Questions about the geoid (Split from Lake Balaton thread)

[michel123456]

this part: that the surface of the ocean follows the bed surface.

This results in a depression of the water surface in the deep ocean and an elevation or bulge in shallow water.

Bottom or bed features such as sea mounts, ridges or trenches are therefore reflected in profile disturbances at the surface.

An ocean floor feature 1km high results in a surface depression of 2 metres.

 

If you like the water surface follows the bed surface more closely than you might think.

That is not of my knowledge.

1.from what I (thought I) knew, the ocean bed is thinner than the continent. Where the mountains rise, the crust is deeper, like an iceberg.

2.I don't understand why the ocean surface should follow its bed. I am guessing that the ocean surface shoud follow the geoid, since it is the definition of what the geoid is.

Edited September 22, 2016 by michel123456

[studiot]

 

Michel 123456 post#203

 

That is not of my knowledge.

1.from what I (thought I) knew, the ocean bed is thinner than the continent. Where the mountains rise, the crust is deeper, like an iceberg.

2.I don't understand why the ocean surface should follow its bed. I am guessing that the ocean surface shoud follow the geoid, since it is the definition of what the geoid is.

 

 

The situation is controlled by both geophysical and geometric factors.

 

My original aim in reviewing the hydraulics was to present only sufficient of the geophysical side to make an assessment of the task and then to work through the geometrical side from the very simple to a stage adequate to meet the project aims.

 

Unfortunately in my haste this geophysical assessment was poorly worded so thank you very much for pointing this out.

 

 

Studiot post#

 

This results in a depression of the water surface in the deep ocean and an elevation or bulge in shallow water.

Bottom or bed features such as sea mounts, ridges or trenches are therefore reflected in profile disturbances at the surface.

An ocean floor feature 1km high results in a surface depression of 2 metres.

If you like the water surface follows the bed surface more closely than you might think.

 

I see that my words could easily be taken to imply absolute values, when I really meant the change due to some influence.

So better phrasing would be

 

"An ocean floor feature 1km high results in a change in surface depression, reducing it by 2 metres."

 

instead of

 

"An ocean floor feature 1km high results in a surface depression of 2 metres."

 

In response to your specific questions

 

1) The force of gravity is the resultant of the attraction of the whole of the earth, not just part of it. Oceanic crust is indeed thinner than continental crust, but it is also denser so you need less of it to create the same mass. However see my long answer to your question (2), since they are linked.

 

2) This question is basically : What are the mechanics of the water surface?

 

Well the water surface largely controlled by gravity, which is a force (Newtonian mechanics is just fine for this).

 

So let us start with Newton, his apple and my Fig1.

 

Here the important points are that bodies are subject to a downward force called gravity and those that are free to move move in the direction of increasing force, which is towards the centre of the large body.

These points are absolutely vital to the development of the argument.

 

Fig 2 is basically asserting that force has a direction as well as a magnitude and shows how to obtain this direction.

This is also important because we call the line between out test point P and the large mass exerting the gravity, the vertical at P.

 

Fig 3 shows that if we have an assembly of large bodies each exerts its own force of gravity as in fig 2 ( just as if the others were not there) and the unique resultant can be found by combining each individual pull vectorially.

 

If we let the large bodies coalesce to form a single body as in Fig 4 the effect is still as if they were separate, but the important point is that we could equally consider dividing up a super large body into conjoined smaller ones.

 

So armed with these principles, let us examine a water surface.

 

Fig 5 shows a water surface where the force of gravity is identical (I have labelled this force as F2) all along, but particularly at points P1, P2 and P3.

This is largely for reference.

 

More exciting things happen in Fig 6 if we introduce a hump at P2, so the surface at P2 is now above P1 and P3.

 

Since the surface at P2 is now higher the force of gravity must be lower as stated in Fig1 and labelled F1.

 

Now it is also stated in Fig 1 that a body free to move will move towards a point of greater force of gravity.

The space immediately below the hump is still subject to the higher force of gravity F2.

But the hump of water is not free to move down as that space is already occupied.

But it can move sideways towards P1 and P3, which are also subject to the higher force of gravity F2.

 

So the water spreads out until all the water surface is again at the same force of gravity.

 

It is important to note that a dip in surface would fill in by the opposite reasoning.

I have not shown this specifically.

 

 

 

But now we must consider what happens if something happens to change the force of gravity at P2

 

In Fig 7 I have shown, for convenience, the position of point in a triangle towards which the force of gravity is directed

and in Fig 8 what happens if we slice of a part of the triangle.

