Time/space series modeling, data processing and inversion

时间/空间序列建模、数据处理与反演

• 批准号: 1804-2007
• 负责人: Ulrych, Tadeusz
• 金额: $ 1.77万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=364962
• 关键词: Time; space; series; modeling; data

The interior of our Earth is, essentially, unavailable to direct observation. With the exception of information that is available from instrumentation that is placed in deep, exceedingly expensive wells, our information is always derived in indirect fashion, for example, by means of active surface seismic sources, passive sources, such as earthquakes, and non seismic techniques, electromagnetic, gravitational and isotopic measurements, to name but a few. The data that we record are, invariably, amplitude variations in time, space or both. The interpretation of the data in terms of Earth parameters entails, basically, three tasks:[1] Time and/or Space Series Modelling. Before the recorded data may be interpreted, we must envisage a process that can be assumed to have generated them. This step is called modeling. A model is desigened on the basis of experience, intuition and luck. The purpose of this model is to enable us to generate, synthetically, a data set that resembles the one recorded.[2] Data Processing. The recorded data are always contaminated by some type of noise. This noise may be random, partly deterministic, additive, convolutional, multiplicative and, as generally happens, an unknown mixture of all of the above. The task is to separate signal from noise, so that this signal may be compared with the signal modelled in step [1]. Many other sub-tasks are involved here, such as deconvolution, resolution enhancement etc., but these will be described in the proposal below.[3] Inversion. Step [1] models the signal in the data in terms of Earth parameters. This is called the "forward problem", i.e., assumed parameters >>> data. The desideratum is, however, data >>> parameters. the "inverse problem". Centrally important, fascinating and hugely difficult. I will not go into reasons why here. Sufficient be it to pose the following, "Given the number 12, find two numbers, a and b that, when added together, give 12. An infinity of answers. The question is, is one of these useful, and if so, which one?

我们地球的内部基本上是无法直接观测的。除了从放置在深的、非常昂贵的威尔斯中的仪器中获得的信息之外，我们的信息总是以间接的方式获得的，例如，通过主动地表地震源、被动源（如地震）和非地震技术、电磁、重力和同位素测量，仅举几例。我们记录的数据总是在时间、空间或两者上的振幅变化。根据地球参数对数据进行解释基本上需要三项任务：[1]时间和/或空间序列建模。在解释记录的数据之前，我们必须设想一个可以假定产生这些数据的过程。这一步称为建模。一个模型是在经验、直觉和运气的基础上设计的。这个模型的目的是使我们能够综合生成一个类似于记录的数据集。[2]数据处理.记录的数据总是被某种类型的噪声污染。该噪声可以是随机的、部分确定性的、加性的、卷积的、乘性的，并且如通常发生的，是所有上述噪声的未知混合。任务是将信号与噪声分离，以便该信号可以与步骤[1]中建模的信号进行比较。这里涉及许多其他子任务，例如反卷积、分辨率增强等，但这些将在下面的提案中描述。[3]反演步骤[1]根据地球参数对数据中的信号进行建模。这就是所谓的“前向问题”，即，假设参数>数据。然而，迫切需要的是数据>参数。“逆问题”。至关重要，引人入胜，而且非常困难。我不会在这里解释原因。只要提出下面的问题就足够了，“给定数字12，找出两个数字a和B，它们加在一起就是12。无限的答案。问题是，其中一个有用吗？如果有用，是哪一个？