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Nonlinear inverse problems are common in science and engineering. In fact the quotation from Feynman shows clearly that the process of discovering physical laws is itself an inverse problem.
What is an inverse problem? Subtraction is the inverse of addition. Division is the inverse of multiplication. Root is the inverse of power. Given the answer (say, the number 4) nd the question (2+2 = ? or 8/2 = ? or p 16 = ?).

Прежде, чѣмъ приступлю къ описанію геогностическаго строенія почвы, распространенной въ трехъ упомянутыхъ уѣздахъ,—я считаю не лишеимъ сдѣлать краткое замѣчаніе о причинѣ, по поводу которой меня командировалъ Штабъ Корпуса Горныхъ Инженеровъ на геогностическія развѣдки, въ подмосковные уѣзды.

Дѣло состояло въ томъ, что нашъ извѣстный Московскій астрономъ Г. Швейцеръ предложилъ Ка-питану Корпуса Межевыхъ Инжеверовъ , Г. Мейену, произвести магнитыыя наблюденія въ окрествостяхъ Мосісвы, для подробваго изсдѣдованія измѣнееій наклоненія и склоненія магнитеой стрѣлки, и для ооре» дѣленія напряжѳнія земнаго магыетизма <...>

This course is an introduction to some of the balkanized family of techniques and philosophies that reside under the umbrella of inverse theory. In this section we present the central threads that bind all of these singular items together in a harmonious whole. That's impossible of course, but what we will do is provide a point of view that, while it will break from time-to-time, is good enough to be going on with. The goal of this chapter is to introduce a real inverse problem and explore some of the issues that arise in a non-technical way. Later, we explore the resulting complications in greater depth <...>

Many contemporary problems faced by Earth sciences and society are complex, for example, climate change, disaster risk, energy and water security, and preservation of oceans. Studies of these challenges require an interdisciplinary approach and common knowledge. This book contributes to closing the gap between Earth science disciplines and assists in utilisation of the growing amount of data from observations and experiments using modern techniques on data assimilation and inversions developed within the same/another discipline or across the disciplines. <...>

This work is the result of contributions from 52 active researchers in geophysics, astrophysics and astronomy. We have followed a philosophy of directness and simplicity, while still allowing contributors flexibility to expand in their own areas of expertise. They are cited in the contributors’ list, but I take this opportunity to thank the contributors for their efforts and their patience. The subject areas of this dictionary at the time of this writing are among the most active of the physical sciences. Astrophysics and astronomy are enjoying a new golden era, with remarkable observations in new wave bands (γ -rays, X-rays, infrared, radio) and in new fields: neutrino and (soon) gravitational wave astronomy.

The theme of this book is the study of basaltic volcanism as a stage in planetary evolution: to use the eruption of lava from the interior of a planet as evidence of the thermal and chemical processes of the planet. All lavas extruded on a planet’s surface can provide information about events in the interior. From a petrologic point of view, however, it is the more primitive lavas, which rise to the surface of a planet with minimal changes, that can provide the most information about the interior. In general, these more primitive lavas are basalts and so in Chapter 1 our sampling has concentrated on basaltic rocks.

The field of ultrasonics is a branch of acoustics dealing with frequencies generally beyond the audible limit. As such, the application of the principles of classical acoustics serves equally well in the audible and ultrasonic regimes. However, as noted by Hubbard (1940), “While it is a logical extension of well-known principles, its growth has been signalized by the discovery of phenomena peculiar to the new ranges of frequency.” It is the research, development and use of the “peculiar phenomena” that has created the very broad field of ultrasonics. The objective of this work will be to review the history of that field. <...>

Paleomagnetic data are useful in many applications in Earth Science from determining paleocurrent directions to analyzing the long-term behavior of the geomagnetic field. Despite the diversity of applications, the techniques required to obtain and analyze the data are similar. This book attempts to draw together the various principles and practices within paleomagnetism in a consistent and up-to-date manner. It was written for several categories of readers:
1)    for Earth Scientists who use paleomagnetic data in their' research,
2)    for students taking a class with paleomagnetic content, and
3)    for other professionals with an interest in paleomagnetic data. <...>