The deformation processes in the western United States were studied, considering both deterministic models and random or statistical models. The role of the intracrustal delamination and mechanisms of crustal thinning were also examined. The application of fractal techniques to understand how the crust is deforming was studied in complex regions. Work continued on the development of a fractal based model for deformation in the western United States. Fractal studies were also extended to the study of topography and the geoid

Turcotte, Donald L.

English

NASA Technical Reports Server

Final Technical Report 
May 1 5 ,  1983 - July 3 1 ,  1986 
NASA Grant No. NAG 5-319 
Title : Mechanisms of Crustal Deformation in the 
Western United States 
Principal Investigator: Donald L. Turcotte, Chairman 
Department of Geological Sciences 
Cornell University 
Snee Hall 
Ithaca, NY 14853-1504 
(607)  255 - 7282 
4E;ASA-CR- 181230) MECHAXISRS CI; CBCSTAL 
E E E O B E A T l G I  I1J ZClE O E S l E R I  OS 15ical 
Technica l  Repcrt, 13 Ea9 1983 - 2 1  J u l .  1986 
(Cornell Uoiv . )  6 E; A v a i l :  BYIS RC 
&C2/fl€ A01 CSCL 086 G3/46 
U n c l a s  
GO92899 
https://ntrs.nasa.gov/search.jsp?R=19870018767 2020-03-20T10:07:04+00:00Z
The basic purpose of the research carried out under this grant was to 
obtain a better understanding of deformation processes in the western 
United States. The research considered both deterministic models and 
random or statistical models. One important aspect of deformation is the 
rheology of the lithosphere. We have been one of the leading proponents 
of an intracrustal asthenosphere. This is a soft zone at mid-crustal 
depths that has an important effect on a variety of tectonic phenomena. 
We examined the influence on faulting and showed that it was essential to 
the understanding of the earthquake cycle (1). We have also examined the 
role of the intracrustal asthenosphere on crustal delamination and on 
mechanisms of crustal thinning. The latter was reported at the XVIII 
General Assembly of the International Union of Geodesy and Geophysics in 
Hamburg, Germany, August 15-27, 1 9 8 3 ,  (12). 
Our work on lithospheric extension with application to the western 
United States included a simple approach to the problem of lithospheric 
boudinage (2). We showed that f o r  a fluid with a Tower Iiw rheology, E - 
an, boudinage is only found for n > 1. Large scale boudinage is one 
explanation for the systems of parallel basins and ranges that cover much 
of Utah, Nevada, and Arizona. 
Our work on the implications of lithospheric rheology was reviewed in 
an invited paper presented at the 27th International Geological Congress, 
Moscow, August 4-14 ,  1984 (16). This review was subsequently written up 
and published (11). A paper on how space based techniques can be used to 
deduce the properties of the lithosphere and asthenosphere was presented 
at the Geopotential Research Science Conference, College Park, Maryland 
October 29-31 ,  1984 (NASA Conference Publication 2390,  pp. 4 4 - 4 5 ) .  
The other principal line of research carried out under this grant was 
to apply fractal techniques in order to understand how the crust is 
deforming in complex regions such as the western United States. The basic 
approach to the understanding of fractal processes is the renormalization 
group method. Our first study applied the renormalization group method to 
the problem of the stick-slip behavior of faults. It was hypothesized 
that the distribution of asperitites on a fault is a fractal. The 
interaction of failed asperitites was modeled as a fractal tree. The 
resulting model showed that the failure of only a few asperitites would 
lead to a propagating failure on a fault. This explains why there is very 
little seismic activity on major faults prior to a large earthquake and 
why stress levels on active faults are generally low. This work was 
written up and published ( 3  & 4 )  and was presented at several meetings 
( 1 3 ,  14, 15, 1 7 ,  & 1 8 ) .  
Work continued on the development of a fractal based model for 
deformation in the western United States. The initial results were 
presented at the Texas A 5r M conference on Intraplzte Defermacion, College 
Station, Texas, April 10-12, 1985.  Regional deformation was hypothesized 
to occur on a scale invariant matrix of faults. Deformation occurs on all 
scales of faults. The fractal dimension determines the fraction of the 
