Motivation
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Applications
CIDRe - a new irregular and parameter constrained approach for the resampling of scattered data Peter Menzel Institut für Geowissenschaften - Christian-Albrechts-Universität zu Kiel, Germany
The 17th annual conference of the International Association for Mathematical Geosciences September 5-13, 2015, Freiberg (Saxony) Germany
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Why do we need irregular resampling?
A vast diversity of highly resolved data sets from different sources (e.g. satellite missions, airborne surveys) is available and used in geosciences. → The initial data density often exceeds the resolution requirements for specific applications. → This oversampling is problematic when real-time capability is required. The amount of data needs to be reduced by resampling. ⇒ Commonly-used homogeneous resampling approaches frequently produce unsatisfactory results for data with strongly varying parameter distribution and locally changing signal content.
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Why do we need irregular resampling?
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Why do we need irregular resampling?
⇒ Homogeneous resampling can never achieve the “best” representation.
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Why do we need irregular resampling?
⇒ Irregluar resampling is able to represent the data parameter in a better way.
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Content
Why do we need irregular resampling? CIDRe - Constrained Indicator Data Resampling Validation using a synthetic data set Real data applications Conclusion and future work
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Applications
Conclusion
Motivation
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Basic idea of CIDRe
• Decimation of initial data amount by analyzing the data
parameter gradients in a local sector. large gradients → high point density
small gradients → low point density
⇒ The resulting data set shows an irregular point distribution.
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CIDRe workflow P
k=1
Pk
preprocessing - sectoring - neighborhood building
Pk+1 = PRk k =k+1
k < nI and PRk 6= Pk
true
loop for 1 ≤ k ≤ nI
PR
iteration result
weighting
Wk ∀P ∈ Pk
false
PRk
resampling
Pk → PRk
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Weighting the data points Each point P is weighted according to the difference quotient dp to its nNP neighboring points PN . For dpN =
|pPN −pP | |P~N −~ P|
WPMean =
nP NP
1 nNP
s WPRMS
=
dpn
n=1
1 nNP
nP NP
dp2n
n=1
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Irregular resampling
• Based on the calculated weights, all points are grouped with
respect to given indicator weights. The underlying decimation uses “kMeans”-clustering (MacQueen, 1967) and is performed separately for each sector and each weight group.
• Groups with lower weights are resampled to less resulting points. • No resampling is applied for groups the highest weights . All
points are kept.
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Irregular resampling - example
initial 200 points
clustering and selection
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remaining 50 points
6 / 16
Motivation
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Irregular resampling - example
clustering and selection
initial 200 points
remaining 50 points
6 / 16
Motivation
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Irregular resampling - example
remaining 50 points
initial 200 points
clustering and selection
6 / 16
Motivation
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Validation
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Conclusion
Irregular resampling - example
initial 200 points
clustering and selection
remaining 50 points
6 / 16
Motivation
Algorithm
Validation
Content
Why do we need irregular resampling? CIDRe - Constrained Indicator Data Resampling Validation using a synthetic data set Real data applications Conclusion and future work
Peter Menzel,
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Applications
Conclusion
Motivation
Algorithm
Validation
Applications
Conclusion
Validation using a synthetic data set 500 000 points, 3 data parameters
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Motivation
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Validation using a synthetic data set 500 000 points, 3 data parameters
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Motivation
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Validation using synthetic data set - 7% of initial points “minimum distance” resampling (S. Schmidt, pers. com.)
