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How accurate are the 1968 P tables?
EARTH AND PLANETARY SCIENCE LETTERS 8(1970) 250-252 . NORTH-HOLLAND PUBLISHING ('OMPANY
HOW. ACCURATE ARE THE 1968 P TABLES? A .DOUGLAS
U.K . Atomic Energy Authority, Blacknest, Brimpron, Nr. Reading, Berks., UK Received 5 February 1970
Errors in the 1968 P travel time tables 151 are unlikely to be anywhere greater than 0.55 . The recent suggestions
13 .41 that the Cleary and Hales curve 161 is a more reliable world average curve is difficult to accept in view of the
limited amount of data used and with the bulk of this data coming from recording stations on the N . American con-
tinent .
Both Lilwall and Douglas [ 1,21 and Cleary and Muirhead [3,41 have questioned the accuracy of the 1968 F travel time tables [51 . Lilwall and Douglas [1,21 have derived independently a set of travel time tables (using different data and different analysis methods) and conclude that ignoring base line errors T :-- 1"1968 - 3.006 A , where T is ilie Lilwill and Douglas (L--D) travel time, T1968 is the 1968 time and A is epicentre) distance . The Lilwall-Dougla,, curve thus differs from the 1968 tables by an amourt that varies linearly with distance ; the 1968 curve is "tilted" relative to the L-D curve . Lilwall and Douglas [41 also found that there are some systematic diffeirenzes between their station (-!ime) corrections and those given in the 1968 tables and suggest tl-,Lt interaction between station corrections and travel times has caused the events used by Herrin [51 to con,erge to biased epicentres, and this has introduced a~ -, error into the 1968 P tables . Lilwall and Douglas [ 1,21 demonstrate that this is a plausible explanation t ocause tlv:y are able to reproduce almost exactly the 1968 P tables by giving systematic errors to the epicentres of the events used to derive the L--D tables . LilwAl and Douglas 11,21 thus show that there are important errors in the 1968 tables but that these errors are unlikely to be anywhere much gre ter than 0.5 sec .
Cleary and Muirhead [3,41 also suggest that the 1968 curve is in error by a "tilt"' but this "tilt" is more than four times that Lilw,dl and Douglas [ 1,21 suggest. The true travel time curve according to Cleary and Muirhead (TCM) is given by Tl968 -- 0.023 0 The "corrected" 1968 tables derived by Cleary and Muirliead [3,41 show close agreement with the curve of Cleary and Hales [61 . Cleary and Muirliead [3,41 conclude that this confirms the Cleary and Hales (C--1-1) curve as the most reliable curve. Over the range 30-100° the C-H curve and the 1968 P curve diverge by up to about 2 sec. Cleary and Muirliead [3,41 explain the supposed error in the 1968 P tables as the result of source bias in the epicentres of the events used in the 1968 analysis . Here we show that this is ;an improbable explanation and that the 19(18 tables are unlikely to be so badly in error. We also sugge~;,t that the Cleary and Hales-Cleary and Muirhead analysis is measuring regional effects and that the C--H curve is riot applicable as a world wide curve. Consider a series of stations pat distances 0 1 , A, . . ., Aj etc. from tree true epicer ,,,tre of all event, all stat .ons lying on a single azimuth from the event . Assume that the arrival times at 0 1 , A, . . are exactly as predicted from the triie ep,centre . Then the
HOW ACCURATE ARE THE 1968 P TABLES?
