Apply the same stress-amplitude convention to S-wave seismic impedance. At limestone–sandstone,
At sandstone–salt,
A stress-amplitude transmission greater than one does not violate conservation of energy: the transmitted energy fraction includes the seismic impedance ratio. For particle velocity, the corresponding pairs are and . At normal incidence in isotropic layers, pure P and pure S waves do not undergo seismic mode conversion.
Specify the amplitude convention. For incident stress/pressure amplitude one, the normal-incidence seismic reflection coefficient and stress seismic transmission coefficient are
At limestone–sandstone, and . At sandstone–salt, and . The first return reverses the chosen stress-pulse polarity; the second interface produces no normal-incidence P return.
For a particle-velocity amplitude convention, and , giving and respectively. These are amplitude coefficients, not fractions of energy. The lossless reflected and transmitted energy fractions are and , which sum to one.
S-wave seismic impedance is . With as documented in part (i),
Unlike the P-wave case, the reservoir base has a nonzero S-wave seismic impedance contrast.
P-wave seismic impedance is . In layer order limestone, sandstone, salt,
The salt's larger P-wave seismic velocity is exactly offset by its smaller printed density, so the second interface has no P-wave seismic impedance contrast in this stipulated model.
For a P-to-S converted seismic head wave, set the transmitted S-wave angle to , giving . At the limestone–sandstone boundary, , so no transmitted S-wave head wave is possible for incidence from limestone.
At the sandstone–salt boundary, using the stated interpretation ,
The P-transmission seismic critical angle is lower, , but this does not forbid the converted S branch: at the transmitted P field is evanescent while the S field reaches grazing incidence.
A transmitted P-wave seismic head wave occurs when its refraction angle reaches , requiring . At the limestone–sandstone boundary the ratio is : there is no P-wave seismic critical angle for incidence from limestone. A slower lower layer cannot carry that transmitted head wave.
At the sandstone–salt boundary,
The head wave travels along the faster salt boundary and radiates energy back into the slower overlying medium. Reversing the direction of incidence would change which interfaces admit such a head wave.
Source notation assumption: the second printed is interpreted as . Otherwise the S-wave velocity in salt is not supplied, and this part and the salt S-wave calculations below would have no numerical answer. Retain the printed densities, including the unusually low salt value, rather than silently replacing them with typical rock properties.
With that interpretation, Snell law for elastic waves gives
For transmission into salt, , so
The transmitted P wave bends away from vertical because it enters a faster medium. The incident angle remains below the P-wave seismic critical angle at this interface.
Now reset the incident medium to sandstone; the new incident P wave has . Its reflected S wave has
The equal result to part (d) follows from the equal ratio in the two incident layers.
For the transmitted S wave in sandstone, Snell law for elastic waves gives
The different transmitted P- and S-wave angles result from their different seismic velocities, despite their common horizontal seismic ray parameter.
The transmitted P wave travels in the sandstone. Conservation of the seismic ray parameter gives
It bends toward the vertical because its seismic velocity is smaller.
For a horizontal interface, Snell law for elastic waves conserves horizontal seismic ray parameter . At the limestone–sandstone interface the incident P wave has . The reflected S wave remains in the limestone, so
from vertical. All angles below use this normal-to-interface convention.
Potential leakage paths are permeable or reactivated faults and connected fractures cutting the sealing sequence; lateral migration through connected reservoir layers into an unsealed outcrop or spill point; and natural or artificial penetrations such as poorly sealed abandoned wells or a compromised injection well. Injection raises pore pressure, potentially overcoming the capillary entry pressure of a seal, hydraulically opening fractures, or causing fault reactivation through reduced effective stress.
Seal continuity and porous permeability matter more than the rock name alone: a fractured or porous limestone need not be an effective caprock. Dissolution, chemical alteration or well-cement degradation can change leakage pathways over time. The underlying salt may be an effective barrier beneath the reservoir, but it does not seal the roof. Conversely, dissolved or residually trapped carbon dioxide is less mobile than a connected buoyant free-fluid phase, so connected porosity and fluid state also affect leakage.
Recommend a three-dimensional multichannel seismic reflection survey, with enough areal aperture, offsets and repeated coverage to image the reservoir top, base, structure and possible leakage faults. A two-dimensional reconnaissance line can be cheaper but cannot map a three-dimensional closure reliably and is vulnerable to out-of-plane reflections. Use seismic migration to position dipping reflectors and faults; repeatable acquisition is desirable if later carbon capture and storage monitoring is intended.
A tuned marine marine air-gun array supplies broadband low-frequency seismic wave energy that can penetrate to . Its trade-offs include bubble oscillations, seismic source ghosts, environmental constraints and limited high-frequency resolution. Sparker seismic source and boomer seismic source sources can provide higher-frequency, high-resolution shallow imaging, but commonly lack the energy and low frequencies needed to make them the first choice for this target. Source energy, bandwidth and repeatability must be balanced against penetration and vertical seismic resolution, approximately ; at and this is about . Required resolution ultimately depends on the unknown reservoir thickness.
