Abstract:The theoretical analysis of random inverse method for wave impedance inversion leads to the conclusion that random inverse method is one damping least square method,which,however,is not general damping least square method because damping item .1=an}Q, has its own physical meaning. Applying adaptive algorithm to this damping item achieves nicely quantitative restriction for solving space in wave impedance inversion. Model parameter variance restricts inversion result to make widely-restricted inversion solution range in the reasonable interval of geo physical parameters. The real inversion example using multihole restriction is given,and the restriction condition for wave impedance inversion is analysed particularly.