IPB

Welcome Guest ( Log In | Register )

89 Pages V  « < 86 87 88 89 >  
Reply to this topicStart new topic
MSL Route Map
HSchirmer
post Jul 6 2019, 12:42 AM
Post #1306


Member
***

Group: Members
Posts: 449
Joined: 24-July 15
Member No.: 7619



QUOTE (Gerald @ Jul 5 2019, 10:22 PM) *
The fractal dimension is scale-dependent and varying with the location. Moreover, Curiosity's wheels are smoothing topographic features smaller than the radius of the wheels, such that we'll get a pretty well-defined two-dimensional manifold on the scale of Curiosity's wheels. Think of the envelope or hull defined by a sphere of the same radius as the wheels placed at any point of the (fractal) surface.
Call smaller topographic features roughness or texture, and separate it from the just-defined smooth 2D hull.
The only remaining uncertainty is soft surface material like dust or pebbles potentially displaced by the rover. Formally, this could be described by error bounds like any empirical measurement. We don't run into 2D infinities for the smoothed surface.


Yep, The distance measured? Depends on the size of the wheel that is doing the measuring.

From that data, you determine the fractal dimension of the material that you are crossing.
Fair-to-middling-chance that such information might reveal something about the sediment you are traversing.

Basically, the human foot informs you about the fractional dimensions of what you are walking on:
concrete, asphalt, packed stone, soil, wet sand or dry sand. Each one feels "different' even if you are wearing shoes.
(Perhaps the next rover should have "toes" to better sample the soil it crosses)

Curiosity has six feet, with a bit of data mining, it should be able to determine the "fractal feel" of the material it "walks over".
Go to the top of the page
 
+Quote Post
HSchirmer
post Jul 6 2019, 09:12 PM
Post #1307


Member
***

Group: Members
Posts: 449
Joined: 24-July 15
Member No.: 7619



Fractal dimension as a way to understand the shallow structural geology in heavily eroded landscapes.


QUOTE
FRACTAL INTERRELATIONSHIPS BETWEEN TOPOGRAPHY AND STRUCTURE
Earth Surf. Process. Landforms 23, 509–525 (1998)

Fractal interrelationships between topography and structure are investigated in two areas of the North American central Appalachian Mountains: one in the intensely deformed Valley and Ridge province and the other in the relatively undeformed foreland area of the Appalachian Plateau province. In the Valley and Ridge province, the fractal dimensions of topographic and structural relief vary systematically along the strike of major folds following a second-order polynomial trend.

Cross-correlation of the fractal dimensions of topography to structure indicates that there is a significant positive correlation between the two. Fractal analysis of topography in the relatively undeformed foreland area of the Appalachian Plateau revealed no significant variation in the fractal characteristics of topography across the study area, consistent with the lack of near-surface structure. However, fractal analysis of deeper structures beneath the Plateau area undertaken using reflection seismic data revealed stepwise increases in fractal dimension from the deeply buried Precambrian basement to the near-surface.

These vertical changes in the fractal dimension can be related to the tectonic history of the area. Taken together, these studies indicate that fractal analysis provides a means to quantify and compare the influence of near-surface structure on topographic development and lateral and vertical structural variability.

The fractal analysis provides a means to characterize the systematic changes in the complex patterns formed by topography and structure and the interrelationships between them. The similarity in their fractal characteristics implies similarity in the relative amplitude and abundance of different wavelength features in the topographic or structural profile
...
CONCLUSIONS
Topographic and structural relief examined in this study exhibit fractal behavior as defined by roughness–length and compass estimates of fractal dimension. Studies conducted in intensely and mildly deformed tectonic environments of the North American Appalachian Mountains suggest that the presence or absence of variation in the fractal characteristics of surface topography are, in part, related to presence or absence of variations in the fractal characteristics of the near-surface structure. The result is not surprising since subsurface structure distributes rocks of contrasting mechanical properties across the Earth’s surface.

The various processes of weathering and erosion then differentially etch topography into the Earth’s surface according to the mechanical and chemical properties of the near-surface rock intervals.

