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设F(x-ξ,y,z,η,ζ,α,…)为一在x方向无限薄的层的异常,若物体的异常可表示为: T(x,y)=integral from n=a to (a+2c)(F(x-ξ,y,z,η,ζ,α,…))dξ T(y)=integral from n=-∞ to ∞(F(x-ξ,y,z,η,ζ,α,…))dξ 则有 式中T(v)和T(u,v)分别为T(y)和T(x,y)的频谱,2c是物体在x方向的宽度,(x,y,z)和(ξ,η,ζ)分别为观测点和物体上任一点的坐标。 如果2c=dξ,则物体即为薄层本身;如果2c=dξ,薄层的面积无限缩小,则物体即为一质点;如果2c=dξ,薄层只有长度而无宽度,则物体即为一曲线。 对于形状复杂的物体,可以将物体分成若干简单而又符合所述条件的物体元,而有式中2c_m为第m个物体元在x方向的宽度,T_m(v)为第m个物体元当其沿x方向的长度为无限长时的异常的频谱。
Let F (x-ξ, y, z, η, ζ, α, ...) be an infinite layer anomaly in the x direction. If the object’s anomaly can be expressed as: T (x, y) = integral from n = a to (a + 2c) (F (x- ξ, y, z, η, ζ, α, ...)) dξ T (y) = integral from n = z, η, ζ, α, ...)) dξ is the spectrum of T (v) and T (u, v) The width, (x, y, z) and (ξ, η, ζ) are the coordinates of the observation point and any point on the object, respectively. If 2c = dξ, then the object is the thin layer itself; if 2c = dξ, the area of the thin layer is infinitely reduced, then the object is a particle; if 2c = dξ, the thin layer has only length but no width, curve. For complex objects, the object can be divided into a number of simple and meet the conditions of the object element, and where the 2c_m is the m-th object element in the x-direction width, T_m (v) for the m-th object yuan Its length in the x-direction is the spectrum of anomalies at infinite length.