37Adams.qxd 859 ANNALS OF GEOPHYSICS, VOL. 47, N. 2/3, April/June 2004 Key words earthquake location – macroseismic locations 1. Introduction Instrumental recording of earthquakes be- gan only in the late nineteenth century. Until then knowledge of earthquakes and their dis- tribution depended entirely on the observing and interpreting of their felt effects. Despite this limitation many creditable studies of seis- micity were undertaken, an example being the map of global earthquake distribution of Mal- let in 1858 (fig. 1), which agrees well with present day knowledge, apart from omitting activity on the oceanic ridges, from where no felt information could be obtained. Because of limitations in the design of ear- ly instruments, and the lack of knowledge of earth structure, the advent of instrumental recording did not immediately result in a major improvement in earthquake location, but rather Re-evaluation of early instrumental earthquake locations: methodology and examples Robin D. Adams International Seismological Centre, Thatcham, Berkshire, U.K. Abstract The difficulties of locating earthquakes in the early instrumental period are not always fully appreciated. The networks were sparse, and the instruments themselves were of low gain, often had inappropriate frequency re- sponse and recording resolution, and their timing could be unreliable and inaccurate. Additionally, there was on- ly limited knowledge of earth structure and consequent phase identification and propagation. The primitive Zöp- pritz tables for P and S, with no allowance for the core, did not come into use until 1907, and remained the main model until the adoption of the Jeffreys-Bullen tables in the mid-1930s. It was not until the early 1920s that stud- ies of Hindu Kush earthquakes revealed that earthquake foci could have significant depth. Although many early locations are creditably accurate, others can be improved by use of more modern techniques. Early earthquakes in unusual places often repay closer investigation. Many events after about 1910 are well enough recorded to be re-located by computer techniques, but earlier locations can still be improved by using more recent knowledge and simpler techniques, such as phase re-identification and graphical re-location. One technique that helps with early events is to locate events using the time of the maximum phase of surface waves, which is often well re- ported. Macroseismic information is also valuable in giving confirmation of earthquake positions or helping to re-assess them, including giving indications of focal depth. For many events in the early instrumental period macroseismic locations are to be preferred to the poorly-controlled instrumental ones. Macroseismic locations can also make useful trial origins for computer re-location. Even more recent events, which appear to be well lo- cated, may be grossly in error due to mis-interpretation of phases and inadequate instrumental coverage. A well converging mathematical solution does not always put the earthquake in the right place, and computer location programs may give unrealistically small estimates of error. Examples are given of improvements in locations of particular earthquakes in various parts of the world and in different time periods. Mailing address: Dr. Robin D. Adams, International Seismological Centre, Pipers Lane, Thatcham, Berkshire, RG19 4NS, U.K.; e-mail: robin.adams1@btopenworld.com in a gradual refinement. Particularly in the ear- ly days the locations could be unreliable, and instrumental information was used to refine macroseismic studies rather than replace them. Even at the present time instrumental and macroseismic investigations can be used to sup- plement each other, and their combined use produces the best results. This paper summarises various location techniques and points out some difficulties as- sociated with them that are not always appre- ciated. 2. Macroseismic locations Macroseismic location was the only technique available until the beginning of the twentieth cen- tury, and in some parts of the world is still the best available. Some general points are obvious. For small events, say of magnitude 2 1/2 or less, the felt area will be small, and the epi- centre must be close to anywhere where it was reported felt. For larger events the pattern of isoseismals may give the epicentre, as being close to the centre of the isoseismal of highest intensity. In some instances epicentres are very well con- trolled by felt effects and may be preferred to poor instrumental determinations. There can be complications, however, in areas above subduction zones, where lateral velocity varia- tions can cause focussing of energy and con- sequent distortion of the felt pattern. In New Zealand, for example, because of the shallow- ing of the zone of deep earthquakes south- wards, intermediate depth earthquakes be- neath the centre of the North Island are often felt only lightly at the epicentre, with the high- est intensities displaced southwards. There is an additional complication with the very largest earthquakes, say of magnitude 7 and greater, where the source dimension can be more than several tens of kilometres in extent. Unless the source rupture is symmetrical the epicentre, above the point of initiation of rup- ture, may be displaced from the region of high- est energy release identified by macroseismic reports. In such cases the epicentre has less significance. The spacing of isoseismals may also give an indication of focal depth. In general isoseismals from a shallow event will have a peak near the epicentre and fall off evenly with distance; those from deeper events will have inner iso- seismals that are wider, with the outer isoseis- mals more closely spaced. Many attempts have been made to quantify this effect, an early one being by Kövesligethy (1906), with more re- cent relations given, for example, by Musson and Cecic (2002). Epicentral intensity may give an indica- tion of magnitude. Various formulae have been developed for this applicable in various regions, see for example, Ambraseys et al. (1994). It must be remembered that for many cen- turies these were the only techniques available for earthquake location. In some areas macro- seismic techniques may now be calibrated by well-controlled instrumental locations, en- abling some re-evaluation of earlier results. 