Both will be needed in what is to follow.

 

In Fig 9 I have divided a circle up into triangular sectors in the manner of Fig 4.

By symmetry the force of gravity at any point P on the circumference is the same, when calculated in the manner of Fig 4.

 

But if we create a depression in the circumference by truncating two sectors, A and B, in the manner of Fig 8 then the situation changes, as shown in Fig 10.

 

In particular the centres of gravity of the individual sectors A and B move towards the centre of the circle and further from the circumference.

So by figs 1 and 2 the force of gravity at point P on the circumference is reduced.

 

So by the discussion in Figs 5 and 6 the water surface will dip below the circumference to the point Q where the force of gravity is the same as on the rest of the perimeter.

 

This explains how and why the water surface of the ocean dips down below the geometrical line and that dip is reduced by undersea ridges and seamounts.

 

Notice that I have not needed to introduce artificially devised surfaces such as the geoid etc.

Simple mechanics is enough.

 

 

 

 

[michel123456]

The situation is controlled by both geophysical and geometric factors.

 

My original aim in reviewing the hydraulics was to present only sufficient of the geophysical side to make an assessment of the task and then to work through the geometrical side from the very simple to a stage adequate to meet the project aims.

 

Unfortunately in my haste this geophysical assessment was poorly worded so thank you very much for pointing this out.

 

 

I see that my words could easily be taken to imply absolute values, when I really meant the change due to some influence.

So better phrasing would be

 

"An ocean floor feature 1km high results in a change in surface depression, reducing it by 2 metres."

 

 

instead of

 

"An ocean floor feature 1km high results in a surface depression of 2 metres."

 

In response to your specific questions

 

1) The force of gravity is the resultant of the attraction of the whole of the earth, not just part of it. Oceanic crust is indeed thinner than continental crust, but it is also denser so you need less of it to create the same mass. However see my long answer to your question (2), since they are linked.

 

2) This question is basically : What are the mechanics of the water surface?

 

Well the water surface largely controlled by gravity, which is a force (Newtonian mechanics is just fine for this).

 

So let us start with Newton, his apple and my Fig1.

 

Here the important points are that bodies are subject to a downward force called gravity and those that are free to move move in the direction of increasing force, which is towards the centre of the large body.

These points are absolutely vital to the development of the argument.

 

Fig 2 is basically asserting that force has a direction as well as a magnitude and shows how to obtain this direction.

This is also important because we call the line between out test point P and the large mass exerting the gravity, the vertical at P.

 

Fig 3 shows that if we have an assembly of large bodies each exerts its own force of gravity as in fig 2 ( just as if the others were not there) and the unique resultant can be found by combining each individual pull vectorially.

 

If we let the large bodies coalesce to form a single body as in Fig 4 the effect is still as if they were separate, but the important point is that we could equally consider dividing up a super large body into conjoined smaller ones.

 

So armed with these principles, let us examine a water surface.

 

Fig 5 shows a water surface where the force of gravity is identical (I have labelled this force as F2) all along, but particularly at points P1, P2 and P3.

This is largely for reference.

 

More exciting things happen in Fig 6 if we introduce a hump at P2, so the surface at P2 is now above P1 and P3.

 

Since the surface at P2 is now higher the force of gravity must be lower as stated in Fig1 and labelled F1.

 

Now it is also stated in Fig 1 that a body free to move will move towards a point of greater force of gravity.

The space immediately below the hump is still subject to the higher force of gravity F2.

But the hump of water is not free to move down as that space is already occupied.

But it can move sideways towards P1 and P3, which are also subject to the higher force of gravity F2.

 

So the water spreads out until all the water surface is again at the same force of gravity.

 

It is important to note that a dip in surface would fill in by the opposite reasoning.

I have not shown this specifically.

 

altimetry1.jpg

 

 

But now we must consider what happens if something happens to change the force of gravity at P2

 

In Fig 7 I have shown, for convenience, the position of point in a triangle towards which the force of gravity is directed

and in Fig 8 what happens if we slice of a part of the triangle.

Both will be needed in what is to follow.

 

In Fig 9 I have divided a circle up into triangular sectors in the manner of Fig 4.

By symmetry the force of gravity at any point P on the circumference is the same, when calculated in the manner of Fig 4.

 

But if we create a depression in the circumference by truncating two sectors, A and B, in the manner of Fig 8 then the situation changes, as shown in Fig 10.

