The joint analysis of refractions with surface waves (JARS) method for finding solutions to the inverse refraction problem

Abstract

The joint analysis of refractions with surface waves (JARS) method offers an approach for finding solutions to the nonunique inverse refraction problem but, more specifically, to the inverse first-arrival traveltime problem (IFATP) because it includes the direct wave and excludes refractions that are not first arrivals. The inverse refraction problem is well known and clearly established to be nonunique (Slichter, 1932; Healy, 1963; Ackermann et al., 1986; Burger, 1992; Lay and Wallace, 1995). However, it wasn't until Ivanov et al. (2005) examined nonuniqueness from the perspective of solving inverse problems that it became clear that the objective function (the one minimizing the difference between the observed and the modeled data) did not have a global minimum (i.e., a unique solution), or only a few global minima, but a continuous range of minima (i.e., a valley of possible solutions). Insight into the significance of the problem was gained from experiments that maintained a constant number of parameters when solving the inverse problem (Ivanov et al., 2005). Furthermore, these observations were shown to apply even when dealing with a simple (very few parameters) three-layer model.