An extremely simple single-trace transmission example shows how an extended source formulation of full waveform inversion can produce an optimization problem without spurious local minima (“cycle skipping”). The data consist of a single trace recorded at a given distance from a point source. The velocity or slowness is presumed homogeneous, and the target source wavelet is presumed quasi-impulsive or focused at zero time lag. The source is extended by permitting energy to spread in time, and the spread is controlled by adding a weighted mean square of the extended source wavelet to the data misfit, to produce the extended inversion objective. The objective function and its gradient can be computed explicitly in this very simple example, and it is easily seen that all local minimizers must be within a wavelength of the correct slowness - that is, cycle-skipping cannot occur. Calculation of the gradient reveals that the minimization avoids cycle-skipping only if the weight operator is differential, a requirement shared with extended source inversion algorithms applicable at field scale.
Presentation Date: Monday, October 12, 2020
Session Start Time: 1:50 PM
Presentation Time: 2:15 PM
Location: Poster Station 3
Presentation Type: Poster
