Static deformations and dislocation theory - Earth Dynamics: Deformations and Oscillations of the Rotating Earth - page 495

C

SUBROUTINE STRIKE3(U3,XI1,XI,X,DIP,R2,R3,Q2,Q3)

C
C This subroutine evaluates the three-component, U3,
C of the double integral for specified limits XI1 and XI.
C

IMPLICIT DOUBLE PRECISION(A-H,O-Z)
DIMENSION X(3)
C Find distance R from fault to field point and
C distance Q from image fault to field point.
R=(X(1)-XI1)*(X(1)-XI1)+R2*R2+(R3-XI)*(R3-XI)
R=DSQRT(R)
Q=(X(1)-XI1)*(X(1)-XI1)+Q2*Q2+(Q3+XI)*(Q3+XI)
Q=DSQRT(Q)
C Find fault plane co-ordinates XI2 and XI3.
XI2=XI*DCOS(DIP)
XI3=XI*DSIN(DIP)
C Evaluate U3.
U3=DCOS(DIP)*(DLOG(R+R3-XI)
1 +(1.D0+3.D0*DTAN(DIP)**2)*DLOG(Q+Q3+XI)
2 -3.D0*DTAN(DIP)*DLOG(Q+X(3)+XI3)/DCOS(DIP))
3 +2.D0*R2*DSIN(DIP)/R+2.D0*DSIN(DIP)*(Q2+X(2)*DSIN(DIP))/Q
4 -2.D0*R2*R2*DCOS(DIP)/(R*(R+R3-XI))
5 +(4.D0*Q2*X(3)*DSIN(DIP)**2-2.D0*(Q2+X(2)*DSIN(DIP))*
6 (X(3)+Q3*DSIN(DIP)))/(Q*(Q+Q3+XI))
7 +4.D0*Q2*X(3)*DSIN(DIP)*(X(3)+XI3-Q3*DSIN(DIP))/Q**3
8 -4.D0*Q2*Q2*Q3*X(3)*DCOS(DIP)*DSIN(DIP)*(2.D0*Q+Q3+XI)/
9 (Q**3*(Q+Q3+XI)**2)
RETURN
END

As an illustration of results from the programme DISPF.FOR, we calculate the
surface displacement components for the 11 March 2011 Japanese earthquake.
It is described by Hayes (2011) and by the article “Preliminary Geodetic Slip
Model of the 2011 M9.0 Tohoku-chiho Taiheiyo-oki Earthquake” on the United
States Geological Survey website (http: /

japan). The Hayes paper identifies the source as a nearly pure thrust fault with
dip 14 ◦ , rake (measured positive from the down-dip direction) 177 ◦ , and seismic
moment 3.85

// earthquake.usgs.gov / earthquakes / world

10 22 Nm. The USGS article gives the total fault length as 700 km,
with the upper and lower edges of the fault at 3 km and 57 km, respectively.
With a dip of 14 ◦ , the top edge is measured 12.4 km down-dip and the
bottom edge is 235.6 km down-dip. This gives a fault area of 223.2km

×

×

10 5 km 2 10 11 m 2 . For a near-surface shear modulus of

= × = ×

700 km 1.56 1.56

10 10 m 2

× /

1.143 N (Cal8), a slip of 21.6 m yields the seismic moment of

10 22 Nm.
Contours of the three components of displacement, computed for the 11 March
2011 Japanese earthquake, are shown in Figures 9.3, 9.4 and 9.5. Contour levels are
given in millimetres for ten fault lengths in the direction of the strike and orthogonal
to the strike.

3.85 ×