A towed hydrophone streamer efficiently records pressure over many channels while a vessel moves. It primarily records P-wave pressure in the water, with flow noise, tow-depth ghosts, acquisition footprint and access restrictions as limitations. Seabed multicomponent nodes use hydrophones and geophones: pressure plus three-component ground motion can separate wavefields and recover converted S-wave information, and nodes permit wide azimuths and repeat surveys. Their costs include deployment, retrieval, coupling and positioning. Direct S waves do not propagate through the water column. The roughly water depth also creates a strong short-period water-layer seismic multiple that must be treated in processing.
The sandstone records deposition of transported sand, followed by burial and cementation. For the Bunter setting, river channels, floodplains with channel sands and arid continental dune systems are plausible environments; a sandstone name alone does not uniquely distinguish them. Well-sorted or weakly cemented sand can retain the connected porosity and porous permeability needed for a saline aquifer.
The Zechstein evaporite suggests restricted marine basins or salinas in an arid climate, where evaporation concentrates seawater until dissolved salts precipitate. Repeated restriction and replenishment can build thick evaporite sequences, including rock salt. The Triassic limestone indicates carbonate accumulation, plausibly in warm, shallow marine settings with limited siliciclastic supply, followed by cementation. Some limestones can also form in lakes; the marine interpretation here uses the stated regional sequence.
For the same geometry, field strength and induced magnetization model at the opposite magnetic inclination, replacing by gives . Thus the north–south asymmetry reverses: the principal low moves to the northern side and the high to the southern side. It is a horizontal reflection of the simple profile, rather than a necessary reversal of every anomaly's sign. At a magnetic pole the induced anomaly is symmetric; at the magnetic equator the symmetry is different again. If remanent magnetization dominates, a hemisphere change alone does not determine the new profile because that remanence direction also has to be specified.
Assume the greenstone belt is more magnetically susceptible than the host rocks and granite, its magnetization is mainly induced magnetization, and the body is roughly east–west elongated so that the south–north line crosses it. At southern magnetic latitudes the main field has negative magnetic inclination in a north-and-down coordinate convention. The total-field magnetic anomaly is then generally asymmetric: the principal negative lobe is on the southern side and the positive lobe is displaced northward for the simple induced source illustrated here. The exact lobe sizes and peak positions depend on body geometry and the actual magnetic inclination.[ref]
An explicit sketching model is an induced magnetic dipole at depth . With northward coordinate , and unit field direction , its normalized total-field magnetic anomaly is
The plot uses only as an illustrative dipole-field inclination for a latitude near south, not a measured modern field at the site. A wide greenstone belt would broaden the response and can produce prominent edge anomalies. Remanent magnetization or a magnetic granite could change the sketch substantially; gravity alone cannot identify the magnetic source.
Figure 1.
Induced-source magnetic anomalies for opposite inclinations on a south–north profile
. Details.
Measure total magnetic field along the same south–north line with a calibrated magnetometer, recording position, time and sensor height. A simultaneous base-station magnetometer measures temporal variation so that diurnal changes can be removed from the moving survey. Avoid disturbed periods and magnetic contamination from vehicles, fences, power lines and equipment. Choose station spacing much smaller than the expected anomaly width, for example tens to hundreds of metres for a kilometre-scale target.
Subtract the epoch-appropriate International Geomagnetic Reference Field or another stated regional main-field model to obtain a total-field magnetic anomaly. Level overlapping traverses and remove offsets or drift where appropriate. Accurate terrain/sensor geometry is needed for comparison with a geological model, but there is no universal magnetic analogue of a constant-density Bouguer slab correction: the effect depends on the distribution and direction of magnetization. Measure magnetic susceptibility and remanent magnetization on representative greenstones, granite and host rock to test the assumed magnetic sources.
Retain the same regional-background assumption as in part (b). The northern pluton is about thick beneath the station near the northern trough, while its gravity anomaly is about . Its anomaly relative to the greenstone maximum is approximately . Therefore the contrast equation is
Using the result of part (b), the second term contributes , leaving a net pluton anomaly of about . Hence , effectively close to the host-rock density at the precision of this diagram.
The apparent trough is strongly negative relative to the greenstone belt, but hardly negative relative to the southern host-rock background. If a northward regional trend is intended instead, it must be stated: in general,
with both gravity values in milligals. For example, a northern background of would give , but the same reference would also change part (b). No regional curve is explicitly identified in the supplied figure, so the numerical result must retain its reference-field assumption. This is the geological nonuniqueness of geophysical inversion of potential-field interpretation, rather than a reason to force a presumed textbook granite density onto the plot.
For a laterally extensive Bouguer slab of thickness and geophysical density contrast ,
The greenstone belt reaches from roughly to near its deepest central part, so use . The gravity maximum is approximately ; the exposed host-rock background in the south is approximately . Taking this as a constant regional reference gives a local excess . Thus
This is an approximate density under a constant-background, infinite-slab model. The finite width, variable thickness and neighboring pluton require a fuller gravity inversion for a precise value. In particular, the absolute value must not be inserted as the local excess.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 5. . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact