<p><strong>Solution:</strong></p>
<p>If <code>gz_max</code> is bigger than the air correction then we're done. because we can measure the signal. and we're done. <code>So gz_max &gt; e_h</code> is the requirement.</p>
<p>(If the error is bigger than the signal anomaly then we can't measure the signal.)</p>

CC BY-SA 4.0
2021-12-08T11:50:42.487Z
2021-12-08T14:00:48.147Z
2021-12-08T14:00:48.147Z
AnaRhisT
<p><strong>Question:</strong> What is the accuracy required in elevation to distinguish the maximal gravity anomaly of a spherical <code>50%</code> Haematite (Iron mineral) ore with a radius of <code>2m</code> at a depth of <code>10m</code> within a shale section.</p>
<p>I'm trying to solve this problem, first we know that the gravity anomaly of a sphere is that of a point mass at the sphere center equal to the product of the density and volume of the sphere, meaning that only the <code>ρ * V</code>
product governs the anomaly and neither the size or density can be determined
individually.</p>
<p>Directly above the sphere the maximum anomaly is:
<a href="https://i.sstatic.net/XcqWH.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/XcqWH.png" alt="enter image description here" /></a></p>
<p>We know that in order to correct for gravity's elevation we need to use free-air formula which decreases the gravity by 0.3086 mGal for every meter above sea-level.</p>
<p>Haematite density is: <code>4.9 - 5.3</code> <code>(Mg/m^3)</code>, let's assume we take the lower bound <code>4.9</code> for this case.</p>
<p>But we'll be taking only <code>50%</code> of <code>4.9</code> because only <code>50%</code> of the ore has haematite.</p>
<p>Also we know that <code>R=2m</code> and <code>h = 10m</code>.</p>
<p>I'm still not sure how to continue from here to find the required accuracy in elevation to distinguish the maximal gravity anomaly because I've some questions like what's the other 50% percent of the iron mineral? should we take in consideration that it's the shale section and above it we have the sandstone? and should we just sum the free air/water correction with the Bouguer correction to get the required accuracy? Any help is highly appreciated.</p>
<p>My approach would be to calculate the free air/water correction first:
Depth is 10m which means it's <code>0.3086 * 10 = 3.086mGal</code></p>
<p>And Bouguer correction is: <code>δgB = 2πGρh = 2π(6.67e-11)(2.45)(-10)</code> and I took <code>h=-10m</code> because it's under the surface.</p>
<p>Should I combine it somehow to <code>gz_max</code> I mentioned above?</p>

CC BY-SA 4.0
2021-12-04T19:30:22.160Z
@Fred Any ideas how to solve this? :)
AnaRhisT
<geology><geophysics>
Elevation accuracy to distinguish maximal gravity anomaly of a sphere with 50% hematite
AnaRhisT
# Elevation accuracy to distinguish maximal gravity anomaly of a sphere with 50% hematite

(Asked by: username_0 on 2021-12-03)

**Question:** What is the accuracy required in elevation to distinguish the maximal gravity anomaly of a spherical `50%` Haematite (Iron mineral) ore with a radius of `2m` at a depth of `10m` within a shale section.

I'm trying to solve this problem, first we know that the gravity anomaly of a sphere is that of a point mass at the sphere center equal to the product of the density and volume of the sphere, meaning that only the `ρ * V`
product governs the anomaly and neither the size or density can be determined
individually.

Directly above the sphere the maximum anomaly is:
[![enter image description here](https://i.sstatic.net/XcqWH.png)](https://i.sstatic.net/XcqWH.png)

We know that in order to correct for gravity's elevation we need to use free-air formula which decreases the gravity by 0.3086 mGal for every meter above sea-level.

Haematite density is: `4.9 - 5.3` `(Mg/m^3)`, let's assume we take the lower bound `4.9` for this case.

But we'll be taking only `50%` of `4.9` because only `50%` of the ore has haematite.

Also we know that `R=2m` and `h = 10m`.

I'm still not sure how to continue from here to find the required accuracy in elevation to distinguish the maximal gravity anomaly because I've some questions like what's the other 50% percent of the iron mineral? should we take in consideration that it's the shale section and above it we have the sandstone? and should we just sum the free air/water correction with the Bouguer correction to get the required accuracy? Any help is highly appreciated.

My approach would be to calculate the free air/water correction first:
Depth is 10m which means it's `0.3086 * 10 = 3.086mGal`

And Bouguer correction is: `δgB = 2πGρh = 2π(6.67e-11)(2.45)(-10)` and I took `h=-10m` because it's under the surface.

Should I combine it somehow to `gz_max` I mentioned above?

**Tags:** geology, geophysics

> **Comments:**
> **username_0**: @Fred Any ideas how to solve this? :)  

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## 1 answers

### Answer by username_0 on 2021-12-08. Score: 1 | Accepted answer

**Solution:**

If `gz_max` is bigger than the air correction then we're done. because we can measure the signal. and we're done. `So gz_max > e_h` is the requirement.

(If the error is bigger than the signal anomaly then we can't measure the signal.)


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