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中文摘要：
截断奇异值方法（TSVD）是解决病态问题的一个有效途径,其关键问题是选择适当的截断参数。首先对TSVD方法克服病态性的原理进行了分析,提出适当的截断参数应当使TSVD解达到两个目标：一是能够消除被小奇异值放大的噪声对真解的污染,二是尽量提高解的分辨率以保持解的准确性。然后提出了基于信噪差异指标的选择截断参数的新方法,该方法以TSVD解在不同截断方式下的信噪差异为指标,对TSVD克服病态性的实际效果进行评估,据此选择截断参数。最后通过对航空重力测量数据向下延拓问题的模拟计算,说明该方法的有效性。
英文摘要：
Truncated singular value decomposition（TSVD） technique is effective to resolve ill-posed problems.The key in this technique is selection of proper truncated parameter.Firsr,principle of TSVD to overcome ill-posed problems was analysised.There were two targets should be attained to TSVD solutions when proper truncated parameter was selected： one was the ability to eliminate the polution which comed from noises and was amplified by little singular value,the other was raising solutions＇ resolving power to preserve solutions＇ accuracy.Second,a new way of truncated parameter selection based on signal-to-noise ratio was put foward.It was used to assess effectiveness of overcoming illness,and then selection method was established according to it.At last,an example of airborne gravity downward to the earth surface was given,which testify the method was effective.
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