It has come to be realized in the present century that the science of Seismology, in addition to providing information on the nature and characteristics of earthquakes, is a central source of knowledge of the mechanics and layering of the Earth's deep interior.It has come to be realized in the present century that the science of Seismology, in addition to providing information on the nature and characteristics of earthquakes, is a central source of knowledge of the mechanics and layering of the Earth's deep interior

Bullen, K. E.

Spanish

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EARTHQUAKE WAVES AND THE MECHANICALPROPERTIES OF THE EARTH'S INTERIORBy K. E. BULLEN •It has come to be realized in the present century that the scienceof Seismology, in addition to providing information on the natureand characteristics of earthquakes, is a central source of knowledgeof the mechanics and layering of the Earth's deep interior.An earthquake is associated with the sudden release of a largequantity of energy inside a confined focal region below the Earth'ssurface. With the largest earthquakes, those of magnitude near 8%,the energy reaches the order of 1024 to 1025 ergs. The energy arisesfrom the accumulation of strain inside the focal region, and spendsitself in the form of earthquake, or seismic, waves which travel outin all directions from the focus.There are two types of bodily seismic waves which can penetratethe deepest interior. These are the primary or P waves, which arecompressional or dilation a], and the secondary or S waves whichare rotational or transverse. Their velocities a and f3 are given to good<~accuracy by the formulae '~(1)(2)respectively. In (1) and (2), p denotes the density, K thesibility (or bulk-modulus), and JJ. the rigidity.The incompressibility is a measure of the resistance of a materialto symmetrical pressure, and the rigidity a measure of the resistanceto distortional stress. On the theory of perfect elasticity, the rigidityof a fluid is zero, and therefore the S velocity is zero. In ordinary• Professor of Applied Mathematics, University of Sidney, Australia. Manuscriptreceived, Sept. 28, 1962.- 25-solids, including rocks of the Earth, S waves travel at about two-thirds the speed of P waves. When the terms 'solid' and 'fluid' areused in respect of the interior of the Earth, they relate to the as-sumption of perfect elasticity, and this assumption is shown frommeasurements of seismic waves to be adequate for stress variationswith periods of the order of those involved in earthquake wave trans-mission.One of the notable seismological results of the present centuryhas been the evolution of reliable travel-time tables for seismic waves.These tables give the times of travel of P and S waves from an earth-quake focus to points of the Earth's surface. The precision reachedby 1940 enabled the values of the P velocity a to be derived to closeaccuracy throughout the whole Earth, and of the S velocity {3 downto a depth of 2.900 km.In addition, it is known that the rigidity between depths of2.900 and 5.000 km is very small compared with the incompressibility.This result comes from seismic evidence, combined with evidence onthe precession of equinoxes and the observed tidal yielding of thesolid Earth. It is therefore legitimate to treat the S velocity as zeroin this part of the Earth.It follows from equations (1) and (2) that observations of re-cords of earthquake waves lead to fairly well determined values ofthe expressions K/p and p./ p down to a depth of nearly 5.000 km, i. e.throughout nearly 9970 of the Earth's volume. (The mean radius ofthe Earth is 6.371 km). Thus seismology supplies, fairly directly, basicinformation on three important quantities (p, K and p.) concerned withthe mechanics of the Earth's interior.Further, by noting the depths at which the P and S velocities, ortheir gradients, change suddenly, it is possible to divide the Earth upinto a series of concentric regions. The values in the table below arebased on a formal solution derived by Jeffreys in 1940. The nomen-clature A, B, ... , G was introduced by the writer in 1942, and hascome to be widely used.Some of the boundaries indicated in the table are much betterdetermined than others, and the following discussion will containcomments both on the principal historical events connected with thetable, and on the degree of reliabili~y of the detail shown.