基于向上延拓的航空重力向下解析延拓解

Analytical solution of downward continuation for airborne gravimetry based on upward continuation method

位场向下与向上延拓之间存在固有的内在联系,向上延拓解算具有稳定可靠的优良特性,本文据此提出了借助向上延拓信息实现航空重力向下延拓稳定解算的两种方法,分别建立了点对点向下解析延拓模型和最小二乘向下解析延拓模型.其核心思想是,依据泰勒级数展开模型,将位场向下延拓解算过程转换为向上延拓计算和垂向偏导数解算两个步骤,通过第一步的处理有效抑制数据观测噪声对解算结果的干扰,通过第二步的处理成功实现向下延拓反问题的稳定解算,较好地解决了向下延拓解算固有的不适定性问题.分析研究了两种解析延拓模型的计算精度及适用条件,利用超高阶位模型EGM2008建立的模拟标准场数据对两种模型解算结果的合理性和有效性进行了数值验证,证明本文新方法实用易行,具有较高的应用价值.

There exists an inherent link between upward and downward continuation of potential field data.It is undoubted that the upward continuation procedure can give a stable and reliable solution.Based on this excellent property of upward continuation,we propose two methods to obtain a stable solution for downward continuation of airborne gravity data using the information of upward continuation.Then a point-to-point analytical model and a least-squares analytical model of downward continuation are established.The key view of the new approaches is that a downward continuation process can be transformed to an upward continuation procedure and the computation of vertical derivatives by means of Taylor series expansion.The effect of data noise on the solution of downward continuation will be suppressed by the operation of first step.And a stable solution of downward continuation can be obtained by the operation of second step.So we avoid the ill-posedness problem of downward continuation successfully.The solution accuracy and applicability of the new models are analyzed and discussed.Finally,a numerical test using a synthetic airborne gravity data set from ultra-high-degree geopotential model EGM2008 has been made to prove the reasonableness and validity of the suggested models.It is shown that the new methods are practical and easy to be realized,and will be of great value to the application of airborne gravimetry.