The use of fractals to compare topography and structure is preferred over regression line analysis since the fractal characteristics of a profile provide specific information about the abundance and relative amplitude of features in the profiles, whereas direct correlation of topographic and structural relief does not provide specific insight into properties that give rise to similarity.


http://pages.geo.wvu.edu/~wilson/pubs/Frac...ntsESPL1998.pdf
Go to the top of the page
 
+Quote Post
Phil Stooke
post Jul 8 2019, 05:37 PM
Post #1308


Solar System Cartographer
****

Group: Members
Posts: 7955
Joined: 5-April 05
From: Canada
Member No.: 227



A small move on sol 2459 is recorded in this new version of the map.

Phil

Attached Image


--------------------
... because the Solar System ain't gonna map itself.
Go to the top of the page
 
+Quote Post
nogal
post Jul 8 2019, 06:28 PM
Post #1309


Member
***

Group: Members
Posts: 335
Joined: 15-June 09
From: Lisbon, Portugal
Member No.: 4824



Following Phil's suggestion I measured 1 degree arcs along the 0 meridian at latitudes of 0, 15, 30, 45, 60, and 75 degrees. I also measured 1 degree arcs along several parallels, between 0E and 1E at the same latitudes. Measurements were made with the GE ruler and having the arc's end-points fully zoomed in (eye altitude of 7m). The results are... interesting.

From the measured arc's length the radius can be derived. Oddly, I obtained an equatorial radius approximately equal to the known polar radius (3,376,200 m).
As expected, the arc segment's length along the parallels steadily diminished from the equator to 75N, by a factor of nearly 4, but did not follow too closely the scale of cos(lat) Phil mentions.

As for the meridian arcs, their measured lengths increased with the latitude. Having the derived radius increase with the latitude seems to imply an ellipsoid like a rugby ball with the big axis vertical. Strange.

Here is the arc-generating kml file: Attached File  TestGrid.kml ( 6.85K ) Number of downloads: 35

and the measurement data: Attached File  TestGrid.txt ( 1.16K ) Number of downloads: 27


All of those measurements depend on how good GE's ruler is. I found the following on the measurement accuracy of the Google Earth ruler:
https://gis.stackexchange.com/questions/951...oogle-earth-pro
https://gis.stackexchange.com/questions/103...in-google-earth

Now what? For the time being I'm sticking with that 1% deficient grid, unless you vote it completely unacceptable. Cheers.
Fernando
Go to the top of the page
 
+Quote Post
Gerald
post Jul 8 2019, 11:38 PM
Post #1310


Senior Member
****

Group: Members
Posts: 2252
Joined: 7-December 12
Member No.: 6780



QUOTE (nogal @ Jul 8 2019, 07:28 PM) *
As expected, the arc segment's length along the parallels steadily diminished from the equator to 75N, by a factor of nearly 4, but did not follow too closely the scale of cos(lat) Phil mentions.

You may need a correction factor of (r_p / r_e)^2, with r_p the polar radius, and r_e the equatorial radius of the approximate Mars spheroid for the tan of your lat value, if coordinates are given in terms of planetographic latitudes. For some more detail, see e.g. the code in this Q&A.
Go to the top of the page
 
+Quote Post
nogal
post Jul 9 2019, 01:05 AM
Post #1311


Member
***

Group: Members
Posts: 335
Joined: 15-June 09
From: Lisbon, Portugal
Member No.: 4824



Thanks Gerald. This apprentice skater has ventured out on the surface of this lake, ignorant of its depth, and now feels the ice cracking under his skates....
Fernando
Go to the top of the page
 
+Quote Post
Phil Stooke
post Jul 16 2019, 02:36 AM
Post #1312


Solar System Cartographer
****

Group: Members
Posts: 7955
Joined: 5-April 05
From: Canada
Member No.: 227



I should add that my cosine rule was an approximation for a sphere.

Map update to sol 2466 showing a nice drive to the south. I'm not sure my name 'Aitken Pit' is in the right place.

Phil

Attached Image


--------------------
... because the Solar System ain't gonna map itself.
Go to the top of the page
 
+Quote Post
Phil Stooke
post Jul 18 2019, 10:03 PM
Post #1313


Solar System Cartographer
****

Group: Members
Posts: 7955
Joined: 5-April 05
From: Canada
Member No.: 227



Here is a map update for sol 2468. We are on the rocks beside Aitken Pit (if the name belongs there).

