向下延拓航空重力数据的Tikhonov双参数正则化法

Tikhonov Two-parameter Regulation Algorithm in Downward Continuation of Airborne Gravity Data

为避免正则化参数对向下延拓过程可靠成分的修正影响,提出Tikhonov双参数正则化法。引进截断参数,将法矩阵的奇异值分为相对较大的奇异值(可靠部分)和相对较小的奇异值(不可靠部分);引进正则化参数,只对法矩阵的小奇异值进行修正,以抑制高频误差对向下延拓解的影响。采用广义交互确认法(GCV)确定截断参数和正则化参数。基于EGM2008重力场模型仿真一组航空重力数据,验证该方法对航空重力数据向下延拓过程的有效性。

In order to avoid the correct effect provided by regulation parameter on the downward continuation credible portion, Tikhonov two-parameter regulation algorithm is presented. Using the truncation parameter, the singular values of the normal matrix are divided into the relative large singular values （the credible portion） and the relative small singular values （the incredible portion）. Using regulation parameter, only the relative small singular values are corrected, and the effect induced by the high frequency error is suppressed. The truncation parameter and the regulation parameter are determined by GCV method. Using the simulative airborne gravity data based on the EGM2008, as true values of the gravity field, the results of numerical calculation examples have clearly demonstrated that this method for downward continuation of airborne gravity data is fairly efficient, and shown significant advantages.