3 the normal matter density ρ$_{0}$ . In fact, because the existence of the anomalous electric field does not directly influence th e real matter density, but only contributes to the electron density of the fault zone, the real matter density of the fault zone ρ$_{f}$ would be smaller than ηρ$_{0}$ , i.e. where n f p is the number density of protons in the fault zone cuboid. The experimental observation indicates that there is a definite relation between ρ ′ f and ρ$_{f}$ , namely as ρ ′ f increases, ρ$_{f}$ increases too. The antineutrino oscillation determines ρ ′ $_{f}$, and with the data on ρ ′ $_{f}$, we would obtain unambiguous infor- mation about ρ$_{f}$ which causes an earthquake. The study of geology focuses on a single fault or single fracture. Instead, we consider a zone that consists of several faults and has a relatively large width. The fault zone is treated as a slab with a uniform effective matter density ρ ′ $_{f}$. The width w of the fault zone can also be estimated from an empirical formula [16] where M$_{S}$ is the magnitude of the earthquake. For the Wenchuan earthquake, M$_{S}$ = 8.0, the width w is about 80 km from Eq. (7), which is the fault zone width we use in our numerical computations. Configuration and result for the reactor antineutrinos.— The Daya Bay reactor located in Shenzhen is an example and we shall use its corresponding data as the inputs of our nu- merical computations. The fault zone cuboid in Wenchuan is about 1418 km to Daya Bay. As is shown in the configuration figure, the ¯ ν$_{e}$ first traverses the normal medium with a matter density ρ$_{0}$ = 2.8 g/cm 3 and then enters the fault zone, which has a width w = 50 km. Since fault zones are not accessible for direct observation, all information concerning details of the zones is still coarse and sparse. Obviously, more concrete and precise informa- tion is needed very badly to forecast disasters. Along with the geologic study, theoretical work and new ideas are also neces- sary. Certainly, abundant geological data and development in seismology are helpful for the improvement of our fault zone picture and further research. In this work, we set η = 3 as a simple demonstration of our scheme. We suppose that the beam would be detected at the Qinghai- Xizang Plateau, which is 200 km away from the fault zone. This description of the total configuration of the trajector y is shown in Fig. 1. Under the approximation of θ$_{13}$ ∼ 0 the vacuum oscilla- tion probability P$_{¯}$ ν$_{e}$ → ¯ ν$_{e}$ within the three-generation scenario can be reduced into the two-generation case. When taking the matter effect into account and considering the normal hierar- chy △ m 2 21 ≪ △ m 2 31 ≃ △ m 2 $_{32}$, the small mass-squared dif- ference △ m 2 21 dominates the oscillation as the effect induced by the larger mass-squared difference △ m 2 31 is averaged out It is noted that the mixing angle θ$_{23}$ does not explicitly show up in the survival probability of ¯ ν$_{e}$ → ¯ ν$_{e}$ . Since sin 2 θ$_{13}$ < 5 × 10 − 2 (99.73% CL) [20], with the assumption θ$_{13}$ ∼ 0 , the two-generation analysis involving two parameters △ m 2 21 and θ$_{12}$ would be a good approximation for the realistic