 

In particular the centres of gravity of the individual sectors A and B move towards the centre of the circle and further from the circumference.

So by figs 1 and 2 the force of gravity at point P on the circumference is reduced.

 

So by the discussion in Figs 5 and 6 the water surface will dip below the circumference to the point Q where the force of gravity is the same as on the rest of the perimeter.

 

This explains how and why the water surface of the ocean dips down below the geometrical line and that dip is reduced by undersea ridges and seamounts.

 

Notice that I have not needed to introduce artificially devised surfaces such as the geoid etc.

Simple mechanics is enough.

 

altimetry2.jpg

 

Great job!

However

_you have no reference (that is the reason you had to create one)

_that would mean that a gravity map of the Earth would show lower gravity under the oceans and higher gravity over mountains. It is overall simplified and not accurate at all .

See http://www.esa.int/Our_Activities/Observing_the_Earth/GOCE/Earth_s_gravity_revealed_in_unprecedented_detail

For the Andes you seem correct but the Himalaya shows less gravity than the North Sea.

Edited September 24, 2016 by michel123456

[studiot]

Great job!

However

_you have no reference (that is the reason you had to create one)

 

Reference to what ? Newton's law of gravity? Do you really need one?

What do you mean I had to create one?

 

_that would mean that a gravity map of the Earth would show lower gravity under the oceans and higher gravity over mountains.

 

That rather depends upon your map. Your terms are too vague to have any meaning.

 

 

It is overall simplified and not accurate at all .

 

I don't follow since I was careful to post no figures or calculations at all (except for the centroid of a triangle which any schoolboy can look up)

 

See http://www.esa.int/Our_Activities/Observing_the_Earth/GOCE/Earth_s_gravity_revealed_in_unprecedented_detail

For the Andes you seem correct but the Himalaya shows less gravity than the North Sea.

 

I have no idea what you mean by this.

I posted no gravity maps at all.

 

I hope that this response has simply suffered from overhaste.

 

I simply do not understand it.

Edited September 24, 2016 by studiot

[michel123456]

 

I hope that this response has simply suffered from overhaste.

 

I simply do not understand it.

I missed how your long post #205 is an explanation of "An ocean floor feature 1km high results in a change in surface depression, reducing it by 2 metre".

 

Your are explaining a variation of the force of gravity caused by a variation of the topographic relief. I posted a link to a map that shows it is not the case.

[studiot]

I missed how your long post #205 is an explanation of "An ocean floor feature 1km high results in a change in surface depression, reducing it by 2 metre".

 

Your are explaining a variation of the force of gravity caused by a variation of the topographic relief. I posted a link to a map that shows it is not the case.

 

As I said it depends upon your map but I could not find a map on the webpage you linked to.

 

 

Have you given any consideration to the difference between the force due to gravity which becomes numerically greater, the closer you are to the centre of the Earth and the gravitational potential which becomes numerically greater the further away you are from the centre of the Earth. That is potentials start at negative infinity at the centre increase with distance towards zero at infinite distance?

 

Which one of these was plotted on your map (can you not post it here ?)

Edited September 24, 2016 by studiot

[michel123456]

http://www.esa.int/spaceinimages/Images/2011/03/New_GOCE_geoid

[studiot]

 

From link in post#210

• The colours in the image represent deviations in height (–100 m to +100 m) from an ideal geoid. The blue shades represent low values and the reds/yellows represent high values.

 

Would you like to explain what this means and how I would relate this to the actual force of gravity on a test mass of 1kg at an actual distance r from the centre of the Earth?

[michel123456]

 

Would you like to explain what this means and how I would relate this to the actual force of gravity on a test mass of 1kg at an actual distance r from the centre of the Earth?

It means that in reality there is a deviation from the idealized situation where the force of gravity acts as you describe.

[studiot]

It means that in reality there is a deviation from the idealized situation where the force of gravity acts as you describe.

 

Deviation of what from where?

 

You don't measure force in metres, let alone hundreds of metres.

 

For your information, my calculations estimate a 15 - 20mm depression in the centre of the lake.

By this I mean that a well set up leveling instrument, leveling between the shores in a double run and closure would detect a depression of this relative to the facing shores.

 

Real measurements in the real world.

[michel123456]

From http://www.esa.int/Our_Activities/Observing_the_Earth/GOCE/Introducing_GOCE

INTRODUCING GOCE

 

 

 

Launched on 17 March 2009, ESA's Gravity field and steady-state Ocean Circulation Explorer (GOCE) mission was the first Earth Explorer mission in orbit.

