What physics do we need?

Before we talk about streamers, vibroseis trucks or ocean-bottom nodes, we need a shared vocabulary for the physics that sits under every design choice. This opening section is a map, not a lecture.

In the figure below, pick a physics section to see which design decisions it feeds, or pick a decision to see which physics it rests on. The figure opens on Section 0.10, the last section of Part 0: ask yourself why attenuation should have anything to say about a question as geometric as bin size.

Reading the map

Plate (a) joins the nine physics sections, 0.2 to 0.10, to ten design decisions by 26 links. Each link says: “to decide this, you need this piece of physics.” Attenuation and $Q$ (0.10) feeds three decisions, source type, receiver type and bin size, and none of them rests on it alone. That is the pattern across the map: only two of the ten decisions, migration aperture and the survey footprint, rest on a single section, and the fold, offset and azimuth plan rests on five. Clicking a physics section opens it (on a touch screen the first tap focuses it and a second tap opens it); plate (b) gives its equation and plate (c) computes one example of it.

The three groups of physics

• Wave physics (Sections 0.2, 0.3, 0.4 and 0.10): how energy radiates from a source, reflects and converts at interfaces, and loses its high frequencies as it travels. This controls what you can detect.
• Arrays and sampling (Sections 0.5 and 0.6): how several sources or receivers combine into a beam, and how finite sampling in time and space limits the signals you can record faithfully. This controls what your geometry must look like.
• Noise and statistics (Sections 0.7, 0.8 and 0.9): what counts as signal and what as noise, how stacking $N$ traces raises the signal-to-noise ratio by only $\\sqrt{N}$, and which properties of the experiment (linearity, reciprocity, stationarity) you can rely on. This controls what your fold and stack must deliver.

Throughout the rest of this textbook we will reach back into this map. Every time a design choice seems to come from nowhere, a link points to the physics that answers it. Why 25 m bins? The largest bin that samples a dip $\\theta$ without aliasing is $\\Delta x \\le V/(4 f\_{\\max}\\sin\\theta)$, and a 30° dip at 60 Hz in 3000 m/s rock gives 25 m: focus bin size and read plate (c). The 60 Hz is not free either: with $Q$ = 100, 2.4 s of two-way travel to a target near 3 km costs 40 dB at about 60 Hz (focus 0.10 and read plate (c)), which is why bin size has two links. Why twelve geophones in a group? Twelve receivers 5 m apart hold 500 m/s ground roll to 22 % of its amplitude or less from 8.3 Hz to about 92 Hz; above that it returns, in full at 100 Hz, where the spacing equals its wavelength (Section 0.5). Why so much fold? Fold 64 raises the signal-to-noise ratio by a factor of about 8, not 64 (Section 0.8).

Design physics vs processing physics

Seasoned students sometimes ask whether this primer overlaps with the Processing textbook’s Part 0. It does not. Processing’s Part 0 teaches the mathematics you need to reason about recorded data: convolution, Fourier transforms, Z-transforms, least squares. Acquisition’s Part 0 teaches the physics you need to design the experiment that produces that data: how a source radiates, how an array of sources or receivers forms a beam, how finely a survey must sample the wavefield, and how much fold a given noise level demands. The two books are complementary; if you are going to plan surveys, you need both.

When you are ready, continue to Section 0.2, wavefronts and rays, or open any physics section from plate (a) to start there.

References

• Sheriff, R. E., Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge University Press.
• Yilmaz, Ö. (2001). Seismic Data Analysis: Processing, Inversion, and Interpretation of Seismic Data (2 vols.). SEG Investigations in Geophysics 10.
• Liner, C. L. (2016). Elements of 3D Seismology (3rd ed.). SEG.
• Bracewell, R. N. (1999). The Fourier Transform and Its Applications (3rd ed.). McGraw-Hill.