the characterization of trough cross-bedded sedimentary
TRANSCRIPT
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The Characterization of Trough Cross-Bedded Sedimentary Structures and Palaeoflow Direction from Down-
Hole FMI Images
Peter Bormann & Paul GloverUniversity of Aberdeen
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Structure
Conventional FMI Analysis for Palaeoflow DirectionProblems with the Conventional TechniqueA New Model for FMI Intersection CurvesApplication to FMI dataSummary
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Conventional FMI Analysis
FMI is an electrical technique used in boreholes to image bedding and fractures around the perimeter of the boreholeFMI images of planar bedforms cut the borehole with sinusoidal intersection curvesThe amplitude of the curves indicate the dip of the beddingThe position of the minimum indicates the azimuth of the maximum dip (palaeoflow direction)
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FMI Intersection Curves - Plane Bedding
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FMI Intersection Curves - Data
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Problems with Conventional FMI Analysis
In many cases the bedding is NOT PLANARTrough cross-bedded structures produce intersection curves that look similar to true sinusoids, but are significantly differentThis gives large errors in dip and azimuthThe problem is recognised and conventionally accounted for by averaging the results from many intersection curvesThen hoping the errors cancel out!!!
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Conventional FMI Analysis
They don’t!
The resulting data loses its vertical resolution (by about 50 times)
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FMI Intersection Curves - Trough Cross-Bedding
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Errors in Conventional FMI Analysis
There is no a priori knowledge of where the borehole intersects the trough
If the borehole intersects the axis of the trough, the curve is similar to the plane case
If the borehole does not intersect the axis of the trough, the side walls have the following effects:
The dip will be overestimated by as much as +40o
The azimuth will be in error by as much as ±90o
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Conventional Model
Based on equations for the intersection of a circular borehole with a planeParameters provided by the model are:
Azimuth, φDip, θ
Blindly applied to all data leads to errors in non-plane bedded systems
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New Model
Based on equations for the intersection of a circular borehole with a hemi-circular troughParameters provided by the model are:
Azimuth, φDip, θRatio of trough radius to borehole radius, dRatio of offset distance to borehole radius, b
Blindly applied to all data does not lead to errors in plane or non-plane bedded systems
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New Model Equation
In its most general form the intersection equation is:
( ) ( )( ) ⎥⎦⎤
⎢⎣⎡ −−−+−= 22 sincossin
cos1 bdz ϕαϕαθθ
θ = Dipd = Ratio of trough radius to borehole radiusb = Ratio of offset distance to borehole radiusAzimuth, φ is derived from ϕ and α by symmetry
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Derivation of Corrected Azimuth
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FMI Intersection Curves
-15
-10
-5
0
5
10
15
-180 -90 0 90 180Azimuth (degrees)
z (c
m)
Conventional Model
Dip=0
Dip=45
Azim
uth
of P
lane
-10
-5
0
5
10
15
20
-180 -90 0 90 180Azimuth (degrees)
z (c
m)
New Model
Dip=0
Dip=45
Azim
uth
of T
roug
h Ax
is
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FMI Intersection Curves - Varying d
-10
-5
0
5
10
15
20
25
-180 -90 0 90 180Azimuth (degrees)
z (c
m)
d=5
d=45Sinusoidal Model
Azimuth of Planeand Trough Axis
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FMI Intersection Curves - Varying b
-10
-5
0
5
10
15
20
25
30
-180 -90 0 90 180Azimuth (degrees)
z (c
m)
b=8
b=1Sinusoidal Model
Azimuth of Planeand Trough Axis
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Testing the New Model
55% Coverage FMI data39 intersection curves50 m of logMixed trough and plane beddingCurves picked, digitised and fitted to conventional and new modelsDip, azimuth, d, and b derived for each bedStatistical tests carried out to determine fit (Durbin-Watson autocorrelation)
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The new model fitted the data better than the conventional model in the majority of cases
Test Conventional New
Sum of Squares 35.4 19.81Absolute Deviation 0.021 0.015Adjusted R2 96.4% 97.9%Durbin-Watson (<0.8) 0.6631 1.050
Mean values for all 39 curves
Testing Results I
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Comparison of Two Methods - Dip and Azimuth
0
10
20
30
40
50
0 10 20 30 40 50
Dip from Conventional Method (degrees)
Dip
from
New
Met
hod
(deg
rees
)
Dip
0
45
90
135
180
225
270
315
360
0 45 90 135 180 225 270 315 360Azimuth from Conventional Model (degrees)
Azi
mut
h fr
om N
ew M
odel
(deg
rees
)
Azimuth
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The difference in the two techniques becomes greater for acute troughs
Testing Results II
0.01
0.1
1
10
100
1000
1 10 100 1000d VALUE
Diff
eren
ce in
Sum
of S
quar
es o
f R
esid
uals
Trough becoming more planar
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Summary I
The conventional method for analysing FMI intersection curves often leads to large errorsand low vertical resolutions in trough-bedded systems
We have produced a new method for analysing FMI intersection curves that can be used to analyse plane and trough-bedded systems accurately with high resolution
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Summary II
The conventional method provides data on mean dip and mean azimuth for sets of curves spanning a significant vertical interval
The new method provides highly accurate values of dip, azimuth, trough radius and offsetfor individual structures
This allows them to be mapped uniquely in the sub-surface
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Acknowledgements
Many thanks to the following, who contributed to this work:
Colin McLachlan (Aberdeen University)Ian Tribe (Schlumberger Geoquest)J.H. Filancier (Schlumberger Geoquest)Patti Oberpriller (University of Toronto)Stuart Buck (Z&S Geoscience)S. Luthi and M. Rider