Emura Kinya

Honda Hirokichi

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Honda, Hirokichi

Emura, Kinya

Tohoku University Repository (TOUR) / 東北大学機関リポジトリ

Some Charts for Studying the Mechanism ofEarthquake著者 Honda Hirokichi, Emura Kinya雑誌名 Science reports of the Tohoku University. Ser.5, Geophysics巻 9号 3ページ 113-119発行年 1958-03URL http://hdl.handle.net/10097/44583     Some Charts for Studying the Mechanism of Earthquake                   By  HIROKICIII  HONDA and KINYA  EI'IuRA                  Geophysical Institute, Faculty of Science,  TOliokiiUniversity                                (Received 25 Dec. 1957)                                Abstract              It is shown that the projectionsimilar to  the mechanism diagram" hitherto         used in illustrating the mechanism of earthquake can inversely be used to         determine the fault and auxiliary planes or the nodal planes for P of an earthquake.         Some charts which facilitate the analysis are given, with some examples of        their practical application. 1 Introduction     The initial motion of the P waves of an earthquake is generally considered to be alternately compressional and dilatational in the quadrantal areas on the focal sphere bounded by two planes which pass through the focus of the earthquake and are perpendicular to each other. One of the planes is interpreted as the fault plane and the other as the auxiliary plane, or both are called the nodal planes for P. There are several methods for determining the orientation of these planes of an earthquake as explained recently by BYERLY (1955),  HODGSON (1957),  KEILIS-BOROI< et al. (1957) and RITSEMA (1956). These methods are almost equivalent to one another in the assumptions adopted, as already pointed out by SCHEIDEGGER (1957).    In Japan, the pattern on a map of compression and dilatation in the first motion of P could be interpreted in terms of the direction of the forces acting in the focus of the earthquake, and the mechanism of the earthquake was illustrated by the so-called mechanism diagram which is the projection of the focal sphere on a horizontal plane passing through the origin of the earthquake.  1  he relations between the various quantities expressed in the diagram were stated previously (HONDA et al.; 1956, 1957).    In the present paper, we will show that the projection which is similar to the mechanism diagram, can inversely be used to determine the orientation of the nodal planes for P of an earthquake from the observations of the initial motions of P. Some charts which facilitate the analysis, are presented and some examples of the practical application of the charts for the study of the mechanism of the earthquake are given. 2 Charts for Studying the Mechanism of Earthquakes    When the tangent  S1'FS2' to the seismic ray S1FS2 (Fig. 1) at the focus F, is taken in place of the actual ray, the stations  S1 and  S2 on the earth's surface correspond to  S1' and  S2' on the focal sphere i.e. a small sphere constructed around the focus of the earthquake. The initial motion of P at  S1' is considered to be directed just opposite114  H. HONDA and K.  EMURA to that at S2'. The station  S2 corresponds to S2" on the surface of the earth stripped to the depth of the focus of the earthquake.    The pattern of the initial motion of P on the upper or lower half of the focal sphere may be illustrated by the vertical projection of the respective half sphere on the horizontal plane passing through the hypocenter. The intersections  n1Qn1' and  s, Earth:7sN  n'                               ,,,,c7ce ---- i                                      ai  Sit1iiQ    ̂\II                              ,....00-0 ^                             , 4,00110rAgs II --- --- A                  \\ Mfa___ 101111,xismioNallit0imal111111 n;                                                                     ir...........--.1111----- Focal  sphere     \ 2                                                 ifilkwagliC.---.....a 1     Fig. 1. Focal sphere.  n2— E                                   IIIVIA11111116110Wilks1IIII.1agir -                                lowillts - ,                    voik,-, VI              Fig. 2. Mechanism  diagram.  --  N\   30 f  Prilli=  AI  iTi—   =45   VINIIIIIIII/1-  ; w -P,  QP1= Q11/1=  —90°,41W601°1/            a2.711-,=cli,11 2—  =900, n90-                 r ;  90°.  10 90° /0                       8 <.',0  20                               70 SO ,,i0  6  0  0170                             so       41 '        40 0,                                                                                           crb.030o  N 20 _a                                                                                                          c,  0  ao /0 or.  c,       oi . a-'  0  ,  tz,  io ........0000011,  30  40  so  60                         $70                                       Fig. 3. Chart I.       