The probabilistic prediction approach can be used not only for obtaining the maximum posterior probability solution but also for uncertainty evaluation. Its prior distribution has a significant impact on the prediction result. An improper prior assumption may lead to prediction deviation. To improve the prediction accuracy of elastic parameters, a Laplace prior with total variation (TV) constraint is introduced in the probabilistic prediction. First, the effect of TV constraint on the probability distribution of elastic parameters is analyzed in detail. Then, two approaches are proposed to handle the cases where the elastic parameters have blocky boundaries and no blocky boundaries: probabilistic prediction scheme for elastic parameters with blocky boundaries and probabilistic prediction scheme with blocky lithology prior constraint. The former imposes a sparse constraint on the elastic parameters, while the latter imposes a sparse constraint on the TV processing lithology. Their posterior probabilities are rederived. Considering that the discrete lithology is more likely to be blocky compared with the continuous elastic parameters, the sparse lithology constraint can handle more general cases. In addition, this approach allows for lithology prediction. The applications of numerical examples and field seismic data verify the feasibility of the proposed approaches.

中文翻译：

---

稀疏先验在弹性参数概率预测中的分析与应用

概率预测方法不仅可用于获得最大后验概率解，还可用于不确定性评估。其先验分布对预测结果有显着影响。不正确的先验假设可能导致预测偏差。为了提高弹性参数的预测精度，在概率预测中引入了具有总变差（TV）约束的拉普拉斯先验。首先，详细分析了TV约束对弹性参数概率分布的影响。然后，提出了两种方法来处理弹性参数有块状边界和没有块状边界的情况：具有块状边界的弹性参数的概率预测方案和具有块状岩性先验约束的概率预测方案。前者对弹性参数施加稀疏约束，而后者对 TV 处理岩性施加稀疏约束。他们的后验概率被重新推导。考虑到离散岩性与连续弹性参数相比更容易出现块状，稀疏岩性约束可以处理更一般的情况。此外，这种方法允许进行岩性预测。数值例子和现场地震资料的应用验证了所提方法的可行性。稀疏岩性约束可以处理更一般的情况。此外，这种方法允许进行岩性预测。数值例子和现场地震资料的应用验证了所提方法的可行性。稀疏岩性约束可以处理更一般的情况。此外，这种方法允许进行岩性预测。数值例子和现场地震资料的应用验证了所提方法的可行性。