Paul L. Stoffa

Hybrid optimization methods for geophysical inversion

Local and global optimization algorithms are used commonly in geophysical data inversion. Each type of algorithm has unique advantages and disadvantages. Here we propose several methods of combining the two algorithms such that we can overcome their drawbacks and make use of the salient features of the two methods. In particular, we combined a local conjugate gradient (CG) method with a global very fast simulated annealing (VFSA) approach to solve problems of geophysical interests. We conducted a systematic study to find an efficient strategy to combine CG and VFSA optimization schemes and recommend a couple of ways for future implementations. Seven different hybrid algorithms were first tested on a set of field 1-D Schlumberger resistivity sounding data and their performances were compared with stand‐alone genetic algorithm (GA), simulated annealing, and local search algorithms. Almost all of the proposed hybrid algorithms were found to be computationally more efficient than the conventional global optim...

3-D Traveltime Calculations

This equation is the basis for both the 2-D and 3-D traveltime code. Figure 1 shows that the update time t is the time of the minimum raypath, t0 for example, added to the time from z0 to the update point at (x,z2). In other words t = t0 + s[(z2 – z0) + Δx2]1/2 To find the minimum raypath location z0, this equation is differentiated w.r.t. z0 giving dt/dz0 = z0w/t0 – s(z2 – z0)[(z2 – z0) + Δx2]-1/2