arrival time predicted at station j from an erroneous epicentre SA nearer to the stations, will differ from the observed arrival time by about -(aT/aA~)aA where aT/aA~ is the partial derivative of the travel time T with respect to A . Now because 5T,`aA is almost a linear function of A, -(aT/aAj )aA also varies linearly with distance . A travel time computed from these residuals would thus appear to be "tilted" relative to the true travel time curve in a similar way to the relative "tilts" in the 1968, L-D and C-H curves. Now to produce a "tilt" of 2 sec over 70° in the 1968 tables tha` Cleary and Muirhead [3,41 require, a°
aT ~aA30
aT
-57 100
must be about 2 sec . As aT/3A30 ::%- 9.0 sec/degree then the error in the Herrin [51 epicentres would have to oe about 40 km - which is very unlikely . However, even if the epicentral errors are so large, there is a compensating effect . On opposite azimuths the curve is "tilted" the opposite way so that a travel time curve deduced using all azimuths would tend to converge towards the correct curve. So that provided all azimuths are used, sources of error front mislocation should average out, although errors might creep in where many more stations lie within one 180° sector of azimuth than in the opposite sector - which often happens in the real world . Chary and Hales (6) however have purposely restricted their study to stations that lie within a narrow band of azimuths from the source regions although as we shall see later this is probably not the main explanation of the tilt in the C -H curve . However, we conclude that of the two curves, the C-I-i curve is more likely to have a tilt error than the 1968 curve . Three sets of data tend to support the C-H curve : (1) The original Clear), and Hales analysis [61, which used data from 1 I events in a line. from Alaska to Formosa, 8 events to the south of the USA between the Mid-Atlantic Ridge and the Caspian Sea ; (2) analysis of travel time data from the Longshot (Aleutian Island) explosion ; and (3) analysis of the travel times from the Nevada Test Site explosion Greeley . (Cleary and Muirhead [41 also claim that data froth the Marshall Island and Sahara explosions support the Cleary and Hales curve. However these data are not significantly different from the 1968 P tables at the 95X
25 1
level .) Apart from many of the recording stations being in N. America one feature is common to all these data. many of the great circle paths from source to receiver tend to lie along or close to large fold belts. This is particularly true of stations at near distances, say out to 45° . Travel times for such station event pairs probably differ from the average because of the deep structure of the fold belts. The Cleary and Hales [61 and Cleary and Muirhead [3,41 results can thus be interpreted as showing that the travel times to distance out to say 45° are slower than predicted by the 1968 (average) P tables. At long range the effects of the fold belt should be less because the rays travel deeper into the mantle and the C-H curve would bo expected to converge towards the 1968 P curve . Cleary [71 and Davies and McKenzie [81 have both suggested that there is seismological evidence for steeply dipping plates of high velocity material beneath fold belts . Here the evidence is for low velocity material. If either of these suggestions is correct travel time curves derived mainly from ray paths beneath fold belts are unlikely to be average for the whole world. To obtain an average world curve, data are required froth a large number of events widely spread over the earth and recorded at a large number of recording stations in as many azimuths as possible . This both Herrin [51 and Lilwall and Douglas [3,41 have tried to do . The travel time residuals about these average curves can now be examined area by area to obtain regional curves which can be interpreted in terms of source, station and regional structure . The C-H curve appears to be such a regional curve . References III
R .C.Lilwall and A .Douglas, Quest for a P travel time standard, Nature 222 (1969) 975 . 121 R .C .Lilwall and A .Douglas, Estimation of P travel times using the joint epicentre method, Geophys . J . (in press) . 131 J .R .Cleary and K .J .MuirYtead, Comparison of the 1968 P tables with times from nuclear explosions (1) . Longshot and Greeley, Fatth Planet . Sci . Letters 7 (1969) 119 . 141 KJ .Muirhcad and J .R .Cleary, Comparison of the 1965 l' tables with times from nuclear explosions 111) . 'Yhe Marshall Wands and Sahara Series, Larth Planet . Sci . Letters 7 (1969) 132 . 151 E .Llerrin (Chairman), 1968 Seismological Tables for P Phases, Bull . Seism . Soc . Am . 5 8 (1968) 1193 .
252
A.DOUGLAS
161 J .R .Cleary and A .L .Hales, An analysis of the travel times
of P wa%es to North American Stations, in the distance range 32 ° to 100 ° , Bull . Seism . Soc . Am . 5 6 (1966) 467 .
171 J.R .Cleary, Azimuthal variation of the Longshot source
term, Earth Planet. Sci . Letters 3 (1967) 29 .
