波动方程逆源问题与地面穿透雷达数据解释问题
Inverse source problem for wave equation and GPR data interpretation problem
AI总结：
本文研究了一维波动方程中未知空间依赖源函数F(x)的逆问题，通过地面穿透雷达数据解释问题建立联系，提出非迭代算法基于傅里叶展开和显式解表示，数值计算显示该算法能准确重建噪声数据下的源函数。
摘要：
本文考虑了一维波动方程中未知空间依赖源函数F(x)的逆问题。测量数据以g(t) := u(0; t)的形式给出。展示了该问题与地面穿透雷达（GPR）数据解释问题的关系。开发了非迭代算法来重建未知源函数F(x)。该算法基于源函数F(x)的傅里叶展开和通过F(x)的显式表示直接问题解。然后将离散形式的Tikhonov函数的最小化问题转化为线性代数系统并数值求解。计算表明，所提出算法能够对无噪声和有噪声数据准确重建空间依赖源函数F(x)。
英文摘要：
The inverse problem of identifying the unknown spacewise dependent source F(x) in 1D wave equation is considered. Measured data are taken in the form g(t) := u(0; t). The relationship between that problem and Ground Penetrating Radar (GRR) data interpretation problem is shown. The non-iterative algorithm for reconstructing the unknown source F(x) is developed. The algorithm is based on the Fourier expansion of the source F(x) and the explicit representation of the direct problem solution via the function F(x). Then the minimization problem for discrete form of the Tikhonov functional is reduced to the linear algebraic system and solved numerically. Calculations show that the proposed algorithm allows to reconstruct the spacewise dependent source F(x) with enough accuracy for noise free and noisy data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