-26 -Region Name Range of depth a 8(km) (km/sec) (km/sec)A Crustallayers 0·33 Widely variable Widely variableB 33·410 8.1- 9.0 4.4 - 5.0C Mantle 410 ·1000 9.0-11.4 5.0·6.4D' 1000·2700 1l.4 - 13.6 6.4-7.3D" 2700- 2900 13.6 7.3E Outer core 2900- 4980 8.1-10.4 Assumed zeroF 4980·5120 10.4 - 9.5 Not observedG Inner core 5120- 6370 1l.2-11.3 Not observedThe regions A, B, C and D (including D' and D") together consti-tute the Earth's mantle. Inside the region A, the velocities vary moreerratically than inside the layers below. The region A is commonlyreferred to nowadays as the crust, and the lower boundary is theMohorovicic discontinuity, so-named because of early work on thesubject by the Balkan seismologist. A. Mohorovicic in 1909. Thethickness of A is 30 to 35 km in continental shield areas, somewhatgreater in general under larger mountain ranges, but only 5 to 10 kmunder the principal ocean floors.The P and S velocity variations in the regions Band C are lesswell determined than in D, and the depths of the boundaries betweenB, C and D are considerably uncertain (by 100 km or more). Theprincipal uncertainties inside Band C are in respect of the velocitygradients, the velocities themselves being reliable within about 39"0.It is clear that somewhere inside the regions Band C the gradientsare much steeper than the average for the Earth (or possibly the ve-locities are discontinuous), and work of the writer in 1936 showedthat there is significant departure from chemical homogeneity in thispart of the Earth (or alternatively phase transitions).Inside D, the P and S velocities are well determined, and workof Birch indicates that the chemical composition of D' is fairly uni-form. Calculations by the writer indicate that the density gradient inthe region D" is about three times the gradient that would be caused-27 -by pressure alone, suggesting the accumulation of some denser mate-rial near the bottom of the mantle.The whole mantle is solid (in the sense defined above) -apartfrom the oceans and isolated pockets of magma- and the rigiditysteadily increases downward to the bottom of the mantle, where thevalue is about four times that of steel at ordinary pressures. The soli-dity of the mantle is established by the fact that 5 as well as P wavesare transmitted throughout.The regions E, F and G together constitute the central core. Theboundary between D" and E is sharp. In 1913, Gutenberg calculatedits depth as 2.900 km, and Jeffreys showed in 1939 that this value iscorrect within a few kilometers. There is no evidence of 5 wave trans-mission below the mantle.The region G, of radius about 1.250 km, is the inner core. Itsexistence was first indicated in 1936 in work by Inge Lehmann ofDenmark. The region E has come to be called the outer core. Workof Jeffreys in 1940 and 1942 pointed to the existence of a transitionregion F between E and G. The solution of Jeffreys gave a negativeP velocity gradient (with increase of depth) inside the region F.In 1962, Dr. B. A. Bolt (of Sydney University), using data bythe writer and Burke-Gaffney from records of certain hydrogen-bombexplosions and some readings of natural earthquakes by Gutenberg,has produced a new solution for the transition zone between E and G.According to this solution, the P velocity gradient falls to zero betweendepths of 4.560 and 4.700 km. At 4.700 km, the P velocity then sud-denly jumps from 10.0 to 10.3 km/sec; and again jumps, from 10.3to 1l.2 km/sec., at 5.150 km depth. From 5.150 km to the center ofthe Earth, the velocity is fairly constant. A physically importantfeature of this solution (which is compatible with all the presentlyavailable data, but is not necessarily the final solution) is that it re-moves the need for a negative velocity gradient anywhere in the core.At the same time, the solution requires a more complicated transitionregion than had been previously envisaged.The initial work of Lehmann showed that, whatever the fine de-tails of the transition region may turn out to be, there is an effectiveincrease of at least 10% in the value of the P velocity a from the outerto the inner core. Inspection of the equation (I) shows that thisincrease must be due to a fairly sudden increase in either K or po,since the density p cannot decrease with increase of depth. From avariety