One-dimensional accurate calculation of transient electromagnetic responses based on B-spline interpolation
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摘要: 基于频谱法的瞬变电磁法一维正演策略中,多个计算环节对瞬变电磁响应计算精度有重要影响。为了提高一维正演效率,通常只直接计算数十个频点的频率域电磁响应,再采用三次样条插值将频率域电磁响应扩展至数百个频点。尽管三次样条插值函数计算的数值结果已能满足大多数正演需求,但其计算精度仍有提升空间。本文将高次B样条插值引入至瞬变电磁法一维正演,用于代替传统三次样条插值,并以磁偶源和圆形回线源为例验证了方法准确性。结果表明,对于多个地电模型,基于高次B样条插值计算的瞬变电磁响应精度均优于基于传统三次样条的计算结果。Abstract: In the one-dimensional (1D) forward modeling of transient electromagnetic (TEM) responses based on spectral methods, multiple calculation steps significantly influence the calculation accuracy of TEM responses. To improve the efficiency of 1D forward modeling, the common practice is to directly calculate the frequency-domain electromagnetic responses of dozens of frequency points and then obtain the responses of hundreds of frequency points through cubic spline interpolation. Although the numerical results calculated using the cubic spline interpolation function can meet the requirements of most forward modeling scenarios, their accuracy can be further improved. This study introduced high-order B-spline interpolation into the 1D forward modeling of TEM responses to replace the conventional cubic spline interpolation and verified the accuracy of the method based on magnetic dipole sources and circle-shaped loop sources. The results show that the TEM responses of several geoelectric models calculated based on high-order B-spline interpolation exhibit higher accuracy than those calculated using conventional cubic spline interpolation.
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