What math do we need?
Learning objectives
- Know which math topic in Part 0 supports which processing step later in the course
- Understand why we teach the math before the processing, not alongside it
- Be able to navigate back to the right math section when a later chapter gets dense
Welcome. Before we touch a single seismic trace, we need to build the mathematical toolkit that every processing step quietly assumes you already have.
Seismic processing is, at its heart, applied signal processing on wavefields. Every workflow — from reformatting raw shot gathers to full-waveform inversion — is ultimately convolution, Fourier analysis, linear algebra, optimization, and wave physics in domain vocabulary. If any of those feel shaky, the rest will feel like memorization. Our goal in Part 0 is that none of them feel shaky.
The map below
Below is an interactive roadmap. On the left are the nine math topics you will meet in Part 0 (§0.2–§0.10). On the right are the processing outcomes those topics unlock — the things you will actually do with seismic data in Parts 2 through 9. Curved lines connect each math topic to every processing outcome it supports.
Click any node to follow its connections. Click a math topic to see which processing steps depend on it. Click a processing outcome to see which math prerequisites you need. The point of this widget is to convince you that every bit of math in Part 0 earns its keep — nothing here is academic filler.
How Part 0 is paced
Part 0 assumes no prior signal-processing, linear-algebra, or wave-physics background. Each §0.X section starts from first principles and builds up with its own widget. If you already know the material well, you can skip the section and come back only for the quiz at §11.1. If you do not, you will not be left behind — every concept is illustrated with something you can play with.
One practical tip: do not read Part 0 linearly and then close the book. The math lives in your muscle memory only after you have used it. Return to these widgets whenever you are reading a later chapter and something feels opaque. The math and the processing are the same material seen from two angles.
What is next
Section §0.2 opens with complex numbers and phasors — the single most leveraged piece of math in processing, and the most consistently under-taught. If you can explain to a colleague what e^{i\omega t} means by the end of §0.2, you are ready for the rest of Part 0.
References
- Yilmaz, Ö. (2001). Seismic Data Analysis (2 vols.). SEG.
- Bracewell, R. N. (1999). The Fourier Transform and Its Applications (3rd ed.). McGraw-Hill.
- Strang, G. (2016). Introduction to Linear Algebra (5th ed.). Wellesley-Cambridge.
- Oppenheim, A. V., Schafer, R. W. (2009). Discrete-Time Signal Processing (3rd ed.). Prentice Hall.