181 D .Davies and D .P .McKenzie, Seismic travel time residuals
and plate, Geophys. J . 18 (1969) 51 .
HOW. ACCURATE ARE THE 1968 P TABLES? A .DOUGLAS
U.K . Atomic Energy Authority, Blacknest, Brimpron, Nr. Reading, Berks., UK Received 5 February 1970
Errors in the 1968 P travel time tables 151 are unlikely to be anywhere greater than 0.55 . The recent suggestions
13 .41 that the Cleary and Hales curve 161 is a more reliable world average curve is difficult to accept in view of the
limited amount of data used and with the bulk of this data coming from recording stations on the N . American con-
tinent .
Both Lilwall and Douglas [ 1,21 and Cleary and Muirhead [3,41 have questioned the accuracy of the 1968 F travel time tables [51 . Lilwall and Douglas [1,21 have derived independently a set of travel time tables (using different data and different analysis methods) and conclude that ignoring base line errors T :-- 1"1968 - 3.006 A , where T is ilie Lilwill and Douglas (L--D) travel time, T1968 is the 1968 time and A is epicentre) distance . The Lilwall-Dougla,, curve thus differs from the 1968 tables by an amourt that varies linearly with distance ; the 1968 curve is "tilted" relative to the L-D curve . Lilwall and Douglas [41 also found that there are some systematic diffeirenzes between their station (-!ime) corrections and those given in the 1968 tables and suggest tl-,Lt interaction between station corrections and travel times has caused the events used by Herrin [51 to con,erge to biased epicentres, and this has introduced a~ -, error into the 1968 P tables . Lilwall and Douglas [ 1,21 demonstrate that this is a plausible explanation t ocause tlv:y are able to reproduce almost exactly the 1968 P tables by giving systematic errors to the epicentres of the events used to derive the L--D tables . LilwAl and Douglas 11,21 thus show that there are important errors in the 1968 tables but that these errors are unlikely to be anywhere much gre ter than 0.5 sec .
Cleary and Muirhead [3,41 also suggest that the 1968 curve is in error by a "tilt"' but this "tilt" is more than four times that Lilw,dl and Douglas [ 1,21 suggest. The true travel time curve according to Cleary and Muirhead (TCM) is given by Tl968 -- 0.023 0 The "corrected" 1968 tables derived by Cleary and Muirliead [3,41 show close agreement with the curve of Cleary and Hales [61 . Cleary and Muirliead [3,41 conclude that this confirms the Cleary and Hales (C--1-1) curve as the most reliable curve. Over the range 30-100° the C-H curve and the 1968 P curve diverge by up to about 2 sec. Cleary and Muirliead [3,41 explain the supposed error in the 1968 P tables as the result of source bias in the epicentres of the events used in the 1968 analysis . Here we show that this is ;an improbable explanation and that the 19(18 tables are unlikely to be so badly in error. We also sugge~;,t that the Cleary and Hales-Cleary and Muirhead analysis is measuring regional effects and that the C--H curve is riot applicable as a world wide curve. Consider a series of stations pat distances 0 1 , A, . . ., Aj etc. from tree true epicer ,,,tre of all event, all stat .ons lying on a single azimuth from the event . Assume that the arrival times at 0 1 , A, . . are exactly as predicted from the triie ep,centre . Then the
HOW ACCURATE ARE THE 1968 P TABLES?