SOME CHARTS FOR STUDYING THE MECHANISM OF EARTHQUAKE 115  n2Qn2' of the sphere with the nodal planes are represented as ellipses in the figure. (Fig. 2). The pole M2 of the great circle  n1Q1z1' lies on  n2Qn,', and the pole  M1 of the great circle  712Qn2' lies on  n1Qn1'. The figure is nothing but the mechanism diagram which has been used to illustrate the mechanism of earthquakes, in Japan.  a1 and  a2 in the figure show the inclination of the nodal planes  n1Qn1' and  n_Qn,'  ,  M, and M2 the motion directions, and  P1 and  T1 the directions of the maximum pressure and tension respectively.    In Fig. 3 is illustrated the Chart I which gives the ellipses corresponding to  n1Qn1' and  n2  Qn2' of various inclinations, and the lines showing the length of the arc along the ellipse measured from the central vertical plane. The scales on the central line serve to determine the position of the pole of an elliptic curve on the diagram. When the compressions and dilatations of the initial motion of P are entered in the projection, the appropriate nodal lines can be found from the chart, and the corresponding poles are obtained. Once the nodal lines are determined, the positions of  P1 and  T1 in the projection can be obtained graphically by use of the same chart.  Though the method relying on the projection similar to the mechanism diagram has various advantages in facilitating the analysis and interpretation, it has a drawback that the area on the focal sphere is not represented uniformly in the diagram. When it is necessary to avoid the inconvenience, we may adopt the following  10 90/0  20                              80    ap70                               60                                                                                            cr 1                                S0                                                               7°                               40                                30                                20                                 /0                               0  /021111111.1.P-                             30  40  SO  60  70  BO  9,                         Fig. 4. Chart  II. Equal area projection.116 H. HONDA and K. EMURA method.     Let us take provisionally the radius of the focal sphere as unity. When any point on the focal sphere whose radius vector is inclined by  a from the vertical, is re-presented by a point whose distance from the center of the horizontal circle of unit radius is  IPS sin  (a/2) in the same azimuth, the figure is known to represent a kind of  FAULT  PLANE  PROJECT Bogota',  Earthquake of Feb. 28, 1950 H-10 20 Sti UT   9= 46°N  A-  iti3°E  Pa'.  h=0.0SR PcP A 0       Ct% 74"  P,Compressiono.  R  Dilatation  A 00  •  0  ° 000 Huanca_yo     R'Compresstonc F,'Dilatation .  0  0                             A  0              Unit Distance  PP  PP  PP  0°0 0  N66°SW 441•444:: A0                                                                000  0  •  „A_ :^•^  Pretoria A A  PP  ••                                                      4PPP PPo A                                   A  PP  AA A  PP  APP  PiD               a                          (a) Analysis by HODGSON (1956).  N                                                                       0                            ;PP                             P            -0 0 e,                                         06.60                              " C8qt, 9)(6 PP                             a,  00  a,  alltlikihia. 2                        PP A  app  PP AR, PP  e  PP  LA  pp  A  PPP  0                                                      •  •  •             (b) Analysis by use of Chart I (lower half of the focal sphere),  Fig. 5.  Earthquake of Feb. 28,  1950 ,       SOME CHARTS FOR STUDYING THE MECHANISM OF EARTHQUAKE 117 projection of the focal sphere by which the area on the sphere is represented  uniformly on the  plane figure. We will call the figure the equal area projection of the focal sphere. In Fig. 4, is given the Chart II for the equal area projection, in which the curves corresponding to the nodal lines and those showing the angular distances along the nodal lines are illustrated. 3 Examples    Some examples of the application of the Chart I or Chart II for studying the mechanism of the earthquakes are given below.    (i) Earthquake of Feb. 28, 1950. Sakhalin Island.  co=46° N,  X=143  1/2° E,  it  —0.05R. The mechanism of the earthquake has been investigated by HODGSON (1956). Fig. 5 (a) shows the results of  HODGSON'S analysis by use of the stereographic projection method initiated by BYERLY. One of the nodal planes dips at 55° in the azimuth N  75.