基于L0范数稀疏约束的地震数据反褶积

地震数据稀疏约束反褶积假设反射系数由一系列稀疏脉冲组成，在进行反褶积时对反射系数进行稀疏约束，避免了子波最小相位和反射系数是白噪声的假设。L0范数是数据稀疏度的最佳度量，最能够反映数据的稀疏性，因此将L0范数稀疏约束引入到地震资料反褶积处理方法研究中。通过对反射系数进行L0范数约束，建立地震数据反褶积的优化目标函数，然后运用迭代硬阈值法求解，得到稀疏分布的反射系数。通过模型试验并与柯西准则约束、L1范数约束进行对比，证明了L0范数稀疏约束反褶积方法的有效性。

Sparse constrained deconvolution of seismic data is built on the assumption that the reflectivity is composed by a series of sparse pulses.Sparse constraint can be applied to reflectivity in deconvolution,avoiding the two hypotheses that the wavelet is minimum phase and the reflectivity is white noise.L0 norm is the most suitable measurement of data sparseness.Therefore,we bring L0 norm sparse constraint in seismic data deconvolution.Through applying L0 norm constraint to reflectivity,the optimization objective function of seismic data deconvolution is built.Iterative hard thresholding method is used to calculate the function and sparsely distributed reflectivity is obtained.The validity of L0 norm sparse constraint deconvolution is proved by the comparison with Cauchy criterion constraint and L1 norm constraint in synthetic model tests.