3. Location with networks - Basic principles Some information about an earthquake’s location may be found from readings at a sin- gle station, such as its distance from the in- terval between different phases, and its ap- proximate azimuth from analysis of horizon- tal motion. The character of the recording and possibly the identification of depth phas- es may also give an indication of focal depth. Recent advances in digital processing allow these parameters to be determined more ac- curately from modern digital stations. For reliable location, however, it is desir- able to compare arrival times of different phases at a network of stations. To determine the origin time and the three spatial co-ordi- nates of the focus at least four independent arrival times are needed from at least three stations, and for a good solution many sta- tions should be used. Computers were not generally available before the early 1960s, so before then it was usual to use graphical methods to locate earthquakes. In this method, the origin time is 860 Robin D. Adams 861 Re-evaluation of early instrumental earthquake locations: methodology and examples F ig . 1. G lo ba l se is m ic it y m ap o f M al le t (1 85 8) b as ed o n m ac ro se is m ic r ep or ts o nl y. 862 Robin D. Adams found from the differences between phases at individual stations, and the travel times of ob- served phases is then used to determine dis- tances to the stations. Arcs corresponding to these distances are drawn on a map or globe, and adjustments made to give the best fit. Graphical methods demonstrate well the prin- ciples involved, and in particular the necessi- ty of having stations well distributed around the epicentre to obtain a reliable solution. Mathematical analysis generally uses the method of least squares, proposed by Geiger (1910). A trial origin is chosen and for each phase the time difference between the ob- served arrival and that expected from the adopted velocity model is calculated, and the origin parameters adjusted to minimise the sum of the squares of these «residuals». Be- fore the advent of computers this procedure could be carried out on mechanical calcula- tors, but this was a laborious task and usual- ly only a single iteration was performed. The difficulties of graphical solutions still remain when computer location is used, and the use of computers cannot overcome bad station geometry. If the station distribution is bad, the solution will still be bad and the formal errors large. Depending on station geometry and choice of trial origin, the program might find a false location or even fail to converge. This method will do exactly what it is asked to do – it will minimise the sum of squares of residuals for the given velocity model. This is not always helpful. For exam- ple the program will try to overcome any de- ficiencies in the velocity model. In subduc- tion zones with large lateral velocity varia- tions, the computer may put the event in quite the wrong place, with an obligingly small but unrealistic error, with no indication that the event is misplaced. This is often the case in the South Pacific. Figure 2 shows an example from New Zealand in which an in- termediate-depth earthquake in the centre of a network of more than 20 stations was giv- en an apparently well-controlled solution us- ing the laterally homogeneous Jeffreys- Bullen velocity model (k = 1.0 in fig. 2). This origin did not fit reported arrival times from stations outside New Zealand, however, nor the felt effects. Assuming a velocity in the deep earthquake zone 10% higher than nor- mal gave a solution in which the epicentre was moved 60 km (k = 0.9) and the focal depth reduced by 50 km. Adopting the new position removed all discrepancies and gave what was clearly a position closer to the true one, but from the mathematical point of view the initial determination was well controlled, with small errors, and there was no reason to doubt its validity (Adams and Ware, 1977). It must be stressed that the formal stan- dard errors given by the least squares proce- dure are a measure of the consistency of the data with respect to the specific model used, and do not necessarily reflect physical errors. 4. Difficulties in earthquake listings and location 4.1. General difficulties Some sources of error are common to all earthquake catalogues and listings, including those from the pre-instrumental era. Errors may be divided into omissions, spurious events and mis-location. 4.1.1. Omissions In pre-instrumental times earthquakes were reported only from populated areas; note for example the lack of earthquakes in oceanic ar- eas in early compilations of global seismicity (e.g., Mallet, 1858). The increasing sensitivity of instruments now means that global cover- age of detection is generally down to magni- tude 4 1/2 at the International Seismological Centre (Willemann, 1999), but detection thresholds are much lower in areas with close local networks. Nevertheless, earthquakes may remain undetected if they occur at times of instrumental failure or excessive microseis- mic noise, or if their record is confused with that of another event. Little can be done to rec- tify such omissions. Earthquakes reported with errors in time or position may result in the omission of the true event. 