°5 W and the other one dips at 76° in the azimuth N 23°.5 E. The results of the approximate study basing on the same data as illustrated in Fig. 1 of  HODGSON'S paper, by our method using the Chart  I, are shown in Fig. 5 (b), which shows the projection of the lower half of the focal sphere.    (ii) Earthquake of Apr. 4, 1932. Off the South coast of Japan,  (p---30°.5N,  X.:=139°.1E,  h-=-0.06R. The mechanism of the earthquake has been studied by HONDA et al. (1932, 1952, 1956). Fig. 6(a) shows the distribution of the initial                                                                                                                                                                                  •  a  utu  Au d  \- • d                                                 d d c4d  o'd                      u \ d U 0 .71C               ^ •                                                ..1"9  0  500km\\ \d                          Fig.  6. (a). Earthquake of Apr. 4, 1932.                                  Initial motion of P. motions of P on a map. The results of the approximate analysis of the data illustrated in  Fig. 6 (a), by use of the Charts I and II, are shown in  Figs. 6 (b) and 6 (c) where the projections show the upper half of the  focal sphere respectively.    The mechanism diagrams of the earthquakes (i) and (ii), are shown in Fig. 7 with various quantities obtained by use of our method of analysis explained in this paper.118 H. HONDA and K. EMURA  0  a  • A AA  0  0  0 A  0  co 0  0  a,  -  E  A                                                        0                           (b). Analysis by use of Chart I.  N  o  0                         oa A  .„  0  °At A  0  0                                          0  00  0  0                                             . •                                                             a,-  —  o                           (c). Analysis by use of Chart II.             Fig. 6. Earthquake of Apr. 4, 1932.  Compression: 0. Dilatation                           (upper half of the focal  sphere).     SOME CHARTS FOR STUDYING THE MECHANISM OF EARTHQUAKE 119  N  N  a •                          iopt           • 8                                                          I                                                                                 -- E                        a21-   •M                                                                 i                                                        •F;7,-#Q  0  T, A     (a) Earthquake of Feb. 28,1950. (b) Earthquake of Apr. 4, 1932.  a1  ; S 76°E  (35°).  a1  ; (0°).          a2 ; S 24°W (14°).  a, ; N 22°W (75°).  ; N  24°F (76°).  M1  ; S  22°F (15°).  M2  ; N 76°W (55°).  M2  ; N  68°F  (90°).  P1 ; N 20°W (55°).  P1  ; N 83°E (47°).  T1 ; S 60°W (76°).  T1  ; S 53°W (47°).         Q  ; S  48°F (38°). Q ; N 22°W (75°).             (Slip  angle)1,2 ;  17°,36°. (Slip  angle),,  ;  75°,0°.              Fig. 7. Mechanism diagram (upper half of the focal sphere).                             References  1.  BYERLY,  P.: Nature of Faulting as deduced from Seismograms.  'Crust of the Earth',          edited by A.  POLDERVAART, 75-85, 1955.  2.  GOTSADZE,U.D.,  V.I.KRILis-BoRox,  et al. : The Study on the Mechanism of the          Earthquake.  Publ. Geophys. Inst.  Acad. Sci., U.S.S.R., No. 40, 1-148, 1957. 3.  Ho  r:  J.  H. : Direction of Faulting in Some of the Larger Earthquakes of the         North Pacific, 1950-1953.  Publ. Dominion Obs. Ottawa, 18, 219-252, 1956.  4.  flonc-soi,r,  J.H. : Nature of Faulting in Large Earthquakes. Bull. Geol. Soc. Am.,         68, 611-644, 1957.  5.  HompA,H. : On the Types of the Seismograms and the Mechanism of Deep Earthquakes.  Geophys. Mag., 5,  301-326, 1932. The focal depth of the earthquake of Apr.4,         1932 given in this paper, is too shallow.  6. HONDA, H., and A.  MASATSUKA  : On the Mechanisms of the Earthquakes and the         Stresses producing Them in Japan and Its Vicinity.  Sci. Rep., T hoku Univ.,         Ser. 5, Geophys., 4, 42-60, 1952.  7. HONDA, H., A. MASATSUKA, and K.  EMURA  : On the Mechanism of the Earthquakes         and the Stresses producing Them in Japan and Its Vicinity (Second Paper).  Sci.  Rep. T  hoku  Univ.,  .Ser. 5, Geophys., 8, 186-205, 1956. 8. HONDA,  H  : The Mechanism of the Earthquakes.  Sci. Rep. T  hoku Univ.,  Ser. 5,          Geophys., 9, Supplement, 1-46, 1957. 9.  RITSEMA, A.  R.  : The Mechanism in the Focus of 28 South-East Asian Earthquakes.  Verhandelingen, Meteorol. & Geophys. Service, Indonesia, No. 50, 1-72, 1956. 10. SCHEIDEGGER, A.  E.: The Geometrical Representation of Fault-Plane Solutions of          Earthquakes. Bull. Seismol. Soc. Am., 47, 89-110, 1957.

Some Charts for Studying the Mechanism of Earthquake

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Some Charts for Studying the Mechanism of Earthquake

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