Backus–Gilbert method

Summary

The Backus–Gilbert method is a technique for linear inverse problems with finitely many data. It estimates local averages of an unknown function instead of the function itself. Each estimate is a linear combination of the data, and it equals a weighted average of the true model. The weight, the averaging kernel, is made as concentrated as possible around the point of interest. The width of this kernel measures the resolution, and a trade-off parameter balances resolution against the amplification of data errors. George Backus and Freeman Gilbert introduced it to interpret the free oscillations of the Earth. It gave geophysical inversion a precise language for resolution.