On amplitudes of P near the shadow zone (*)

core ABSTRACT 51 short-period vertical North American and Canadian records of the Samoa earthquake 14 Aprii 1957 were examined. Amplitudes of P ivere very largo at the western stations (A < 84°) and small at the stations to the cast, 8 of which recorded P at distances greater than 100°. There ivas a lack of stations at intermediate distances. At the greatest distance, 108°.2, the P waves were not diffracted ioaves, for the pliase had the same general character as at sliorter distances-, the period, ivas 2 sec. From 70° to about 90° the Samoa P timedistance curve is steeper than the J.-B. curve. It had been found previously that from about 90 0 epicentral distance onivards the variation of the P amplitude with distance ivas not always the same and also that the sliadow zone seemed to begin at different distances. It is suggested that this be due to small regional differences of velocity in the deepest layer D" of the mantle.

Some years ago I iliade a studv (Lehmanu 1953) in order to find out whetlier or not there was a sudden drop in the P amplitude at 105° or another neiglibouring distance marking clearly the beginning of the shadow zone. I made use partly of the I.S.S. data and partly of Copenhagen records.
It is well known that P is often recorded at distances greater tlian 105°, but usually it is small and it is considered to be a diffracted wave. I found, however, that in the I.S.S. there were sometimes series of P entries up to 110° or more the residuals of wliich were consistenti enough to show that the onset was sharp and therefore not likely to be due to a diffracted wave. On the otlier hand I sometimes found that P of an earthquake had considerable uncertainty al ready at distances of about 95° or so and yet was recorded beyond 105° as if no deerease of amplitude took place at that distance.
Using-Copenhagen records I found also that in some earthquakes P was very clearly recorded up to and considerably beyond 105° while in otlier earthquakes of similar magnitude P became small and insignificant already at distances smaller than 100°. Thus the variation of amplitude with distance is diiferent in differente earthquakes.
The shadow zone seems to begin at diiferent distances and it is usually not possible to say exactly wliere it begins; there is no sudden deerease of amplitude to mark its boundaiy.
At the Laniont Geologica! Observatory the surface waves of the Samo aearthquake (*) Lamont Geological Observatory (Columbia University) Contribution N° 319.
14 Aprii 1957 were being studied witli the object of fìnding variations of phase velocity and hence of crustal thickness aerosa the United States and Canada. 51 records of short-period vertical mstruments had been collected. They were from epicentral distances ranging from 71° to 114°.
It was suggested to me by Dr. Ewing that I examine the records for the greatest distances in order to see how P varied near the shadow zone.
It was immediately apparent that there was a considerable drop in amplitude from the nearer to the greatest epicentral distances, but it was clear also that no precise determination of the variation of amplitude with distance could be iliade, for the instruments varied and their responso was not accmately known. Also, the distances are subject to errors, an epicentre in the Samoan region not being determinable with great precision. However, the two independent determinations of the U.S.C.G.S. and the Central Bureau at Strasbourg differed by less than 1°.
The seismological stations are not evenly distributed over the continent. There are a great many stations in the western part and they were at epicentral distances ranging from 71° to 84°. There were 10 stations in the eastern part at distances greater than 100° and there were not many stations in between. P amplitudes were very large at the western stations, the phase being marked by a group, or two groups, of large swings continuing for about a minute. The wave period was two seeonds or a little less. Eapid City at an epicentral distance of 87° stili had very large amplitudes thougli somewhat smaller than tlie western stations. Fayetteville at 90°.4, however, hacl considerably smaller amplitudes though the phase was stili quite large.
Columbia at distante 100°.2 was the nearest of the 10 stations at distances greater than 100° and Halifax at 114° 6 the most distant.
This station and Palisades at 106°.9 did not record P, but ali the others did record it.
greater magniftcation than the Sprengnether instrument in the period range in question, but tliat would be of no avail if the core boundary were grazed by tlie ray emerging at 105°. It is obvious that the path to Shawinigan Falls has the sanie general character as tliose to the nearer stations and that the waves recorded are not difEracted waves. The reason why the Cleveland record is shown and not tlie one Samoa earthquake recorded at Cleveland, A = 101°, 3 Tlie Cleveland record from epicentral distance 101°.3 is shown in the figure. It is from a Sprengnether short-period vertical instrument. Tlie P amplitudes are here quite small as compared with tliose at the western stations. Where and how quickly the amplitudes fall off cannot be said because of a lack of stations at intermediate distances. The wave period is about 2 sec. as at the smaller distances.
The Kirkland Lake record from a distance of 103°.4 is almost exactly like the Cleveland record. The pattern is the sanie and the amplitudes are equal. It is also from a Sprengnether instrument. Chapel Hill at 102°.2 has similar amplitudes but the pattern is dilferent; there is not the same division of the phase.
It is somewhat surprising to And that Shawinigan Falls at an epicentral distance of 108°.2 has a record similar to the Cleveland record and only slightly smaller. Tlie pattern is the sanie and the waves have period of about 2 sec. The seismograph is a Willmore instrument and it may have from Shawinigan Falls is that the trace of the lattei-is a little fainter.