of considerations, I have shown that K is not likely to increasesufficiently to account for the increase in a. Hence it follows that there- 28-is likely to be an increase in the rigidity p. between outer and innercore. This carries the implication, which I set down in 1946, that theinner core, unlike the outer core, is solid (in the sense above defined).I have estimated that the rigidity of the inner core probably liesbetween 2 and 4 times that of steel at ordinary pressures.As already mentioned, knowledge of the P and S velocity valuesin the Earth gives knowledge of the values of K/ p and p./ P: By bring-ing to bear additional information, including data on the Earth's massand moment of inertia and various supplementary data, I made adetermination in 1936 (which I have refined over the years) of theseparate distributions of p, K and p. throughout the Earth, as well asof other mechanical properties such as the pressure p and the gravi-tational attraction g per unit mass.Starting from an assumed value of 3.3 g/ em" for the density justbelow the crust, I have calculated that the density increases to a valuenear 5~ g/ em" at the bottom of the mantle, then jumps suddenly toabout 9~ g/ em" at the top of the central core, and reaches II ~ g/ em"at the bottom of the region E. The density in the inner core is lesscertainly determined, but J have shown that the central density mustbe at least 12.3 g/cm3• In 1942, on the basis of these calculations andtaking an arbitrary value of 17.3 g/cm3 for the central density, 1constructed a model set of values of density, incompressibility andrigidity for the Earth which is called Model A.A remarkable feature in the results of the Model A calculationwas the fairly smooth variation of the incompressibility K with thepressure p below a depth of 1.000 km in the Earth. This led me in1950 to construct a second model, Model B, in which smooth variationof K with p was taken as a central postulate. The numerical detail inModel B is not greatly different from that in Model A; Model B dif-fers from Model A principally in that K is entirely continuous at themantle-core boundary and that the density variation is rather differentin the outermost 400 km of the Earth.An important result of the Model B calculations is that, on theJeffreys P velocity distrihution of 1940, a density of at least 18 g/cm3is entailed at the Earth's centre. On the velocity distribution latelyderived by Bolt for the core, it becomes possible, however, to lowerthe Earth's central density to 15 to 16 g/cm3• The latter figure is morein line with surmises from other types of evidence.The calculations on the density p, in addition to yielding valuesof K and p., also led to determinations of the distribution of the pres-sure p, and the gravitational attraction g throughout the Earth. At- 29-the base of the mantle, the pressure is reliably determined as about1% million atmospheres, and at the centre as between 3~ and 4million atmospheres.The value of g keeps within about I % of 990 cm/ sec'' betweenthe Earth's surface and a depth of 2.400 km, rises to a maximum ofabout 1.040 cm/ see'' at the base of the mantle, and then sinks steadilyto zero at the centre of the Earth.The distributions of density and pressure throughout the Earthare indicated in Fig. I, and of the incompressibility and. rigidity inFig. 2. Fig. 3 gives an artist's impression of the interior of the Earthas revealed by seismology.REFERENCESBULLE!'O, K. E. - Introduction to the Theory 0/ Seismology, 3rd. edn., CambridgeUniversity Press, 1963.BULLEN, K. E. - Seismology, Methuen, 1954.- 30-Ii-- +-L Modlle14 ';- ModllEC•v·v12:<;--'"v..•A10 •·EE•..II)• >-...tilZIIIaiII IJ-!BELOW2000EA liTH'SlOOOI+1I I\- --lL _II I1-1I...IioE-e,01~I/)I/)I:- ISUIIFACE I Kilo","trlS I4000 5000 6000SOLID NAN TLE FLUID OUTER CORE INNER COREFig. 1. Variation of density and pressure and pressure inside the Earth.- 31-T--+-I /I4SOLID MANTLE FL U ID OUTER CORE INNER COREFig. 2. Variation of incompressibility and rigidity inside the Earth.- 32-,Fig. 3. Picture of thequi k interior fa c waves. 0 the E hart as hroadl y revealed

Earthquake waves and the mechanical properties of the earth's interior

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Earthquake waves and the mechanical properties of the earth's interior

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