This novel mission delivered a wealth of data to bring about a whole new level of understanding of one of Earth's most fundamental forces of nature – the gravity field.

This sleek, high-tech gravity satellite embodied many firsts in its design and use of new technology in space to map Earth's gravity field in unprecedented detail.

As the most advanced gravity space mission to date, GOCE data are realising a broad range of fascinating new possibilities for oceanography, solid Earth physics, geodesy and sea-level research, and significantly contributing to furthering our understanding of climate change.

Although invisible, gravity is a complex force of nature that has an immeasurable impact on our everyday lives. It is often assumed that the force of gravity on the surface of Earth has a constant value, but in fact the value of 'g' varies subtly from place to place.

 

 

GOCE geoid

 

 

These variations are due to a number of factors such as the rotation of Earth, the position of mountains and ocean trenches and variations in density of Earth's interior.

GOCE mapped these variations in the gravity field with extreme detail and accuracy.

This resulted in a unique model of the 'geoid', which is the surface of equal gravitational potential defined by the gravity field – crucial for deriving accurate measurements of ocean circulation and sea-level change, both of which are affected by climate change.

GOCE-derived data are also being used to understand more about processes occurring inside Earth and for use in practical applications such as surveying and levelling. In addition, the measurements are being used to improve estimates of polar ice-sheet thickness and their movement.

On 21 October 2013, the mission came to a natural end when it ran out of fuel. Three weeks later, on 11 November, the satellite disintegrated in the lower atmosphere.

Although its flight is over, the wealth of data from GOCE continues to be exploited to improve our understanding of ocean circulation, sea level, ice dynamics and Earth’s interior.

The image produced of the geoid is a direct reflect of the gravity field.

And i am realizing that my interpretation of the colours must be wrong: where the color is red = higher distance from the Earth center = weak gravity and reversely where blue on the map= lower elevation=stronger gravitational field.

[studiot]

I said at the beginning of my last big post (post#205)

 

 

studiot

The situation is controlled by both geophysical and geometric factors.

My original aim in reviewing the hydraulics was to present only sufficient of the geophysical side to make an assessment of the task and then to work through the geometrical side from the very simple to a stage adequate to meet the project aims.

 

I wanted to go through the geometry first because it is that which causes the greatest confusion.

This is because we have both real world measurements and theoretical constructs and models, some of which are extremely sophisticated.

 

It is my view that most of this sophistication is an unnecessary impediment to the aims of this project.

This should be set out clearly in the statement of aims I have repeatedly called for.

 

For interest here is the geometry and mathematics of satellite altimetry extracted from

 

Engineering Surveying Technology, edited by Kennie and Petrie, in the section written by P. Cross, Professor of Surveying at Newcastle University

 

You will note the multiple 'correction factors' between the real world and the artificial constructs.

 

Edited September 25, 2016 by studiot

[michel123456]

Dear Studiot, since your post #197 have received +3 support, I still would like to have a reference for your statement (bolded by me) here below

 

The surface of larger bodies of water is mostly influenced by gravitational forces.

Water collects in depressions in the land surface.

Because continental crust is about 2.5 times the density of water and oceanic crust 3 times as dense, the material in the depressions is less dense than the average.

This results in a depression of the water surface in the deep ocean and an elevation or bulge in shallow water.

Bottom or bed features such as sea mounts, ridges or trenches are therefore reflected in profile disturbances at the surface.

An ocean floor feature 1km high results in a surface depression of 2 metres.

 

If you like the water surface follows the bed surface more closely than you might think.

No calculation needed, a simple reference to a peer reviewed paper is sufficient.

[Mordred]

Have you tried googling Geoid? The process Studiot is describing has a decent article on wiki.

 

https://en.m.wikipedia.org/wiki/Geoid

[studiot]

Sigh.

 

I am sorry Michel, I'm quite sure you have better reasoning powers than this,

all I am trying to do is develop an explanation. If you can genuinely contribute, so much the better.

 

But you seem to have entered 'skim and query mode',

dashing off stuff and trying to find fault without proper thought.

 

If you read my posts properly you would find better than 'peer reviewed paper' references.

 

Meanwhile you have posted some pretty pictures, from an august organisation that I have no doubt are the most correct to date.

 

But do you understand them?

 

I have asked several times for your explanation of what they mean and what their relevance is to this thread, without any satisfactory answer.

