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What is Inversion? The word inversion has been used in science and engineering to mean a wide variety of things. Thus it is no surprise that there exists confusion amongst practitioners as to what that word means and skepticism over what inversion can do. In general, what one considers inversion depends on his background, whether it is engineering, mathematics, scattering theoretical physics, or whatever else. Common perceptions appears to be (Stolt 1989) “what I am doing is inversion - I don’t know what you are doing”. “What they’re doing is inversion, so it can’t be of practical use”. Occasionally, segments of inversion community have promoted an elitist image, which has encouraged this response by those outside that community.
Derivation of model of earth from geophysical data means
Physical Variables Measurements
Direct Inversion is some sort of reverse physics and is generally very unstable for most applications. Model based inversion is iterative model fitting. If it is said that inversion is optimization, then a question arises what is wrong with this definition? The problem is ill-posed. It has non-uniqueness: multiple solutions satisfy the data. Some parts of the model are not identifiable by data. In place of continuous model space one has set of finite data. Data are noisy. A practical definition suggested by D. D. Jackson is “Interpretation of inaccurate, insufficient and inconsistent Data”. It should, however, be remembered that lack of Information cannot be remedied by any mathematical tricks.
Inverse theory is a set of mathematical techniques for reducing data to obtain useful information about the physical world on the basis of inferences drawn from observations. In general, laws of physics provide the means for computing the data values given a model. The problem of generating theoretical data given a model is termed a forward problem. In this talk, I will restrict myself to observations and questions that can be represented numerically.
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