We have spent the last five chapters dwelling on the uses of wave equation imaging. In this chapter, we gaze into our “crystal ball” and look toward the directions that wave equation modeling and imaging might take in future years.
The technologies used in the numerical forward modeling of the wavefield have provided a general method for the simulation of seismic wavefields. The many applications of such methods have been outlined in an SEG reprint volume by Kelly and Marfurt (1990).
Just as importantly, these numerical wavefield modeling methods can be adapted to seismic imaging by the use of reverse-time migration. Advantages of reverse-time migration include generality of applications as well as relative ease of coding. Disadvantages include the high computational costs and memory requirements.
What are possible future developments for such highly versatile, yet expensive, algorithms. In order to address the computational costs for the application of useful wave equation algorithms, Phil Bording developed the idea of designing a computer, a “wave machine”, in his PhD thesis.
Machines are mans way of reducing work, saving human effort, and in general making life more enjoyable. The use of digital computers as a tool for problem solving has expanded to all aspects of modern life. Prior to the digital era many computational machines were built to aid in problem solving. The sextant and slide rule are good examples. Machines were built to compute latitude, tell time, and to predict the tides. These mechanical devices reached a remarkable state of refinement over the centuries of the industrial revolution. The development of interchangeable parts, a by-product of mass production helped Charles Babbage in his effort to build the first digital computer, the Difference Engine. This pioneering engineering project of the early 1800’s attempted to construct a mathematical difference engine, to compute Newton's difference calculus. It did function as designed but was plagued by friction and mechanical troubles.
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Seismic Modeling and Imaging with the Complete Wave Equation
“Seismic modeling and imaging of the earth's subsurface are complex and difficult computational tasks. The authors present general numerical methods based on the complete wave equation for solving these important seismic exploration problems.”