 

I was preparing a some sketches to help you understand gravitational potential equipotential and the geoid, but since you don't seem interested in understanding I don't see the point of continuing.

 

Edit

Thanks , Mordred, for the link. It seems to largely coincide with what I am saying, although there are one or two flaky pieces of explanation, which is why consideration of the geoid so often leads to misunderstanding.

Edited September 25, 2016 by studiot

[michel123456]

Have you tried googling Geoid? The process Studiot is describing has a decent article on wiki.

 

https://en.m.wikipedia.org/wiki/Geoid

Studiot is not talking about the geoid.

When he says:

 

An ocean floor feature 1km high results in a surface depression of 2 metres.

 

and

For your information, my calculations estimate a 15 - 20mm depression in the centre of the lake.

 

He is hypothesizing that the water surface somehow follows the topographic relief of the bottom.

I am arguing that it is not the case. The surface of the waters follow the geoid.

 

If the level of waters would follow the topographic relief, then the geoid would coincide with topographical maps. And it is not.

 

-----------------

And he still haven't referenced his claim.

Edited September 25, 2016 by michel123456

[studiot]

 

Michel123456

He is hypothesizing that the water surface somehow follows the topographic relief of the bottom.

 

 

 

https://en.m.wikipedia.org/wiki/Geoid

but even if the earth were perfectly spherical, the strength of gravity would not be the same everywhere, because density (and therefore mass) varies throughout the planet. This is due to magma distributions, mountain ranges, deep sea trenches, and so on.

If that perfect sphere were then covered in water, the water would not be the same height everywhere. Instead, the water level would be higher or lower depending on the particular strength of gravity in that location.

 

 

Isn't that exactly what this says?

Except that I did say "in miniature" so the topography would not be the same, the figures quoted imply a scale reduction factor of

500 : 1

[/edit]

 

 

 

I have said before that the geoid, though an interesting discussion, is a red herring for the purposes of this thread which is about the actual surface shape of Lake Balaton.

 

I therefore propose that global geoid discussion should be hived off to another thread.

 

To provide a starter for this here is an extract from Mordred's link about the geoid

 

https://en.m.wikipedia.org/wiki/Geoid

 

 

 

 

 

 

 

 

 

 

https://en.m.wikipedia.org/wiki/Geoid

Simplified example

The gravitational field of the earth is neither perfect nor uniform. A flattened ellipsoid is typically used as the idealized earth, but even if the earth were perfectly spherical, the strength of gravity would not be the same everywhere, because density (and therefore mass) varies throughout the planet. This is due to magma distributions, mountain ranges, deep sea trenches, and so on.

If that perfect sphere were then covered in water, the water would not be the same height everywhere. Instead, the water level would be higher or lower depending on the particular strength of gravity in that location.

 

Now my question is

 

If the Earth were perfectly spherical, homogeneous and isotropic, what would be the shape of the geoid?

Edited September 25, 2016 by studiot

[maximillian12]

Studiot is not talking about the geoid. He is hypothesizing that the water surface somehow follows the topographic relief of the bottom.

I am arguing that it is not the case. The surface of the waters follow the geoid.

 

If the level of waters would follow the topographic relief, then the geoid would coincide with topographical maps. And it does not.

 

-----------------

And he still hasn't referenced his claim.

 

I will ditto this.

 

By "reference", what I guess Michel means is a link to a study in which the shape of the bed of a body of water is shown to impact on the shape of its surface.

 

In another post, for example, you linked to Seasat. Does that mean there is somewhere where we can read that Seasat measured what you are saying?

[studiot]

 

I will ditto this.

By "reference", what I guess Michel means is a link to a study in which the shape of the bed of a body of water is shown to impact on the shape of its surface.

 

In another post, for example, you linked to Seasat. Does that mean there is somewhere where we can read that Seasat measured what you are saying?

 

Hello, maximillian,

 

I think the Wikipedia link I provided to seasat and subsequent satellites was in the other thread in post#202.

 

I did post further information from another (fully referenced) textbook here in this thread in post #12 which described the calculation used by seasat and subsequent satellites to determine the distance from the satellite to the water surface.

 

The original Seasat information I provided was in post#197 of the other thread

 

http://www.scienceforums.net/topic/98386-laser-curvature-test-on-lake-balaton/page-10

 

and took the form of a measured (by seasat) world ocean surface relief map showing the measured surface which clearly shows the bottom features reflected in the surface topography.

This is a public domain image produced by the seasat team, which I took from another textbook, "Image Interpretation in Geology" by Drury,

along with some other explanatory text which Michel seems to object to.

