Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2022 / Paper 1 / 6 / g

The Nyquist–Shannon sampling theorem gives a Nyquist rate of $200$ samples per second for a $100$ Hz upper frequency. In practice choose $f_s>200$ Hz, for example $500$ Hz with $\Delta t=2$ ms, and use an anti-aliasing filter whose passband retains the required signal below the Nyquist frequency. Exactly $200$ Hz leaves no filter transition band and can entirely miss a $100$ Hz sinusoid at an unfortunate phase; it is a limiting rate, not a robust acquisition choice.

Choose shot and receiver intervals to sample the shortest relevant spatial wavelength and steepest event moveout without spatial aliasing. A simple bound isusing the smallest apparent velocity of the events one needs to retain or separate. Using $1500\mathrm{m}{\mathrm{s}}^{-1}$ and $100$ Hz alone suggests $7.5$ m, but slower surface waves or dipping events can demand finer spacing. It is not a universal final design interval.

Also consider target depth and lateral resolution, reflector dip, near-surface heterogeneity, source strength and coupling, maximum offset and aperture, common-midpoint bin size and seismic acquisition fold, refraction crossover distances, access and budget. Receiver spacing and source spacing jointly determine coverage and cannot be selected from temporal sampling alone.

First measure the generator’s spectrum, timing and propagation pattern on quiet records. If practicable, coordinate shutdowns or quiet acquisition windows; otherwise place source/receiver lines to reduce coupling to the noise source and use good ground coupling and adequate instrument dynamic range. Saturated channels cannot be repaired by a later filter.

Separate noise using its measured frequency and moveout: a band-pass/high-pass filter can reject frequencies below the useful seismic band, and an appropriate narrow notch can reject a narrow coherent component. Avoid deleting wanted low-frequency arrivals along with the generator noise. Dense spatial sampling enables frequency–wavenumber filtering or array methods to separate low-apparent-velocity surface noise from target arrivals. A reference sensor near the generator can support coherent-noise subtraction when the transfer is stable.

Repeated shots/sweeps and stacking improve the signal-to-noise ratio for uncorrelated noise; persistent coherent generator noise does not necessarily average down. Known-sweep Vibroseis correlation also helps reject unrelated noise. Verify the final processing against test gathers to ensure that real arrivals have not been mistaken for noise.