Model the Seismic Response
Type the earth in, get the seismic out. Wavelets, convolution, and the full wave equation, ending in a modeling lab where you build the model and simulate its response. The craft behind every synthetic you will ever trust.
You can build an earth model, choose the right rung of the modeling ladder for the question at hand, generate convolutional and finite-difference synthetics without fooling yourself, and read AVO gathers you made from elastic first principles.
Why model
Forward modeling maps a known earth to its data, and the modeling ladder is the menu of physics you can afford.
Synthetics test algorithms, tie wells, and train networks, and the inverse crime is how they quietly lie; learn both on day one.
Wavelets
Every synthetic starts with a wavelet; the Ricker is the workhorse and the zoo tells you what else is in the stable.
Phase moves events without changing spectra, and sampling sets the frequency ceiling; both burn people who skip them.
Resolution is bandwidth wearing field clothes; this is where the quarter-wavelength rule comes from and when it fails.
The convolutional model
Impedance to reflectivity to trace: the two-step machine that makes ninety percent of the synthetics the industry runs on.
The wedge model is the most instructive synthetic ever built; tuning is why thin beds brighten before they vanish.
The well tie is the convolutional model earning its keep: log to impedance to synthetic, with noise and the judgment of when convolution is enough.
2D earth models
Faults, layers, and geology-to-impedance: the model you build here is the label your synthetic will carry forever.
Convolving a whole section makes an image; pairing it with the fault mask you drew makes machine-learning training data, and knowing where 2D convolution lies keeps the pairs honest.
The wave equation
The wave equation from first principles, then onto a grid: finite differences are how the full physics becomes runnable.
CFL is the speed limit and numerical dispersion is the fine for ignoring grid rules; every FD run answers to both.
Kill the grid-edge reflections and fire a source: the shot record is the payoff, synthetic field data with known geology underneath.
What the wave equation buys
The two wave phenomena convolution cannot make; seeing them appear in your own FD run is where the ladder's price makes sense.
Head waves and gas-cloud pushdown are field headaches you can rehearse in a model where you know the answer.
Same earth, two engines: the definitive side-by-side that tells you which rung of the ladder your question actually needs.
Elastic and AVO
The earth is elastic whether your model is or not; shear and converted modes are what the acoustic shortcut throws away.
Reflection amplitude versus angle is rock physics speaking; Zoeppritz is the full sentence and Shuey the usable summary.
Making your own gathers, and choosing acoustic or elastic on purpose, is how AVO stops being a plot you were handed.
Anisotropy
Real rocks are faster along the grain; epsilon, delta, and gamma are the accepted shorthand for how much.
Model building
Layer-cake earths teach; stochastic heterogeneity tests. A modeling shop needs both dials.
Marmousi and its siblings are the shared benchmarks of the field, and model QC is what keeps your own earths from lying to you.
Synthetic datasets
A labeled fault-detection dataset end to end: the synthetic data product that trains the networks the ML paths deploy.
A plume you can watch grow because you grew it: synthetic 4D for storage monitoring, with the truth attached.
The modeling lab
Build the earth, pick the physics, run the simulation, defend the result: the lab is this whole path with your hands on it.
The whole modeling ladder on one reference card: which physics, for which question, at what cost.