 

Because many are confused by the nature of the geoid I provided a simpler newtonian mechanics explanation of why there is a dip in the cente of a large enough lake and why a hump in the water surface tends to spread out sideways or level itself out, in post#2 here.

 

The usual explanation involves vector calculus on potential surfaces and spherical hamonic theory.

 

It is also important to note what is meant by a 'gravity map'

Most are not absolute values but show deviations from some theoretical shape, which is why the scales run from +100m to -100m in Michel's references.

 

I have also fully answered his query in the post immediately preceding yours with reference to the Wikipedia article in post#12 by Mordred where it states explicitly what I have said.

 

Have you thought about my question posed at the end of post#17

 

If the Earth were perfectly spherical, homogeneous and isotropic, what would be the shape of the geoid?

Here is a hint. The geoid is not completely governed by gravity.

[Mordred]

where it states explicitly what I have said.

 

Have you thought about my question posed at the end of post#17

If the Earth were perfectly spherical, homogeneous and isotropic, what would be the shape of the geoid?

Here is a hint. The geoid is not completely governed by gravity.

Lol I was curious as to the range of answers as well

[studiot]

Lol I was curious as to the range of answers as well

 

Lol indeed, the answer is also stated in the article you linked to, though no proper explanation/analysis is provided.

 

[michel123456]

A few days have passed and I am realizing I got it wrong.

From here https://en.wikipedia.org/wiki/Geoid

The geoid is the shape that the surface of the oceans would take under the influence of Earth's gravitation and rotation alone, in the absence of other influences such as winds and tides. This surface is extended through the continents (such as with very narrow hypothetical canals). All points on the geoid have the same gravity potential energy (the sum of gravitational potential energy and centrifugal potential energy). The force of gravity acts everywhere perpendicular to the geoid, meaning that plumb lines point perpendicular and water levels parallel to the geoid.

 

So the geoid have the same gravity potential energy.

The surface of the geoid represents a surface where gravity is the same (the sum of gravitational potential energy and centrifugal potential energy).

IOW I was wrong when saying

And i am realizing that my interpretation of the colours must be wrong: where the color is red = higher distance from the Earth center = weak gravity and reversely where blue on the map= lower elevation=stronger gravitational field.

 

And I was wrong before when I believed it was the reverse.

Gravity is the same, what changes is the elevation of the surface of the geoid.

I am completely confused because it is not the way I would do to describe a variation of the gravity potential. For example I would have taken a theoretical simpler geoid and draw on it lines of equipotential (like contour lines on a map).

I believe this way would have shown the red areas of the globe as having more gravity.

Is that correct?

 

I was also confused by this:

Because if one goes to sea and measures gravity, he should find the same everywhere since the level of the sea is supposed to be the geoid. (surface of the sea=geoid=same gravity) so, instead of measuring gravity, one has to measure altimetry.

 

Anyway, I still don't see any corelation between the geoid map and the topographical map. Where is the higher gravity in the Himalaya? Where is the mid-atlantic ridge?, where are the coast lines? The only mountains that are recognizable are the Andes. This map below shows something different than a topographical map.

Which means to me that Studiot's explanations are very logical & very sensible but do not seem to be what is actually happening.

Edited September 30, 2016 by michel123456

[studiot]

+1, Michel for listening, we can move on and try to answer your worries.

 

 

Michel123456 post#22

 

Which means to me that Studiot's explanations are very logical & very sensible but do not seem to be what is actually happening.

 

Indeed this is so.

 

I did say, at the outset of this discussion, that my preferred order of business was to deal with the geometry first and the geophysics second.

 

So let us consider sufficient geometry to develop an understanding of the situation.

 

 

What are the observables?

 

Traditionally distances and angles on the ground or water surface and angles on the celestial sphere and more recently distances to satellites (GPS).

 

So we are measuring on an a surface of unknown shape (that is why we are measuring )

 

But we want to record and display the results in a consistent way and until the hollywood holographic projectors as seen in Star Wars and the latest Hunger Games become reality, we are stuck with flat surfaces like scraped animal skins, paper etc. In other words we want to make maps.

All this started with cartography.

 

Now the problem is that we live on irregularly shaped a 3D world that is not conformable with flat surfaces.

(The correct term for a 3D surface that can be perfectly represented or mapped to a plane is a developable surface.)

 

And we do not have a direct transformation from our unknown irregular surface that we are measuring to our flat map.

