Book Smart

Parameter Estimation and Inverse Problems
Cliff Thurber, professor of geology and geophysics
Elsevier/Academic Press, 2005

You fling wide the refrigerator door, after a raw egg to make a batch of chocolate chip cookies. You see several eggs, but hmmm. Which are the ones you boiled yesterday to go on top of the salad?

A little research on the Web reveals that raw eggs don’t spin very well, but if you are able to spin one and then stop it for a second, a raw egg will start spinning again when you let it go. The egg you selected from the fridge spins beautifully until you stop it. It must be one for the salad, you surmise.

Congratulations! You have just solved a simple inverse problem. Generally speaking, an inverse problem is one in which you observe an outcome but don’t know its cause.

“How can you derive a physical model from a finite set of observations containing errors?” muses Thurber.

Actually, Thurber and his fellow authors (Richard Aster and Brian Borchers, both of the New Mexico Institute of Mining and Technology) intend the audience for their book to be students and professionals in astrophysics, applied mathematics, atmospheric science, geological engineering, geophysics, hydrology, oceanography and related fields.

“We believe that our book will be adopted by many dozens of professors in both geophysics and mathematics, based on initial sales and the list of interested people we have,” Thurber says. “It can serve as both a textbook and as a monograph for researchers.”

Because the approaches that the book outlines can be applied to virtually anything falling within the scope of an inverse problem, Thurber says that the book has some admittedly indirect implications for the prediction of situations like the recent tsunami in South Asia.

“Observations of the seismic waves and tsunami could be used to improve physical models of faults and tsunami propagation, which could lead to reduced earthquake risk, including the prediction of future tsunamis,” he says. “This is the opposite of using a physical model to calculate something that can be observed, for example, a numerical, computer model of the Sumatra earthquake and of the ocean which used to compute the resulting tsunami.”

This semester, Thurber is teaching a course on faults and earthquakes and another class on inverse theory. His research centers on faults, volcanoes and geologically active areas known as subduction zones, such as the area of the great Sumatra earthquake. Seismic tomography, which is imaging the interior of the earth, is his main specialty, he says, although he also does work in nuclear explosion monitoring.