total regional displacement that occurs on faults of a particular scale. 
The value of the fractal dimension can be obtained from the frequency- 
magnitude relation for earthquakes. The results were applied to the San 
Andreas fault in central California. The model predicts that the relative 
velocity across the main strand of the fault is 2 . 9 3  cm/year while the 
remainder of the relative velocity of 5.5 cm/year between the Pacific and 
North American plates occurs on other faults in the system. The predicted 
value is in quite good agreement with the value 3 . 3 9  2 0 . 2 9  cm/year 
inferred from geological studies. The concept that only a fraction of the 
relative velocity occurs on the primary strand of the fault has important 
implications regarding the occurrence of great earthquakes in California. 
Our model also predicts recurrence rates on smaller faults in southern 
California. This work was written up and published in the proceedings of 
the conference (6). This work was also presented at the Centre National 
d' Etudes Spatiales (CNRS) Summer School held in Toulouse, France in July 
1984 and was published as part of the lecture notes of the summer school 
(5). Aspects of this work were presented at several meetings ( 1 9 ,  20, & 
21). This work also formed a substantial part of an invited paper given 
at the 1986 National Meeting of the Society of Industrial and Applied 
Mathematitions (SIAM) held in Boston, Massachusetts, July 21-25, 1986 
( 2 4 ) .  
Our fractal studies have also been extended to the study of 
topography and the geoid. If the spectral energy density has a power law 
dependence on wave number a fractal is defined. In nrder  to better 
understand deformation in the western United States, the fractal dimension 
in several regions has been obtained. The fractal dimension was obtained 
from a one dimensional spectral analysis of the topography. In general 
the fractal dimension was near the value 1.5 that corresponds to Brown 
noise with the amplitude proportional to wave length. Thus the topography 
is truly self similar. The fractal dimension was also obtained using the 
dependence of path length on step size following a topographic contour. 
In this case fractal dimension was in the range 1.15 - 1 . 2 5 .  The 
difference is attributed to the difference between a self similar fractal 
defined by the path length method and the self affine fractal defined by 
spectral techniques. This work was published (7). 
We also applied fractal techniques to fragmentation (8 & 10) and to 
the relationship between ore grade and tonnage ( 9 ) .  In order to model the 
distribution of seismicity in a region we developed a fractal analog. The 
analog consisted of a third order parallel and series network of elements 
with a fractal distribution of sizes; each element was given a random 
strength. The system effectively modelled the occurrence of foreshocks 
and aftershocks. The distribution of failures of elements of various 
sizes was effectively modelled by the empirical Richter frequency 
magnitude relation and a reasonable b-value was obtained. This work was 
presented at the Spring Annual Meeting of the American Geophysical Union, 
Baltimore, Maryland, May 19-22, 1986, (22). 
The fractal concept also provides a means of  testing whether 
clustering in time or space is a scale-invariant process. We have 
analyzed a catalog o f  earthquakes from the New Hebrides for the occurrence 
of  temporal clusters that exhibited fractal behavior. In all cases 
significant deviations from random or Poisson behavior were f a m d .  This 
method introduces a new method for qualifying the clustering of 
earthquakes. This work was presented at the Spring Annual Meeting of the 
American Geophysical Union, Baltimore, Maryland, May 19-22, 1986, (23). 
PUBLISHED PAPERS 
1. D.L. Turcotte, J . Y .  Liu, and F.H. Kulhawy, The role of an 
intracrustal asthenosphere on the behavior of major strike-slip 
faults, J. Geophys. Res. 89, 5801-5816 (1984). 
2. S.H. Emerman and D.L. Turcotte, A back-of-the-envelope approach to 
boudinage mechanics, Tectonophys. 110, 333-338 (1984). 
3. R.F. Smalley, D.L. Turcotte, and S.A. Solla, A renormalization group 
approach to the stick-slip behavior of faults, J. Geophys. Res. 90, 
1894-igoa (1985). 
4. D.L. Turcotte, R.F. Smalley, and S.A. Solla, Collapse ofloaded 
fractal trees, Nature 313, 671-672 (1985). 
