Full-Waveform Inversion in Practice
Run a real adjoint-state inversion on Marmousi2, then learn to steer it: starting models, low frequencies, cycle skipping, compute, more than one parameter, and the evidence that makes a result worth defending.
You can run an FWI from a starting model to a converged result, tell a cycle-skipped run from a healthy one by its diagnostics, price the run and its encoding, say what elastic and multiparameter inversion can and cannot separate, and defend the model with synthetic-against-recorded evidence.
The method, run for real
One forward simulation, one backward simulation of the residuals, and their product is the gradient: the whole method in two runs of the wave equation per shot.
The site's lab runs a real adjoint-state inversion on the real Marmousi2 grid in your browser, so every later claim on this path can be checked against an inversion you ran yourself.
Getting it to converge
FWI only refines what the starting model already gets nearly right; tomography and model building decide whether the first iteration is inside the basin or outside it.
The lowest frequencies see the long wavelengths that no other band can recover, which is why every schedule climbs from the bottom and why the lowest usable frequency is a survey decision.
A prediction more than half a period late fits the wrong cycle and the gradient pulls the model the wrong way; recognising that landscape is the core diagnostic skill of the trade.
Paying for it
Cost scales with shots, bands and iterations; blending shots into supershots buys speed with cross-talk, and only some acquisition geometries can afford the trade.
Learned low-frequency extrapolation and learned starting models can rescue a run the data alone cannot, and fail quietly outside the conditions they were trained for.
More than one parameter
P velocity, S velocity and density each leave a different signature with angle, and an inversion can only separate what its range of angles actually records.
When two parameters can trade against each other and fit the same data, the inversion settles anywhere along the valley; seeing the valley is how you know which answer the data cannot give.
Defending a result
A falling misfit proves the model fits; overlaying synthetics on the recorded data, trace by trace and window by window, is how you show it fits for the right reason.
The misfit, the model update, the gradient norm and the step size tell four different stories, and a stuck or cycle-skipped run gives itself away in how they disagree.
A single best model hides how many others fit the data as well; uncertainty-aware inversion and learned priors turn that spread into something a decision can use.
In the field
Under salt an image needs both light and position: long offsets and reverse-time migration light the target, but only a correct velocity model puts it in the right place, the step FWI took at Thunder Horse.
A wide-azimuth marine inversion and a deep-water node survey in salt put every decision on this path into one project, with the budget and the schedule that real projects carry.