Phil


Attached thumbnail(s)
Attached Image
 


--------------------
... because the Solar System ain't gonna map itself.
Go to the top of the page
 
+Quote Post
Phil Stooke
post Jul 23 2019, 10:33 PM
Post #1314


Solar System Cartographer
****

Group: Members
Posts: 7955
Joined: 5-April 05
From: Canada
Member No.: 227



This update includes the drive to the sol 2473-2474 position.

Phil

Attached Image


--------------------
... because the Solar System ain't gonna map itself.
Go to the top of the page
 
+Quote Post
Phil Stooke
post Jul 25 2019, 06:58 PM
Post #1315


Solar System Cartographer
****

Group: Members
Posts: 7955
Joined: 5-April 05
From: Canada
Member No.: 227



Update to sol 2476, where we are at the Southern Outcrop.

Phil

Attached Image


--------------------
... because the Solar System ain't gonna map itself.
Go to the top of the page
 
+Quote Post
Phil Stooke
post Jul 28 2019, 07:24 PM
Post #1316


Solar System Cartographer
****

Group: Members
Posts: 7955
Joined: 5-April 05
From: Canada
Member No.: 227



Sol 2477, climbing onto the outcrop.

Phil

Attached Image


--------------------
... because the Solar System ain't gonna map itself.
Go to the top of the page
 
+Quote Post
Phil Stooke
post Jul 31 2019, 10:33 PM
Post #1317


Solar System Cartographer
****

Group: Members
Posts: 7955
Joined: 5-April 05
From: Canada
Member No.: 227



Sol 2481, on the edge of the outcrop looking for a drill site.

Phil

Attached Image


--------------------
... because the Solar System ain't gonna map itself.
Go to the top of the page
 
+Quote Post
nogal
post Aug 6 2019, 10:20 PM
Post #1318


Member
***

Group: Members
Posts: 335
Joined: 15-June 09
From: Lisbon, Portugal
Member No.: 4824



Happy Anniversary Curiosity! 7 Earth years on Mars!

Update to sol 2481. Both the 16 miles and the 21 km marks are already in the "rear mirror".
The problem with the distance grid is solved. Thanks again to Phil and Gerald for the information shared here.
Fernando
Attached File  The_Martian_Way_MSL_Curiosity_Sol_2481_2019AUG06.kmz ( 748.08K ) Number of downloads: 59
Go to the top of the page
 
+Quote Post
PaulH51
post Aug 7 2019, 01:53 AM
Post #1319


Senior Member
****

Group: Members
Posts: 1728
Joined: 30-January 13
From: Penang, Malaysia.
Member No.: 6853



QUOTE (nogal @ Aug 7 2019, 06:20 AM) *
Update to sol 2481. Both the 16 miles and the 21 km marks are already in the "rear mirror".

Works like a charm smile.gif Thanks Fernando
Go to the top of the page
 
+Quote Post
nogal
post Aug 7 2019, 05:51 PM
Post #1320


Member
***

Group: Members
Posts: 335
Joined: 15-June 09
From: Lisbon, Portugal
Member No.: 4824



Many thanks for the feedback Paul
Fernando
Go to the top of the page
 
+Quote Post

89 Pages V  « < 86 87 88 89 >
Reply to this topicStart new topic

 



RSS Lo-Fi Version Time is now: 18th August 2019 - 09:34 PM
RULES AND GUIDELINES
Please read the Forum Rules and Guidelines before posting.

IMAGE COPYRIGHT
Images posted on UnmannedSpaceflight.com may be copyrighted. Do not reproduce without permission. Read here for further information on space images and copyright.

OPINIONS AND MODERATION
Opinions expressed on UnmannedSpaceflight.com are those of the individual posters and do not necessarily reflect the opinions of UnmannedSpaceflight.com or The Planetary Society. The all-volunteer UnmannedSpaceflight.com moderation team is wholly independent of The Planetary Society. The Planetary Society has no influence over decisions made by the UnmannedSpaceflight.com moderators.
SUPPORT THE FORUM
Unmannedspaceflight.com is a project of the Planetary Society and is funded by donations from visitors and members. Help keep this forum up and running by contributing here.