Inversion
Seismic inversion is by nature an iterative procedure. At each iteration we perform the following steps.
To perform a model inversion, the following steps need to be done.
1. Forward simulation
Given a velocity model as input, the forward simulation returns synthetic seismograms as output.
Since your velocity model is different from the real-world model, the synthetic seismograms are also different from the observed data recorded by the seismometers. Thus, the key point here is how to use the difference between observed data and synthetic data to update your velocity model, which we call the Seismic Inversion in tomography. After the first iteration, forward simulations performed as part of optimization procedure can simply be carried over to the next iteration.
More information about the forward solver(the software that can run forward simulation) could be found in the solver page.
2. Pre-processing
In our terminology, pre-processing includes all operations performed on seismic traces prior to the adjoint simulation. Signal processing operations, window selection of obervations and synthetics, and creation of adjoint sources fall into this category.
Signal Processing The signal processing includes steps like removing trend, tapering data, removing instrument response and etc. Observed and synthetic data will be filtered into targeted period band.
Window Selection If you do not want to make measurements on the whole seismograms, then selecting windows on the seismograms are required. We use some criterial to generate windows and afterwards measurement will only be made inside those windows.
Adjoint Source Generation Adjoint sources are calculated inside windows. There are different kinds of adjoint sources you can choose.
More information could be found in the pre-processing page
3. Adjoint simulation
Given adjoint traces as input, the adjoint simulations returns sensitivity kernels as output.
More information about the adjoint solver(the software that can run adjoint simulation) could be found in the solver page.
4. Post-processing
In our terminology post-processing includes all operations performed on sensitivity kernels following the adjoint simulation. After post-processing, we will turn the kernels into gradient, and the gradient will be used in the optimization stage. Projection, regularization, and preconditioning fall into this category.
More information could be found in the post-processing page.
5. Optimization
Given the gradient direction, the optimization procedure returns an updated model. Conventionally, the optimization procedure consists of separate search direction and line search computations.
More information could be found in the optimization page.