863 Re-evaluation of early instrumental earthquake locations: methodology and examples 4.1.2. Spurious events Errors in timing are a common source of spurious events; sometimes the event is also reported at the correct time, resulting in du- plication. Errors of minute, day, month, year or even century occur. Minute and day errors are particularly common in recent instrumen- tal listings and ISC uses a program to seek these. A felt report can sometimes help re- solve an ambiguity, but these too may be sub- ject to error. Different agencies can also locate the same event far enough apart to cause a «split» event. An example of such a three-way split is shown in fig. 3. Three national agencies each used their own network to locate a small earthquake off Central America at widely different positions; ISC was able to combine the readings into a sin- gle event (Adams and Richardson, 1996). Fig. 2. New Zealand earthquake of 4 January 1975. Stars show epicentres determined by USGS and by New Zealand procedures using standard (k = 1.0), and modified (k = 0.9) velocity models. 864 Robin D. Adams On the global scale spurious events can be formed by chance mis-association of unrelated readings. The automatic «search» procedure at ISC regularly found several hundred of these spurious events each month, which had to be removed from the files; occasionally, however, such spurious events would remain in the list- ings. Improved procedures now reduce the chance of such mis-associations. Mis-interpretation of phases can also result in spurious events. There is a tendency for small local networks to interpret arrivals from teleseisms as a local event. Core phases from Pacific earthquakes have been interpreted in Europe as local readings, and a false local earthquake postulated. In an extreme case the Large Aperture Seismic Array in Montana (LASA) during the early 1970s mis-interpret- ed steeply arriving core phases as direct P ar- rivals from earthquakes near the far limit of al- lowable distance, resulting in a ring of false events at distances near 110º (Ambraseys and Adams, 1986). Figure 4 shows these events in Cameroon, where by chance they could be as- sociated with a line of volcanic activity. Catalogues may also be contaminated with non-seismic events such as explosions, and other disturbances. A final source of false events arises simply from mistakes in copying information from oth- er sources. Such mistakes may propagate through many generations of catalogues. Cases have occurred of transposition of latitude and longitude, and north-south and east-west confu- Fig. 3. Small stars show the locations given by three national agencies for a Central American earthquake on 3 September 1992. Large star shows position obtained by ISC by combining all readings. 865 Re-evaluation of early instrumental earthquake locations: methodology and examples sion. There can also be confusion between the order of day and month. 4.2. Difficulties in early period of earthquake location It is sometimes difficult for present-day seis- mologists to appreciate the difficulties our early colleagues faced. There are fundamental record- ing difficulties arising from several sources. 4.2.1. Sparse networks Early networks developed slowly. In some areas of strong local activity, such as Japan and California, regional networks grew reasonably rapidly after the development of instruments, but on a global scale the coverage was initially sparse, enabling only the largest events to be detected and located. Nevertheless, the early global network of about 30 Milne instruments set up by the British Association for the Ad- vancement of Science in the late 1890s was the first attempt to provide global coverage (fig. 5, Milne, 1900), and provided early locations, al- beit with limited sensitivity and precision. 4.2.2. Instrumental difficulties Early instruments were mainly insensitive and had inappropriate characteristics. For ex- ample, the Milne seismographs were un- damped, of low gain and slow recording speed. They were of intermediate period (about 12s) and were not good for recording body waves. 4.2.3. Timing difficulties Again, it is hard for present-day seismolo- gists to appreciate the difficulty in obtaining accurate timing in the era before crystal clocks and radio transmission. It is not by chance that many early seismological stations Fig. 4. False events in Africa mis-located by LASA by interpreting core phases from Pacific earthquakes. Nu- merals give the proposed magnitudes. 866 Robin D. Adams were installed at astronomical observatories, for example, Mount Wilson in California and Wellington in New Zealand. Here the obser- vatory clocks could be rated by astronomical observations, but large errors could accumu- late during cloudy periods. Up till the 1960s marine chronometers remained one of the most reliable timing sources, in later periods checked against radio time signals. 4.2.4. Lack of knowledge of seismic phases and travel times In early seismology knowledge of earth structure and earthquake location developed together, each helping to improve the other. The earliest travel-time tables in common use were those of Zöppritz (1907), for P and S phases, with no allowance for the core. The existence of the core was proposed in 1910, and the possibility of deep events recognised in the early 1920s, but the Zöppritz tables re- mained in common use until Jeffreys and Bullen developed their tables in the 1930s. The inner core was not discovered until 1936. Thus early seismologists, even if they could pick arrivals from their records, lacked the knowledge of earth structure to enable them to interpret them with certainty. 