in the orientation of the stress field, so these variations can be deduced from the pattern of dikes.
The traces of dikes are correlated (Fig. 6.37) to the
trajectories of maximum compressive stress determined from the solution to a boundary value
problem of elasticity theory (Pollard and Muller,
1976; Muller and Pollard, 1977). For comparison
purposes the trajectories and dike traces are presented in alternating vertical strips across the
map. Here the correlation is surprisingly good
and there is a unique relationship among the
values for the remote principal horizontal stress
components, S H and S h , the magma pressure, P,
the radius of the magma chamber, r o , and the distance from the magma chamber to the Sangre de
Cristo Mountain front, d:
(6.121)
For the model result shown in Fig. 6.37 the orientation of the greatest regional compression is 082
o
and the estimated difference between the principal values is (S H Ϫ S h ) ϭ 0.03P. Given an estimated
upper bound for the magma pressure of
P Յ 100 MPa, based on the strength of rock surrounding the magma chamber, the regional stress
difference is less than 5 MPa. For comparison an
average value of 2.1 MPa is reported for 26 measurements of horizontal principal stress difference from seven wells in the Piceance Basin of
Colorado using the hydraulic fracturing technique (Bredehoeft et al., 1976).
The analysis used to estimate the regional
stress difference is based upon the solution for an
elastic body with a pressurized hole (the magma
chamber), a rigid boundary (the Sangre de Cristo
range), and a regional stress field. No account is
made of the perturbation of the stress field by the
(S H Ϫ S h )d 2
Pr 2
o
Ϸ 0.5
240
FORCE, TRACTION, AND STRESS
Fig 6.36 Map of western Canada with directions of least
horizontal compressive stress inferred from wellbore
breakouts. Reprinted from Bell and Babcock (1986) with
permission of Elsevier.
R
O
C
K
Y
M
O
U
N
T
A
I
N
S
C A N A D I A N
B A S I N
108
o
112
o
116
o
0
100
km
LEGEND
Well location number
Major population
Minor population
The traces of dikes are correlated (Fig. 6.37) to the
trajectories of maximum compressive stress determined from the solution to a boundary value
problem of elasticity theory (Pollard and Muller,
1976; Muller and Pollard, 1977). For comparison
purposes the trajectories and dike traces are presented in alternating vertical strips across the
map. Here the correlation is surprisingly good
and there is a unique relationship among the
values for the remote principal horizontal stress
components, S H and S h , the magma pressure, P,
the radius of the magma chamber, r o , and the distance from the magma chamber to the Sangre de
Cristo Mountain front, d:
(6.121)
For the model result shown in Fig. 6.37 the orientation of the greatest regional compression is 082
o
and the estimated difference between the principal values is (S H Ϫ S h ) ϭ 0.03P. Given an estimated
upper bound for the magma pressure of
P Յ 100 MPa, based on the strength of rock surrounding the magma chamber, the regional stress
difference is less than 5 MPa. For comparison an
average value of 2.1 MPa is reported for 26 measurements of horizontal principal stress difference from seven wells in the Piceance Basin of
Colorado using the hydraulic fracturing technique (Bredehoeft et al., 1976).
The analysis used to estimate the regional
stress difference is based upon the solution for an
elastic body with a pressurized hole (the magma
chamber), a rigid boundary (the Sangre de Cristo
range), and a regional stress field. No account is
made of the perturbation of the stress field by the
(S H Ϫ S h )d 2
Pr 2
o
Ϸ 0.5
240
FORCE, TRACTION, AND STRESS
Fig 6.36 Map of western Canada with directions of least
horizontal compressive stress inferred from wellbore
breakouts. Reprinted from Bell and Babcock (1986) with
permission of Elsevier.
R
O
C
K
Y
M
O
U
N
T
A
I
N
S
C A N A D I A N
B A S I N
108
o
112
o
116
o
0
100
km
LEGEND
Well location number
Major population
Minor population