case. In fact, the mixing between ν$_{µ}$ and ν$_{τ}$ is sizable [21], therefore for the long-distance propagation, the oscillation between ν$_{µ}$ and ν$_{τ}$ is almost complete, i.e. sin 2 2 θ$_{23}$ ≈ 1 . Thus for the practical mixing between ¯ ν$_{e}$ and ¯ ν$_{x}$ , ¯ ν$_{x}$ really is the superposi- tions of ¯ ν$_{µ}$ and ¯ ν$_{τ}$ . In the study of the solar neutrino flux miss- ing where only two generations are considered, the updated values of the input parameters are determined as sin 2 2 θ$_{0}$ = 0.86 and Δ m 2 = 8 × 10 − 5 eV $^{2}$. The energy of the reactor electron-antineutrino of E$_{ν}$ = 3.6 MeV [10] is another input parameter for our numerical computation. The complete for- mulation involving three generations would make the whole where s$_{ij}$ ≡ sin θ$_{ij}$ , c$_{ij}$ ≡ cos θ$_{ij}$ and A$_{cc}$ = 2 E$_{ν}$V ( x ) . Under the approximation θ$_{13}$ ∼ 0 , the amplitude ˆ ψ$_{α}$$_{3}$ is de- coupled from the evolution equations for ˆ ψ$_{α}$$_{1}$ and ˆ ψ$_{α}$$_{2}$ , and the effective survival probability P (3) ¯ ν$_{e}$ → ¯ ν$_{e}$ within the three- generation scenario just reduces into P (2) ¯ ν$_{e}$ → ¯ ν$_{e}$ which is the ex- pression in the two-generation case as where ˆ ψ$_{αk}$ ( α = e, µ, τ ; k = 1 , 2 , 3) is the ν$_{α}$ → ν$_{k}$ effective evolution amplitude and ˆ M is given as [10] for the long propagation [10]. Then the evolution equation is FIG. 2: The differences (in percent) in survival probabilities of the reactor electron antineutrino between cases without and with an anomalous accumulation of electrons whose η =3 and width w = 20, 50, 80 and 100 km, respectively. i d dx ( ˆ ψ$_{α}$$_{1}$, ˆ ψ$_{α}$$_{2}$, ˆ ψ$_{α}$$_{3}$ ) T = 1 2 E$_{ν}$ ˆ M ( ˆ ψ$_{α}$$_{1}$, ˆ ψ$_{α}$$_{2}$, ˆ ψ$_{α}$$_{3}$ ) $^{T}$, (8)   s 2 12 △ m 2 21 + c 2 $_{13}$A$_{cc}$ c$_{12}$s$_{12}$ △ m 2 21 − c$_{13}$s$_{13}$e − $^{iδ}$A$_{cc}$ c$_{12}$s$_{12}$ △ m 2 21 c 2 21 m 2 21 0 − c$_{13}$s$_{13}$e $^{iδ}$A$_{cc}$ 0 △ m 2 31 + s 2 $_{13}$A$_{cc}$   , w = 2 × 10 0 . 414 M$_{S}$ − 1 . 696 km , (7) 2 m$_{N}$n f e = ρ ′ f = ηρ$_{0}$, 2 m$_{N}$n f p = ρ$_{f}$ < ηρ$_{0}$, (6) P (3) ¯ ν$_{e}$ → ¯ ν$_{e}$ = (1 − sin 2 θ$_{13}$ ) $^{2}$P (2) ¯ ν$_{e}$ → ¯ ν$_{e}$ + sin 4 θ$_{13}$. (9) 1575 1600 1625 1650 1675 1700 L GLYPH<LParen1> km GLYPH<RParen1> 0 0.2 0.4 0.6 0.8 1 1.2 1.4 GLYPH<CapDelta> P GLYPH<LParen1> Ν GLYPH<OverBar> GLYPH<RArrow>Ν GLYPH<OverBar> GLYPH<RParen1>GLYPH<LParen1> % GLYPH<RParen1> w GLYPH<Equal> 80km, ΗGLYPH<Equal> 3 1575 16001625165016751700 L GLYPH<LParen1> km GLYPH<RParen1> 0 0.5 1 1.5 GLYPH<CapDelta> P GLYPH<LParen1> Ν GLYPH<OverBar> GLYPH<RArrow>Ν GLYPH<OverBar> GLYPH<RParen1>GLYPH<LParen1> % GLYPH<RParen1> w GLYPH<Equal> 100km, ΗGLYPH<Equal> 3 1450 1500 1550 1600 1650 L GLYPH<LParen1> km GLYPH<RParen1> 0 0.1 0.2 0.3 0.4 0.5 0.6 GLYPH<CapDelta> P GLYPH<LParen1> Ν GLYPH<OverBar> GLYPH<RArrow>Ν GLYPH<OverBar> GLYPH<RParen1>GLYPH<LParen1> % GLYPH<RParen1> w GLYPH<Equal> 20km, ΗGLYPH<Equal> 3 1575 160016251650167517001725 L GLYPH<LParen1> km GLYPH<RParen1> 0 0.1 0.2 0.3 GLYPH<CapDelta> P GLYPH<LParen1> Ν GLYPH<OverBar> GLYPH<RArrow>Ν GLYPH<OverBar> GLYPH<RParen1>GLYPH<LParen1> % GLYPH<RParen1> w GLYPH<Equal> 50km, ΗGLYPH<Equal> 3