同源重磁场及其对应转换的数学模型研究

Mathematical model of cogenetic gravity-magnetic field and its corresponding conversion

运用重磁力场强度与位势的微积分关系,建立了简捷的重磁力场的数学模型,并在重磁误差允许的范围内将任一地质异常体当作可分解为可数个密度、磁性均匀分布的充分小的地质异常体(体积元)集合,进而导出了同源重力强度、位势与磁力强度和位势的对应转换模型。该模型不仅把重磁位场的复杂关系简化为力与功的关系,把重磁单向转换的波哇松公式拓展成为双向转换的关系式,更重要的是还可把其在场论中所遵循的拉普拉斯方程、泊松方程、高斯通量定律等作为日趋成熟的重磁反演的约束条件和渐见端倪的重磁震联合反演的理论依据。

According to the relationship between gravitymagnetic field intensity and calculous of potential,the mathematical model of gravitymagnetic field has been concisely built up.Also,the conversion model of cogenetic gravity intensity and potential corresponding to magnetic intensity and potential is derived by taking the set of any geological anomalous body as decomposably countable,little enough and evenly distributed geological anomalous bodies(volumetric units) within the allowable error.This model not only simplifies complex relation of gravitymagnetic potential field as the relation between force and work,but also expands unidirectional conversion gravitymagnetic Poisson formula into bidirectional one.Furthermore,it can take Laplace equation,Poisson equation and Gaussian flux law which are observed in field theory as constraints of gravitymagnetic inversion and the theoretical basis of gravitymagneticseismic combination inversion.