5. D. L. Turcotte, Deformation mechanisms in the continents in Internal 
GeoDhvsics and Space, pp. 465-486, Cepad, Toulouse, France, (1985). 
6. D. L. Turcotte, A fractal model for crustal deformation, Tectonophys. 
- 132, 261-269 (1986). 
7. D.L. Turcotte, A fractal interpretation of topography and geoid 
spectra on the earth, moon, Venus, and Mars, J .  Geophys. Res. 92, 
E597-E601 (1987). 
8. D.L. Turcotte, Fractals and fragmentation, J. Geophys. Res. 9 l ,  1921- 
1926 (1986). 
9. D.L. Turcotte, A fractal approach to the relationship between ore 
grade and tonnage, Econ. Geol. 8 l ,  1528-1532 (1986). 
10. D.L. Turcotte, Fractals, fragmentation, and failure, Trans. 4th Army 
Conf. Ap. Math. Comp., ARO Report 87-1, pp. 117-122, (1987). 
11. D.L. Turcotte, Rheology of the oceanic and ccmtinental lithosphere i n  
Composition. Structure and Dynamics of the Lithosphere-Asthenosphere 
System, K. Fuchs and C. Froidevaux, eds., Geodynamics Series Vol. 16, 
pp. 61-67, American Geophysical Union, Washington, DC, (1987). 
ABSTRACTS OF PAPERS PRESENTED AT MEETING 
12. D.L. Turcotte, Mechanisms of crustal and lithospheric thinning and 
the associated stress fields, Presented at the XVIII General Assembly 
of the International Union of Geodesy and Geophysics, Hamburg, 
Germany, August 15-27, 1983, Inter-Union Commission of the 
Lithosphere, Programme and Abstracts, pp. 22-23, (1983). 
13. R.F. Smalley and D.L. Turcotte, A renormalization group model for the 
stick-slip behavior of faults, Trans. Am. Geophys. Un. 6 4 ,  851 
14. 
15. 
1 6 .  
17. 
18. 
19. 
20. 
21. 
22. 
23. 
(1983), Presented at the 1983 Fall Annual Meeting of the American 
Geophysical Union, San Francisco, CA, Dec. 5-9, 1983. 
S.A. Solla, R.F. Smalley, and D.L. Turcotte, A renormalization group 
appraoch to the stick-slip behavior of faults, Presented at the 
Spring Meeting, American Physical Society, Washington, DC, April 23- 
26, 1984, Bull. Am. Phys. SOC. 2, 759 (1984). 
R.F. Smalley, D.L. Turcotte, and S.A. Solla, The role of asperities 
and barriers in the propagation of rupture as predicted by the 
renormalization group appraoch, Trans. Am. Geophys. Un. 65, 189 
(1984), Presented at the 1984 Spring Annual Meeting of the American 
Geophysical Union, Cincinnati, Ohio, May 14-17, 1984. 
D.L. Turcotte, ,Rheology of theoceanic and continental lithosphere, 
Presented at the 27th International Geological Congress, Moscow, 
August 4-14, 1984, Twenty-seventh International Geological Congress, 
Abstracts, Vol. 9, p. 8 6 ,  (1984). 
D.L. Turcotte, A renormalization group appraoch to the collapse of 
fractal trees with applications to the earthquake instability, 
Presented at the Workshop on instabilities in Continuous Media, 
Venice, Italy, Dec. 3-7, (1984). 
R.F. Smalley, D.L. Turcotte, and S.A. Solla, Fractals and faulting, 
Presented at the 1984 Fall Annual Meeting of the American Geophysical 
Union, San Francisco, California, December 3-7, 1984, Trans. Am. 
Geophys. Un. 65, 1113 (1984). 
J. Huang, D.L. Turcotte, and R.F. Smalley, Fractals and tectonics, 
Presented at the 1985 Spring Meeting of the American Geophysical 
Union, Baltimore, Maryland, May 27-31, 1985, Trans. Am. Geophys. Un. 
- 66, 3 6 2  (1985). 
D.L. Turcotte, Fractal tectonics, Presented at the 1985 Fall Meeting 
of the American Geophysical Union, San Francisco, California, 
December 8-13, 1985, Trans. Am. Geophys. Un. 66, 1068 (1985). 
D.L. Turcotte and R.F. Smalley, Fractals and tectonics, Presented at 
the 1986 Spring Meeting of the American Geophysical Union, Baltimore, 
Maryland, May 19-22, 1986, Trans. Am. Geophys. Un. 67, 364 (1986). 
J. Huang and D.L. Turcotte, A finite element analog for fractally 
distributed seismicity, Presented at the 1986 Spring Meeting of the 
American Geophysical Union, Baltimore, Maryland, May 19-22, 1986, 
Trans. Am. Geophys. Un. 67, 309 (1986). 
R.F. Smalley, J.L. Chatelain, D.L. Turcotte, and R. Prevot, A fractal 
appraoch to the clustering of earthquakes: Applications to the 
seismicitjr of the New Hebrides, Presented at the 1986 Spring Meeting 
of the American Geophysical Union, Baltimore, Maryland, May 19-22, 
1986, Trans. Am. Geophys. Un. 67, 308 (1986). 
24. D.L. Turcotte, Mathematical modelling in geodynamics, Presented at 
the SIAM 1986 National Meeting, Boston, Massachusetts, July 21-25, 
1986, Final Program SIAM 1986 National Meeting, p. 2. 


Mechanisms of crustal deformation in the western US

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