Uncertainty Quantification in Seismic Inversion by Nonlinear Sampling

非线性采样地震反演中的不确定性量化

基本信息

批准号：
1723019
负责人：
Mrinal Sen
金额：
$ 40.79万
依托单位：
University of Texas at Austin
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-07-15 至 2022-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1723019&HistoricalAwards=false
关键词：
Uncertainty Quantification Seismic Inversion Nonlinear

项目摘要

In many branches of science and engineering construction of an image of targets from remotely sensed data is an essential task for drawing meaningful inferences. The data, however, are often far from being ideal in that they are generally contaminated with noise and may be inadequate because of issues such as the geometry or density of the recording stations with respect to the targets to be imaged. In addition, resolution of the target is often chosen in an ad-hoc manner, introducing uncertainty in the resulting answer. Quantitative measures of uncertainty are, therefore, crucial to establishing confidence in the results of data analysis. Existing methods of characterizing uncertainty are often based on simplistic assumptions primarily because of limitations of computing powers. The objective of this proposal is to develop a technique for estimation of uncertainty using nonlinear sampling that will be applied to imaging of seismic data.Seismic tomography is the primary tool for estimating Earth?s subsurface images from seismic travel time, amplitude and waveform data. The data are often inadequate and noisy, and the forward modeling is generally based on approximate physics. Ad hoc parameterization of subsurface model parameters adds further complication in estimation of subsurface characteristics. The non-uniqueness in the solution estimates has been well recognized in the past and the need for uncertainty quantification has been promoted by the geophysics community. The Bayesian approach to describing our inverse problems has been found appropriate for this purpose. It enables us to describe our answer in terms of a probability density function, called the posterior probability density (PPD). A simple functional description of the PPD is generally not available, however. Thus, estimating samples from the PPD which is generally highly multi-modal is a challenging task. The common practice is to derive the maximum a posterioi (MAP) model and represent the uncertainty using the Hessian at the MAP point. This method assumes that the PPD is Gaussian ? an assumption often violated due to the nonlinear nature of the forward problem and the noise characteristics in the data. On the other hand, Metropolis-Hastings based Markov chain Monte Carlo methods are computationally very expensive, often requiring over a million forward model evaluations. Here we propose to develop computationally efficient MCMC methods for uncertainty quantification with application to seismic tomography. A Reversible jump Monte Carlo method (RJMCMC) in which the data themselves are allowed to find suitable number of model parameters required, addresses some of the shortcomings of the commonly used methods. The method, however, is computationally expensive. The researchers propose to develop and implement a new method called Reversible jump Hamiltonian Monte Carlo (RJHMC) method to seismic inversion. This method can be demonstrated to be two times faster than the conventional RJMCMC since it uses gradient information to take large jumps in MCMC steps. It will be applied to a 2D marine multi-channel seismic dataset.

在科学和工程的许多分支中，来自遥感数据的目标图像是绘制有意义推断的必不可少的任务。但是，数据通常远非理想之处，因为它们通常被噪声污染，并且由于诸如录制站相对于要成像的目标的几何形状或密度等问题而可能不足。此外，通常以临时方式选择目标的分辨率，从而在结果答案中引入不确定性。因此，不确定性的定量度量对于建立对数据分析结果的信心至关重要。现有表征不确定性的方法通常基于简单的假设，主要是因为计算能力的局限性。该提案的目的是开发一种用于使用非线性抽样来估算不确定性的技术，该技术将应用于地震数据的成像。地震层析成像是从地震旅行时间，振幅和波形数据中估算地球地下图像的主要工具。数据通常不足和嘈杂，并且正向建模通常基于近似物理学。地下模型参数的临时参数化增加了地下特征估计的进一步并发症。过去，解决方案估计值的非唯一性在过去得到了广泛认可，并且对地球物理学界的不确定性量化需求已促进。为此目的发现了描述我们的反问题的贝叶斯方法。它使我们能够用概率密度函数（称为后概率密度（PPD））来描述答案。但是，通常不可用PPD的简单功能描述。因此，从通常高度多模式的PPD中估算样本是一项具有挑战性的任务。常见的做法是得出最大的postterioi（MAP）模型，并在地图点使用Hessian表示不确定性。此方法假设PPD是高斯？由于正向问题的非线性性质和数据中的噪声特征，通常违反了一个假设。另一方面，基于大都会的马尔可夫链蒙特卡洛方法在计算上非常昂贵，通常需要超过一百万个前向模型评估。在这里，我们建议开发出在地震层析成像中应用计算有效的MCMC方法，以进行不确定性定量。可逆的跳跃蒙特卡洛法（RJMCMC），其中允许数据本身找到所需的合适数量的模型参数，该方法解决了常用方法的某些缺点。但是，该方法在计算上很昂贵。研究人员建议开发和实施一种称为可逆跳跃汉密尔顿蒙特卡洛（RJHMC）方法的新方法，以进行地震反转。该方法可以证明是传统的RJMCMC的两倍，因为它使用梯度信息在MCMC步骤中进行大幅度跳跃。它将应用于2D海洋多通道地震数据集。