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Motivation
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Validation using synthetic data set - 7% of initial points CIDRe
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Motivation
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Conclusion
Validation using synthetic data set - difference to initial parameters “minimum distance” resampling, RMSE: ≈ 8.5 (R), ≈ 6.8 (G), ≈ 7.6 (B)
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Validation using synthetic data set - difference to initial parameters CIDRe, RMSE: ≈ 2.7 (R), ≈ 3.1 (G), ≈ 2.8 (B)
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Validation using synthetic data set
root mean squared error
comparing RMSE for different resampling rates
10
8
7%
CIDRe: R−Channel CIDRe: G−Channel CIDRe: B−Channel min. dist.: R−Channel min. dist.: G−Channel min. dist.: B−Channel
6
4 3 2 1 20
15
10
5
% of initial point count Peter Menzel,
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10 / 16
Motivation
Algorithm
Validation
Content
Why do we need irregular resampling? CIDRe - Constrained Indicator Data Resampling Validation using a synthetic data set Real data applications Conclusion and future work
Peter Menzel,
[email protected]
Applications
Conclusion
Motivation
Algorithm
Validation
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Conclusion
Resampling of gravity station data: advantage for density modeling What’s the problem?
For highly resolved gravity station data, gravity forward modeling is time-consuming.
Workflow for this example 1. Reduce the number of stations using CIDRe. 2. Set up and adjust the 3D geometry of density structures with the resampled data as constraint. 3. Final adjustments and interpretations are done with initial stations.
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Motivation
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Resampling of gravity station data: advantage for density modeling Gravity data with 66 000 stations
• Bouguer anomaly
−19 350 7 300
−21 2 latitude [o]
5 −23
250
3 200
−25
6
150 100
−27
Bouguer anomaly [10−5 m/s2]
14
based on satellite altimetry (Andersen & Knudsen, 1998)
• off-shore Northern Chile
• dashed box: study
area Schaller et al, 2015
cities: Iquique (1), Tocopilla (2), Antofagasta (3),
50 −29
Pozo Almonte (4), Calama (5), Taltal (6), Pica (7)
−78
−76
−74 −72 longitude [o]
−70
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Resampling of gravity station data: advantage for density modeling Resampled data with 8% of initial stations 1
−20
−19 350 1
3 −24
300
6
250
−21 −28 −78
200 −74 longitude [°]
2
−70
150 100
−23 3
−74
−72
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Bouguer anomaly [10−5 m/s2]
latitude [°]
2
50
−70 12 / 16
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Resampling of gravity station data: advantage for density modeling Difference in calculated fields [ 1
200
initial resampled
100 −74
−73
−72
−71
longitude [°]
2
−21 profile at latitude o
0
approx. −21.3
2 −2 −4
−23 profile at latitude approx. −21.3o
calculations with IGMAS+ modeling software
4
3
−74
for density model from Schaller et al, 2015
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−72
difference in gravity effect [10−5 m/s2]
6
300
latitude [°]
calc. gravity effect [10−5 m/s2]
−19
−6
−70
longitude [°]
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Resampling of a LIDAR-based topography Study area: Karasjok, Northern Norway (25.5◦ E, 69.6◦ N)
• 500 000 full tensor gravity (FTG) measurements
• LIDAR-based DTM with 30 Mio. points (10×10m)
For the given data, topographic correction needs ≈100 days of calculation with our in-house software.
Google Maps
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Motivation
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Resampling of a LIDAR-based topography Study area: Karasjok, Northern Norway (25.5◦ E, 69.6◦ N)
• 500 000 full tensor gravity (FTG) measurements
• LIDAR-based DTM with 30 Mio. points (10×10m)
For the given data, topographic correction needs ≈100 days of calculation with our in-house software.
airborne measurements by FUGRO (2011) with NGU and Store Norske Gull AS
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Motivation
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Resampling of a LIDAR-based topography
measurements
• LIDAR-based DTM with 30 Mio. points (10×10m)
For the given data, topographic correction needs ≈100 days of calculation with our in-house software.
7720
400 300
7714
200
442 448 XUTM [km]
topography [m]
• 500 000 full tensor gravity (FTG)
Y UTM [km]
Study area: Karasjok, Northern Norway (25.5◦ E, 69.6◦ N)
airborne measurements by FUGRO (2011) with NGU and Store Norske Gull AS
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Motivation
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Can CIDRe help to reduce the DTM for terrain correction? • A global external weighting with respect to minimum station distance WP(ext.) =
1 dmin
is applied for each DTM-point.
