Felix made some minor edits. Make sure you add juxtoposition WISE. Al…

…so, image is huge in file size. You may need to do something about that.

WISER/paper.qmd

@@ -8,18 +8,18 @@ bibliography: paper.bib
 
 ## Abstract
 
-We introduce a cost-effective Bayesian inference method for full-waveform inversion (FWI) to quantify uncertainty in migration-velocity models and its impact on imaging. Our method targets inverse uncertainty due to null-space of the wave modeling operators and severe observational noise, and forward uncertainty where the uncertainty in velocity models is propagated to uncertainty in amplitude and positioning of imaged reflectivities. This is achieved by integrating generative artificial intelligence (AI) with physics-informed common-image gathers (CIGs), which greatly reduces reliance on accurate initial velocity models. In addition, we illustrate the capability of fine-tuning the generative AI networks with frugal physics-based refinements for an out-of-distribution scenario.
+We introduce a cost-effective Bayesian inference method for full-waveform inversion (FWI) to quantify uncertainty in migration-velocity models and its impact on imaging. Our method targets inverse uncertainty due to null-space of the wave modeling operators and severe observational noise, and forward uncertainty where the uncertainty in velocity models is propagated to uncertainty in amplitude and positioning of imaged reflectivities. This is achieved by integrating generative artificial intelligence (genAI) with physics-informed common-image gathers (CIGs), which greatly reduces reliance on accurate initial migration-velocity models. In addition, we illustrate the capability of fine-tuning the generative AI networks with frugal physics-based refinements for an out-of-distribution scenario.
 
 ## Amortized variational inference
 
-Our method concerns estimation of velocity models from noisy seismic data through the inversion of wave modeling operator. Instead of seeking only a single velocity model, our method aims to draw samples from the posterior distribution of velocity models conditioned on the observed shot data. To this end, conditional normalizing flows (CNFs) are trained to approximate this posterior distribution. After training, the inverse of CNF turns random realizations of the standard Gaussian distribution into posterior samples (velocity models) conditioned on any seismic observation that is in the same statistical distribution as the training data, shown in the upper part of the flowchart.
+Our method concerns estimation of migration-velocity models from noisy seismic data through the inversion of the wave modeling operator. Instead of seeking only a single velocity model, our method aims to draw samples from the posterior distribution of migration-velocity models conditioned on observed shot data. To this end, conditional normalizing flows (CNFs) are trained to approximate this posterior distribution. After training, the inverse of CNF turns random realizations of the standard Gaussian distribution into posterior samples (velocity models) conditioned on any seismic observation that is in the same statistical distribution as the training data, shown in the upper part of the flowchart.
 
 ## Physics-based refinement
 
-While the trained CNF can generate posterior velocity samples instantaneously at inference, the accuracy of CNFs might be deteriorated due to out-of-distribution issues --- i.e., the observed data is generated by an out-of-distribution velocity model, or through a slightly different forward modeling operator (e.g. acoustic-elastic, attenuation effect, unremoved shear wave energy, etc). To meet this challenge and bridge the so-called *amortization gap*, we apply a physics-based refinement approach to fine-tune the trained network. We compose a shallower invertible network with the trained CNFs, where the shallower network is initialized with random weights and acts on the latent space. Following a transfer learning scheme, we freeze the weights of the trained CNF and only update the weights of the shallower network in order for the posterior samples to fit the observed shot data. This process is shown in the lower part of the flowchart.
+While the trained amortized CNF can generate posterior velocity samples instantaneously at inference, the accuracy of CNFs might be deteriorated due to out-of-distribution issues --- i.e., the observed data is generated by an out-of-distribution velocity model, or through a slightly different forward modeling operator (e.g. acoustic-elastic, differing source function, attenuation effect, unremoved shear wave energy, etc). To meet this challenge and bridge the so-called *amortization gap*, we apply a physics-based refinement approach to fine-tune the trained network. We compose a shallower invertible network with the trained CNFs, where the shallower network is initialized with random weights and acts on the latent space. Following a transfer learning scheme, we freeze the weights of the trained CNF and only update the weights of the shallower network in order for the posterior samples to fit the observed shot data. This process is shown in the lower part of the flowchart.
 
 ## Downstream imaging
 
-To understand how the uncertainty in the velocity models propagates to imaged reflectors, forward uncertainty is assessed by carrying out high-frequency imaging for different posterior velocity samples, shown in the right-hand side of the flowchart. The uncertainty in the imaged reflectors is revealed in variance in both the amplitude and the positioning of the reflectors.
+To understand how the uncertainty in the migration-velocity models propagates to imaged reflectors, forward uncertainty is assessed by carrying out high-frequency imaging for different posterior velocity samples, shown on the right-hand side of the flowchart. The uncertainty in the imaged reflectors is revealed in variance in both the amplitude and the positioning of the reflectors.
 
 ![](./figs/workflow.png){width=99%}