 

So what was done traditionally was to invent or create more or less suitable regular or near regular shapes as an intermediate.

The plots on the intermediate are then mapped to the flat sheet.

 

The raw data is thus subject to two transformations, firstly from the real 3D surface to the artificial one and then from the artificial surface to the flat map.

 

Both the spheroid (ellipsoid) and the geoid are such intermediate artificial constructs.

 

Modern satellite technology has allowed another method to be employed, that of direct measurement in 3D, dispensing with the artificial intermediate and one transformation.

 

But this comes with the penalty or cost of widespread loss of understanding since GPS is just a black box' that performs all the corrections and calculations for you so you have to take the results on trust.

 

I appreciate and admire that you want to know more.

 

I think that is enough rambling for this post, but , like the other Hollywood man said, "I'll be back"

 

P.S. The answer to my question is that a the geoid for a perfectly spherical, isotropic and homogeneous Earth is an oblate spheroid.

I'll explain next time, along with a proper explanation of why the gravity anomaly map you show (that is its corrrect name) is the way it is.

[michel123456]

+1, Michel for listening, we can move on and try to answer your worries.

 

 

Indeed this is so.

 

I did say, at the outset of this discussion, that my preferred order of business was to deal with the geometry first and the geophysics second.

 

So let us consider sufficient geometry to develop an understanding of the situation.

 

 

What are the observables?

 

Traditionally distances and angles on the ground or water surface and angles on the celestial sphere and more recently distances to satellites (GPS).

 

So we are measuring on an a surface of unknown shape (that is why we are measuring )

 

But we want to record and display the results in a consistent way and until the hollywood holographic projectors as seen in Star Wars and the latest Hunger Games become reality, we are stuck with flat surfaces like scraped animal skins, paper etc. In other words we want to make maps.

All this started with cartography.

 

Now the problem is that we live on irregularly shaped a 3D world that is not conformable with flat surfaces.

(The correct term for a 3D surface that can be perfectly represented or mapped to a plane is a developable surface.)

 

And we do not have a direct transformation from our unknown irregular surface that we are measuring to our flat map.

 

So what was done traditionally was to invent or create more or less suitable regular or near regular shapes as an intermediate.

The plots on the intermediate are then mapped to the flat sheet.

 

The raw data is thus subject to two transformations, firstly from the real 3D surface to the artificial one and then from the artificial surface to the flat map.

 

Both the spheroid (ellipsoid) and the geoid are such intermediate artificial constructs.

 

Modern satellite technology has allowed another method to be employed, that of direct measurement in 3D, dispensing with the artificial intermediate and one transformation.

 

But this comes with the penalty or cost of widespread loss of understanding since GPS is just a black box' that performs all the corrections and calculations for you so you have to take the results on trust.

 

I appreciate and admire that you want to know more.

 

I think that is enough rambling for this post, but , like the other Hollywood man said, "I'll be back"

 

P.S. The answer to my question is that a the geoid for a perfectly spherical, isotropic and homogeneous Earth is an oblate spheroid.

I'll explain next time, along with a proper explanation of why the gravity anomaly map you show (that is its corrrect name) is the way it is.

Thank you for the +1

i don't care admitting being wrong. Like the Chinese proverb says: when you ask a question you look like a fool once, when you don't ask you will remain a fool forever.

 

However,

there was no need to explain Mercator projections.

This thread has slipped away from the tracks.

Your original claim was that if the bottom of lake Balaton was flat (not level but flat) then eventually the surface of the lake would be flat too (instead of being level).

You came back and eventually calculated that the surface of the lake would be curved downwards about 20mm down (instead of being level- that is to say curved as the surface of the Earth).

i asked for references for both statements. You have provided calculations that look perfect to me, but no reference. i have also found this below that supports Studiot's argument:

Now, researchers led by geophysicist David Sandwell, of Scripps Institution of Oceanography in San Diego, California, have used [/size]data collected from satellite-based radar altimeters to fill in huge swaths of missing seafloor. What's incredible is that these satellites map the ocean deep not by scanning the seafloor, but by repeatedly scanning the waters' surface. Correcting for waves and tides creates a picture of sea-surface topography that reflects features of the seafloor far below. "A seamount, for example, exerts a gravitational pull, and warps the sea surface outward," said Sandwell, in an interview with [/size]Science News, "so we can map the bottom of the ocean indirectly, using sea-surface topography

from http://io9.gizmodo.com/explore-the-worlds-most-detailed-map-of-the-seafloor-r-1642315933

 

But this is not what I call a reference.