• Station hight above ground is
di erence [m]
70 - 120m.
RMSE 1.6 m
RMSE 0.52 m Peter Menzel,
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Motivation
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Conclusion
Differences in the FTG-effect of resampled DTM . . . . . . are small compared to amplitude of complete terrain-correction (± 150 Eötvös, FUGRO, 2011).
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Motivation
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Conclusion and future work • CIDRe results in smaller errors than commonly-used approaches for comparable downsampling rates.
• Highest benefits for point sets with locally strongly varying data parameters. • Results can easily be used for visualization, geophysical modeling, data processing and interpretation.
Future work . . . . . . real data applications for multi-parameter CIDRe, e.g. resampling of complete gravity gradient data sets. . . . outlier detection/removal based on calculated point weights and irregular resampling. . . . maintenance and further improvements of GUI_CIDRe software.
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Thank you!
Menzel, P.: “CIDRe - a parameter constrained irregular resampling method for scattered point data” (in review in GEOPHYSICS) Peter Menzel,
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References Alvers, M. R. and Götze, H.-J. and Barrio-Alver, L. and Schmidt, S. and Lahmeyer, B. and Plonka, C. (2014). A novel warped-space concept for interactive 3D-geometry-inversion to improve seismic imaging. First Break, Volume 32(4), pp. 61–67 . European Association of Geoscientists and Engineers Andersen, O. B. and Knudsen, P. (1998). Global marine gravity field from the ers-1 and geosat geodetic mission altimetry. J. Geophys. Res.: Oceans (1978-2012), Volume 103(C4), pp. 8129–8137 . Wiley Online Library FUGRO AIRBORNE SURVEYS Pty Ltd (2011). Alta, Norway FALCON
TM
Airborne Gravity Gradiometer Survey - Processing Report.
Holzrichter, N. (2013). Processing and interpretation of satellite and ground based gravity data at different lithospheric scales. Dissertation, CAU Kiel.
Motivation
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References
MacQueen, J. (1967). Some methods for classification and analysis of multivariate oberservations, in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (Volume 1: Statistics). University of California Press Menzel, P. (2015, under review). CIDRe - a parameter constrained irregular resampling method for scattered point data. Geophysics, SEG Schaller, T. and Andersen, J. and Götze, H.-J. and Koproch, N. and Schmidt, S. and Sobiesiak, M. and Splettstößer, S. (2015). Segmentation of the Andean Margin by Isostatic Models and Gradients. Journal of South American Earth Sciences, Volume 59(0), pp. 69–85. Elsevier
Conclusion
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Motivation
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Validation
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Conclusion
Adapted weighting Each point P is weighted according to the difference quotient dp to its nNP neighboring points PN . For dpN =
|pPN −pP | |P~N −~ P|
with 1 ≤ N ≤ nNP and wN =
1 |P~N −~ P|
power
power = {1, 2, . . .}
WPMean =
1 nNP
s WPRMS =
1 nNP
nP NP
dpn
n=1
nP NP n=1
dp2n
WPMeana = WPRMSa
nP NP
1 nP NP
vn=1 u 1 =u t nP NP n=1
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dpn wn
wn n=1 nP NP wn2
(dpn wn )2
n=1
with
Motivation
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Validation
Applications
Validation by sythetic data - single parameter 500,000 points, 1 data parameter
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Conclusion
Motivation
Algorithm
Validation
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Validation by sythetic data - single parameter 7% result
RMSE: approx. 5
RMSE: approx. 1.8
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Conclusion
Motivation
Algorithm
Validation
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Validation by sythetic data - single parameter RMSE for different resampling rates
7%
root mean squared error
CIDRe minimum distance 10
8
6
4 3 2 1 20
15
10
% of initial point count Peter Menzel,
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5
Conclusion