arrival time predicted at station j from an erroneous epicentre SA nearer to the stations, will differ from the observed arrival time by about -(aT/aA~)aA where aT/aA~ is the partial derivative of the travel time T with respect to A . Now because 5T,`aA is almost a linear function of A, -(aT/aAj )aA also varies linearly with distance . A travel time computed from these residuals would thus appear to be "tilted" relative to the true travel time curve in a similar way to the relative "tilts" in the 1968, L-D and C-H curves. Now to produce a "tilt" of 2 sec over 70° in the 1968 tables tha` Cleary and Muirhead [3,41 require, a°
aT ~aA30
aT
-57 100
must be about 2 sec . As aT/3A30 ::%- 9.0 sec/degree then the error in the Herrin [51 epicentres would have to oe about 40 km - which is very unlikely . However, even if the epicentral errors are so large, there is a compensating effect . On opposite azimuths the curve is "tilted" the opposite way so that a travel time curve deduced using all azimuths would tend to converge towards the correct curve. So that provided all azimuths are used, sources of error front mislocation should average out, although errors might creep in where many more stations lie within one 180° sector of azimuth than in the opposite sector - which often happens in the real world . Chary and Hales (6) however have purposely restricted their study to stations that lie within a narrow band of azimuths from the source regions although as we shall see later this is probably not the main explanation of the tilt in the C -H curve . However, we conclude that of the two curves, the C-I-i curve is more likely to have a tilt error than the 1968 curve . Three sets of data tend to support the C-H curve : (1) The original Clear), and Hales analysis [61, which used data from 1 I events in a line. from Alaska to Formosa, 8 events to the south of the USA between the Mid-Atlantic Ridge and the Caspian Sea ; (2) analysis of travel time data from the Longshot (Aleutian Island) explosion ; and (3) analysis of the travel times from the Nevada Test Site explosion Greeley . (Cleary and Muirhead [41 also claim that data froth the Marshall Island and Sahara explosions support the Cleary and Hales curve. However these data are not significantly different from the 1968 P tables at the 95X
25 1
level .) Apart from many of the recording stations being in N. America one feature is common to all these data. many of the great circle paths from source to receiver tend to lie along or close to large fold belts. This is particularly true of stations at near distances, say out to 45° . Travel times for such station event pairs probably differ from the average because of the deep structure of the fold belts. The Cleary and Hales [61 and Cleary and Muirhead [3,41 results can thus be interpreted as showing that the travel times to distance out to say 45° are slower than predicted by the 1968 (average) P tables. At long range the effects of the fold belt should be less because the rays travel deeper into the mantle and the C-H curve would bo expected to converge towards the 1968 P curve . Cleary [71 and Davies and McKenzie [81 have both suggested that there is seismological evidence for steeply dipping plates of high velocity material beneath fold belts . Here the evidence is for low velocity material. If either of these suggestions is correct travel time curves derived mainly from ray paths beneath fold belts are unlikely to be average for the whole world. To obtain an average world curve, data are required froth a large number of events widely spread over the earth and recorded at a large number of recording stations in as many azimuths as possible . This both Herrin [51 and Lilwall and Douglas [3,41 have tried to do . The travel time residuals about these average curves can now be examined area by area to obtain regional curves which can be interpreted in terms of source, station and regional structure . The C-H curve appears to be such a regional curve . References III
R .C.Lilwall and A .Douglas, Quest for a P travel time standard, Nature 222 (1969) 975 . 121 R .C .Lilwall and A .Douglas, Estimation of P travel times using the joint epicentre method, Geophys . J . (in press) . 131 J .R .Cleary and K .J .MuirYtead, Comparison of the 1968 P tables with times from nuclear explosions (1) . Longshot and Greeley, Fatth Planet . Sci . Letters 7 (1969) 119 . 141 KJ .Muirhcad and J .R .Cleary, Comparison of the 1965 l' tables with times from nuclear explosions 111) . 'Yhe Marshall Wands and Sahara Series, Larth Planet . Sci . Letters 7 (1969) 132 . 151 E .Llerrin (Chairman), 1968 Seismological Tables for P Phases, Bull . Seism . Soc . Am . 5 8 (1968) 1193 .
252
A.DOUGLAS
161 J .R .Cleary and A .L .Hales, An analysis of the travel times
of P wa%es to North American Stations, in the distance range 32 ° to 100 ° , Bull . Seism . Soc . Am . 5 6 (1966) 467 .
171 J.R .Cleary, Azimuthal variation of the Longshot source
term, Earth Planet. Sci . Letters 3 (1967) 29 .
181 D .Davies and D .P .McKenzie, Seismic travel time residuals
and plate, Geophys. J . 18 (1969) 51 .