# Cave large enough to detect with a pendulum?

• Ulysees
In summary: Bouguer correction is a refinement of the free-air correction that takes into account the fact that the Earth's surface is not a perfect sphere, and that there are variations in the height of the land above sea level. This correction is applied by subtracting a constant (approximately 1.5%) from the measured gravity value to compensate for the effects of the irregularities on the surface.
Ulysees
We can measure gravity gradients quite accurately with a pendulum: just take two measurements of the period at different places, and their inverse ratio is the gravity ratio along the vertical axis. So if there's a large cave underneath, our pendulum will be a little slower as we get closer to the cave.

But to do this we have to acount for the noise due to density variations of rock.

Anyone know how large those variations are?

Can't really help you much, but you might want to look up gravity anomalies and the http://www.Earth'sci.unimelb.edu.au/ES304/MODULES/GRAV/NOTES/densities.html .

I've only really heard of gravity anomaly being useful in identifying large scale very deep structures such as fault-bound basement blocks buried under later rocks, areas of thicker crust, or large igneous intrusions such as batholiths. I suspect there might be too much 'noise' or insufficient resolution in data to determine anything on such a small scale as a cave. If I'm wrong however, I'd think you'd probably also have difficulty telling a cave from something like an igneous intrusion or salt upwelling.

I'm by no means an expert so don't take my word for it.

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The Earth gravity is roughly somewhere between 9.78 and 9.82 m/s^2, variable with local effects and lattitude, so there is no fixed gravity for a certain point. http://nasadaacs.eos.nasa.gov/articles/2005/2005_gravity.html .

Let's throw in some figures. Suppose that you're standing on the roof of a large spherical cavity right under your shoes. You can calculate the 'loss' of gravity if that cave had been solid rock by some very simple formulas for volume and Newtons law for gravity.

For a cave of 100 meters radius that would be about 10^-5 m/s^2 difference for 1000 meters that's about 10^-3 m/s^2. That might go unnoticed accounting for the measured variations as shown in the link.

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Are you aware of any other, low-cost technologies to detect caves? I think ELF radar goes quite deep, is that so? What about sonar?

Ground Penetrating Radar (GPR) is a possibility, although you would need to calibrate it carefully and the method could still fail if the geological conditions were unfavourable. Magnetometetry would be another possibility, provided that the limestone had some magnetic susceptibility to differentiate it from the cavity (i.e. the absence of rock). Seismics would also work but you would need to deal with high frequencies and would therefore need quite specialist geophones to detect a small cavity. Perhaps even some kind of neutron or gamma ray detector could work, although I somehow doubt unless you were presented with very accomodating geological conditions. Gravitometry is the most tried and tested method here, and by far the most reliable - why would you want to account for density variations in the rock? Surely that is exactly what you are trying to detect - or to put it more precisely - you are trying to detect the density variation in the subsurface, a cavity would stand out like a sore thumb. There are lots of other corrections you might want to apply however, eg: instrument drift, tidal, free-air, Bouguer, latitude, etc...

> Seismics would also work but you would need to deal with high frequencies and would therefore need quite specialist geophones to detect a small cavity.

Seismics are measurements during an earthquake? Why would high frequencies be involved?

> There are lots of other corrections you might want to apply however, eg: instrument drift, tidal, free-air, Bouguer, latitude, etc...

Could you explain free-air and Bouguer?

Ulysees said:
> Seismics would also work but you would need to deal with high frequencies and would therefore need quite specialist geophones to detect a small cavity.

Seismics are measurements during an earthquake? Why would high frequencies be involved?

Not strictly true, exploration seismology utilises controlled sources, e.g. explosions, airgun (marine), or vibroseisTM etc... High frequencies are necessary to detect small reflectors, low frequency energy may well pass straight through a small cavity without "seeing" it.

> There are lots of other corrections you might want to apply however, eg: instrument drift, tidal, free-air, Bouguer, latitude, etc...

Could you explain free-air and Bouguer?

Free-air is a correction based on your elevation from a datum, the further you are from the centre of the Earth the lesser g will be, since you are measuring g (with your gravitometer or perhaps even a pendulum!) you can remove the effects of elevation from your data by adding 3.086 g.u. per metre you are above the datum. (Note, if you were using a pendulum this correction would be well within the error of your measurement so would not be applicable.)

You might well say that the free-air correction is flawed because there is not "free-air" between your instrument and the datum, but there is solid rock - this solid rock would add to your measured value of g. This is where the Bouguer correction comes in, the Bouguer correction is applied in the opposite direction to the free-air correction by subtracting the effect an infinite slab of constant density rock between the datum and instrument would have on g. The so-called Bouguer plate produces a gravity field equal to 2*pi*density*G*height above datum (Milsom, Field Geophysics).

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I was trying to evaluate gravity numerically for any arbitrary distribution of mass. Soon I faced the problem of evaluating gravity on the surface of an object: no matter how small you make the integration step, you always have to ignore mass too near the point of evaluation, or you get very wrong values.

What is the proper way to evaluate gravity on the surface of an object?

## 1. What is a pendulum and how does it work in detecting caves?

A pendulum is a weight suspended from a pivot so that it can swing freely. When placed inside a cave, its movement can be used to detect the presence of open spaces, such as large caverns or tunnels, underground.

## 2. How does the size of the pendulum affect its ability to detect caves?

The size of the pendulum directly affects its sensitivity and range in detecting caves. A larger pendulum will have a wider range and can detect larger cavities, while a smaller pendulum may be more sensitive to smaller caves or crevices.

## 3. What materials are commonly used for a cave-detecting pendulum?

The most commonly used material for a cave-detecting pendulum is a metal weight, such as lead or brass. Other materials, such as wood or stone, can also be used depending on the desired weight and sensitivity of the pendulum.

## 4. Can a pendulum detect caves that are far underground?

Yes, a pendulum can detect caves that are deep underground, depending on the size and sensitivity of the pendulum. However, other factors such as the type of rock or soil above the cave can affect the pendulum's ability to detect it.

## 5. Are there any limitations to using a pendulum to detect caves?

While pendulums can be effective in detecting caves, there are some limitations to their use. Factors such as varying types of rock or soil, water levels, and the presence of man-made structures can affect the accuracy of the pendulum's readings. Additionally, the pendulum can only detect open spaces and may not be able to accurately map the shape or size of the cave.

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