Of the other stations beyond 100° Columbia at 100°.2 has a much smaller P phase than tlie stations mentioned, but the pattern is the same. This is also trae for Ottawa at 106°.0. Montreal at 107°.5 has quite a small but distinct P. State College at 103°.9 has also a clear but small P.
We have seen that the P amplitudes are small in the 8° range of distance 100° to 108°.
No precise determination of the variation of amplitude with distance can be iliade, not even for the distances of tlie many western stations, but the decrease of amplitude between 84° and 100° is very great, undoubtedly far greater than the decrease between 71° and 84°. The strong decrease of amplitude will be due to a marked decrease of velocity gradient at deptli. The lack of observations at intermediate distances makes it impossible to say whether the decrease is graduai or abrupt or to determine even roughly the deptli at which it occurs. But our fìnding is in suppoi't of the assumption that K. E. Bullen's region D divides itself into two regions of wliich the inner one, D", is cliaracterised by a velocity gradient that is very small and distinctly smaller than that of D' (see e. g. Bullen 1956).
The fact that the time-curve straightens before the shadow zone is reached has led to this result. The Jeffreys-Bullen P curve straightens at about 90° and has very little curvature from there onwards. The Samoa P curve runs practically parallel to it at these distances.
It does not, however, run parallel to the J.-B. curve ali the way from 70° to 108°. Taking the time of occurrence of the earthquake to be 19:17:57 as determined by the U.S.C.G.S. we fincl the following mean residuals: There is some scatter of the residuals near 85°. Between 90° and 100° there are only 1 observations; the mean of their residuals is 2 S .23 ± 0 S .22. The azimuths of ali the observing stations is between 30° and 58° so it is evident that the Samoa earthquake P curve is steeper than the J.-B. curve from 70° up to about 90°. The distances taken were geographie distances, but ellipticity corrections were applied to the transmission times. Silice the amplitude of the direct P wave usually is quite small at the greatest distances where it occurs it will not be easy to decide whether a P phase as recorded is due to a direct or to a diffracted wave and to iind where the shadow zone begins. There is as a rule no short period waves in distant P's, and this has been taken to indicate diffraction. Whether it is a sure criterion is not known and it is not applicatale unless the recording instruments have a good response to short period waves. It does not seem to have been attempted to fix the beginning of the shadow zone of an individuai earthquake by a method similar to the one applied here, by direct comparison of records. To obtain definite results it would be necessary to clioose earthquakes well recorded at the distances in question by a dense net-work of stations as e. g. that of western Xortli America. Stations equipped witli short period instruiiients would be required and it would be higlily desh'able that the relative response of the instruments as mounted should be known. This lattei' requirement is not easily fulfìlled, but it may be indispensable if we are to succeed in deriving more detailed knowledge about the Earth's interior from seismological data.
Unless the error in the epicentre is unusually large, Shawinigan Falls is at an epicentral distance greater than 105°, and the shadow zone of our Samoan shock does not begin at this distance.
Taking the direct P ray to reach out to different epicentral distances in diiferent shocks, and the relative amplitudes to differ, we shall have to look for a possible explanation, and we find that slight regional variations in the coniposition of the region D" would account for it. The velocity gradient in D" is quite small and a small regional variation would alter slightly the curvature in D" of the rays having their deepest points in the region. The rays are long and therefore a small bending or straightening of them in their deepest portion would give rise to an appreciable change in the epicentral distance at wliich they emerged. It would alter also the spreading of the rays and therefore affect amplitudes. Actually it is not known at present whether the difference in amphtude variation is regionally conditioned, but it would be of great interest to have it investigated.
My thanks are due to Dr. Maurice Ewing by whose kind invitation I worked at the Lamont Geologica! Observatory and who allowed me to use the records of the Samoa earthquake collected there.
Silice the precedili»' was written the study by A. Vogel: Uber Unregelmàssigkeiten der àusseren Begrenzung des Erdkerns (doctor's tliesis, not printed) has become known to me. Observed regional variations in the transmission times of the waves reflected at the core boundary are put down to irregularities in this boundary.
Undulations in the core boundary would account also for the sliadow zone for P beginning at diflerent epicentral distances in different earthquakes, but not for the observed differences in amplitude variation They seem to require for their explanation the (additional) assumption of regional variation of velocity in D".
ABSTRACT 51 short-period vertical North American and Canadian records of the Samoa earthquake 14 Aprii 1957 were examined.
Amplitudes of P ivere very largo at the western stations (A < 84°) and small at the stations to the cast, 8 of which recorded P at distances greater than 100°.
There ivas a lack of stations at intermediate distances.
At the greatest distance, 108°.2, the P waves were not diffracted ioaves, for the pliase had the same general character as at sliorter distances-, the period, ivas 2 sec.
From 70° to about 90° the Samoa P timedistance curve is steeper than the J.-B. curve.
It had been found previously that from about 90 0 epicentral distance onivards the variation of the P amplitude with distance ivas not always the same and also that the sliadow zone seemed to begin at different distances. It is suggested that this be due to small regional differences of velocity in the deepest layer D" of the mantle. È stato precedentemente trovato che da una distanza epicentrale di circa 90° ed oltre, la variazione dell'ampiezza della P con la distanza, non era sempre la stessa e inoltre che la zona d'ombra sembrava cominciare a distanze diverse.