Ocean surface topography does not mention it

The ocean surface has highs and lows, similar to the hills and valleys of Earth's land surface depicted on a topographic map. These variations, called ocean surface topography (or sea surface topography), also dynamic topography, are mapped using measurements of sea surface height relative to Earth's geoid. Earth's geoid is a calculated surface of equal gravitational potential energy and represents the shape the sea surface would be if the ocean were not in motion. Topography is the arrangement of natural and artificial features of an area. Ocean surface topography is specifically the distance between the height of the ocean surface from the geoid. Ocean surface topography is caused by ocean waves, tides, currents, and the loading of atmospheric pressure. The main purpose to measure ocean surface topography is to understand the large-scale circulation of the ocean. The height variations of ocean surface topography can be as much as two meters and are influenced by ocean circulation, ocean temperature, and salinity.

 

Not a word about surface topography being influenced by the shape of the bottom.

[studiot]

 

michel123456 post#24

 

This thread has slipped away from the tracks.

Your original claim was that if the bottom of lake Balaton was flat (not level but flat) then eventually the surface of the lake would be flat too (instead of being level).

 

It hasn't slipped from anything.

 

I asked the moderators to split discussion about global gravitational geophysics from the local discussion about a local survey at Lake Balaton, because it is quite irrelevant to that survey.

 

And they agreed.

 

I did indeed say that since the lake is very shallow, the surface can never be more than a small amount different from the bottom.

So if the bottom is flat and therefore deviates from the Earth's curvature, the water surface cannot be different from flat by more than the depth.

I also supplied details of geological investigations by the Hungarian technical institutes which suggest a flat bottom to the lake and a proposed geological mechanism for this measured result.

 

All this was fully referenced in the post in which it appeared so please stop claiming I do not supply references, where appropriate. This is particularly poignant as you have completely failed to provide any reference whatsoever in the last "quote" in your post # 24!

 

Nevertheless I will answer the question you asked there, since you cannot work this out for yourself.

 

 

Unreferenced quote from post#24

 

 

 

The ocean surface has highs and lows, similar to the hills and valleys of Earth's land surface depicted on a topographic map. These variations, called ocean surface topography (or sea surface topography), also dynamic topography, are mapped using measurements of sea surface height relative to Earth's geoid. Earth's geoid is a calculated surface of equal gravitational potential energy and represents the shape the sea surface would be if the ocean were not in motion. Topography is the arrangement of natural and artificial features of an area. Ocean surface topography is specifically the distance between the height of the ocean surface from the geoid. Ocean surface topography is caused by ocean waves, tides, currents, and the loading of atmospheric pressure.

 

 

question in post#24 by Michel 123456

Not a word about surface topography being influenced by the shape of the bottom.

 

 

 

Here is a quote from my copy of reference 2 in the Wikipedia article linked to by Mordred (Fowler : The Solid Earth (an introduction to global geophysics) : Cambridge University Press

 

 

Fowler page 167

John Milne (1906) gave an interesting example of a anomaly:

"When a squad of 76 men marched within 16 or 20 feet of Oxford University Observatory it was found that a horizontal pendulum measured a deflection in the direction of the advancing load"

 

Look again at the list of influences on a reading of gravity.

 

They fall into three categories.

 

1) Those which are permanent and can be readily calculated (estimated by calculation)

 

2) Those which are permanent but of unknown cause and magnitude (until the measurement)

 

3) Those which are transitory and depend on the prevailing conditions at the time of measurement

 

Factors included in (1) form the basis of the calculation of the geoid, which is the 'expected' shape at any place. These are principally the gravitational force and the rotation of the Earth.

 

Factors included in (3) are such as those mentioned in the above quotes, such as tide heights, the marching of men and so forth are removed by making auxiliary measurements

 

Factors included in (2) are principally mass deficit and mass excess and form the basis for reporting the gravitational anomaly.

 

That is the anomaly is the difference between the measured gravity in, after correction for transitory effects in (3) and the calculated gravity in (1).

 

Gravitational anomaly is a small fraction of the total gravitational force so it is not practicable to plot both gravitational equipotentials and anomaly variation contours on the same map, their scales are too many orders of magnitude apart.

 

This is why gravity maps usually show a plot of the anomaly itself, measured in milligals (standard gravity is 10,000 milligals) or in metres at sea level since the variation results in an elevation or depression of sea level by about 3 metres per milligal.

Edited October 1, 2016 by studiot