in the slab. In a uniform slab, the elements of the R -matrices are 

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where x is the antineutrino path length in the slab. we cal- culate the survival probabilities without and with the anoma- lous accumulation of electrons at the fault zone. In Fig. 2 we present the differences in survival probabilities of the re- actor electron antineutrino between cases without and with an anomalous accumulation of electrons for η =3 and differ- ent widths. For oscillations in medium with and without the anomalous electron accumulation, the maximal difference in P$_{¯}$ ν$_{e}$ → ¯ ν$_{e}$ is up to 2% when the width w = 100 km. 

Among all of the fault zone parameters, the width and the η value play important roles in antineutrino oscillations. For reactor electron antineutrinos, the dependence of the differ- ences of survival probabilities on η is plotted in Fig. 3 with antineutrino energy E$_{ν}$ = 3.6 MeV for different width values. Fig. 3 indicates that for η < 1 , the effect is tiny, and for η is 

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larger than one, the predicted probability difference undergoes a relatively larger change with the increase in η . 

Neutrino factory.— Neutrino beams from a neutrino fac- tory [23] can also be employed in the neutrino oscillation to- mography. In our configuration, we choose an electron neu- trino beam with energy E$_{ν}$ = 7 GeV. Our calculation indi- cates that the difference in survival probabilities correspond- ing to the cases with and without the anomalous electron ac- cumulation is not obvious. Indeed, an observable difference of about 0.01% may be detected if the detector is 6000 km away from the source. However, such a length of baseline is much beyond the maximal distance in the crust layer and such a small difference may not be detected with the accuracy of 

the present neutrino facilities in our configuration. The re ason is obvious that the accelerator neutrinos have much larger en- ergy than the reactor antineutrinos, thus the oscillation length L M osc for neutrinos from a neutrino factory is much longer than that for the reactor ones as shown in Table I. 

Result from perturbation method.— In a low matter den- sity medium, V ≪ Δ m $^{2}$/ 2 E$_{ν}$ , Ioannisian and Smirnov [24] developed a perturbation method where ϵ = 2 V E$_{ν}$/ Δ m 2 is taken as the expansion parameter for calculating the oscilla- tion probability. For the maximal matter density ηρ$_{0}$ in our case, one can determine 

for E$_{ν}$ = 3.6 MeV and η = 3. With the perturbation method, the exact adiabatic phase shift in matter is obtained as 

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