| Since 1960s, the inverse question, of which are effects, manifestation (output), original image (input) has been put forward in numerous science technology fields, such as physical geography, life sciences, material sciences, remote sensing technology, mode identification, signal transact, industrial control as well as economic policy decision. It is generally called math-physics inverse question. many scholars birth at home and aboard are attracted to go in for the inverse question theory study because of its widely important applying background and the distinct novelty and challenge of its theory. So far, it has expanded a demanding subject direction to crossing calculating math, applying math and systematic science. While it is also one of the pretty extensive problems on the applying prospect of numerous inverse problem. We will mainly discuss the forward and inverse problem of wave equation.Wave fields forward problem is to study how earthquake waves spreads during the underground media by researching the position, shape and distributing situation of the source of the earthquake. And wave fields inversion problem is to study the situation of the source of the earthquake by getting some information about the earthquake, such as the density of the media, elastic parameter and the speed of the wave. The research on wave fields lies in dealing and analyzing data. Originally dealing and analyzing data belong to the tasks of the information science. But the data on the earth physics have special character, that is the data can be used in corresponding wave equations, so mathematical problems on the earth physics are actually Partial differential equation problems. In the 1970s, with the development of prospecting, people need to study the characters of rocks, but the old methods could not meet the needs. So people started noticing the researches on inversion problems. In a way, the changes make match developed more rapidly. As the earth is a complicated and changing object, we can only get some data about the surface and few distance under the surface during the researches on the earthquakes. In order to find the best way to explain the data, improve their dependability reduce the cost used in searching now oil fields, it is necessary for us to study the problems on Partial differential equations concerning the earth physics.Research on wave equations have a decades history, but sill are; a hot problem. During the researches on earthquake, people produce earthquake waves by using artificial earthquake sources and then get the information from receivers. This kind of records just give people partial data. According to that, people can assume a model of the earthquake, that is a forward model. And basing on the model, people can simulate a real earthquake research in order to get a complete data. And the whole data can be used to solve the inversion problems. In the case of math, forward problems equal to solving partial differential equations. Forward computes mainly use difference method and definite unknown numbers methods. During the course of compute, people first change wave equations into linear equations and then work them out. The inversion problems are a quite complicated subject. The reason for that are three: 1.its unsteadiness 2. based on forward computes 3.complicated computes. Thos are the key to the inversion problems. The history of research for wave equation inverse problem has lasted no more than twenty years, but it is still a hot question, in seismological observation, using man-made focus of earthquake to excite the earthquake wave, then writing down the vibration of medium particle, brought from earthquake wave that was received by receiver. This record is filled earthquake record, it only presents part of message about wave field. Based on this field record to suppose geology model, it is forward model, simulating seismological observation based on it, to get the academic earthquake composed record, as the append condition of inversion, and confirm the inversi...
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