5. Data available There are several sources of data for re- evaluating early earthquake locations. For global coverage the publications of the British Association (BAAS) provide the fullest source. With their support Milne pub- lished lists of phases recorded at his global network from 1899 onwards. These are gen- erally referred to by the name of his home town in the Isle of Wight off the south coast of England as the «Shide Circulars». BAAS later published epicentral estimates for the period 1899-1917, after which this work was taken over by the International Seismologi- cal Summary (ISS), originally set up in 1921 by the newly-formed International Union of Geodesy and Geophysics. ISS was reconsti- tuted as the present International Seismolog- ical Centre (ISC) in 1964. Between them the bulletins of ISS and ISC remain the most complete source of seismic readings avail- able for re-evaluation of global seismology (Adams, 2002). Other agencies also contributed to the col- lection and analysis of global earthquake in- formation. The Bureau Central de Séismolo- gie (BCIS) in Strasbourg published global bulletins for 1903 to 1963, after which it con- centrated mainly on European seismicity. Successive governmental agencies in the United States have carried out global earth- quake location since 1928; at present this is undertaken by the National Earthquake Infor- mation Center of the US Geological Survey. Many regional agencies also undertake some global analysis as well as the detailed study of the seismicity of their own region. The In- stitute of Physics of the Earth in Moscow and the Japanese Meteorological Agency are fore- most among these. An extremely valuable source of informa- tion on early earthquakes is the bulletins reg- ularly published by networks and individual stations throughout the world. These often contain much more information than was submitted to international agencies, includ- ing later phases and details of amplitude and period of recorded phases, that are invaluable in the estimation of magnitude. The bulletins of the Swedish network published by Upp- sala University are a particularly rich source of information. Sadly, with the growth of modern technology and automated data ex- change, such bulletins have now almost to- tally disappeared. 6. Re-evaluation techniques Some experience is required in identifying poor solutions in catalogues. Obvious clues that suggest that an event warrants closer investiga- tion are unusual positions, unusual groupings of stations, unsatisfactory residuals and discrepan- cy with felt reports. The first step is to re-assess the data. This involves looking at the given station readings 867 Re-evaluation of early instrumental earthquake locations: methodology and examples F ig . 5. G lo ba l ne tw or k of s ei sm og ra ph s ta ti on s in st al le d by M il ne a bo ut 1 90 0. N um be rs g iv e ap pr ox im at e lo ca ti on s of d et ec te d ea rt hq ua ke s. to see if they could have been mis-interpret- ed, or if they might have been mis-associated from another event, or even if they contain systematic timing errors. Phase mis-identifi- cation is a common error, sometimes simply confusion between P and S phases, but also gross mis-identifications, such as interpreting core phases as P arrivals from a fictitious event. It is also worthwhile searching for ad- ditional readings from station bulletins or other sources, and checking for any available felt information. If enough readings are available a computer re-location may be attempted; this may be es- pecially relevant for earthquakes previously lo- cated only by graphical means. Often, however, the quality and quantity of data are not enough for a computer solution to converge, and in such cases simple graphical methods can improve a poor solution. A technique that is useful in the re-inter- pretation of early earthquakes, particularly those recorded by Milne instruments is to make use of the reported time of arrival of the maximum phase M of surface waves (Am- braseys and Adams, 1986). Assuming that this travels at a velocity of about 3 km/s en- ables distances from stations to be calculated and locations estimated by graphical means. Although the timing may not be known accu- rately, the slow velocity reduces correspon- ding errors in distance. An example is shown in fig. 6 for an earthquake in 1906, originally located by BAAS in the Mediterranean off the coast of Egypt. Re-interpreting later ar- rivals at ten stations ranging in distance from 15º (Helwan) to 69º (Batavia) showed the event to be at a more usual location in the Red Sea. The arcs drawn in this figure show that such locations are not well determined by present standards, but a gross mis-locations has been corrected. An example of systematic re-location of early events in a given region is found in Am- braseys and Adams (2001) for earthquakes in Central America. Here a variety of techniques was used, with great reliance being given to macroseismic reports for early events. Some instrumental information was available from 1898 onwards; at the beginning of the period this could only be shown to be consistent with the felt information, but later could more 868 Robin D. Adams Fig. 6. Solid star shows position of earthquake originally located off coast of Egypt; arcs show re-location in Red Sea, using Milne readings from stations shown by small stars. 0° 30° 60° 90° 60° 30° 0° 20 March 1906 ∆° Helwan 15 Beirut 15 Bombay 30 Kodaikanal 37 Calcutta 42 Shide 43 San Fernando 44 Edinburgh 50 Irkutsk 65 Batavia 69 869 Re-evaluation of early instrumental earthquake locations: methodology and examples Fig. 7. Earthquakes in Central American region for which positions re-located by Ambraseys and Adams (2001) were at least 500 km from those originally assigned. Triangles show original positions, circles relocations. Fig. 8. Solutions of earthquake near south of France in 1990 with improved ISC position about 50 km from that given by NEIC after re-interpretation of crustal phases. 870 Robin D. Adams confidently confirm the macroseismic posi- tion. The earliest event for which a reliable instrumental position could be determined was on 1 July 1907, in Honduras. Figure 7 shows events for which our re-determinations in this region were at least 500 km from ear- lier solutions. The quality of published instru- mental locations improved with time, and particularly after the advent of the World- wide Standard Seismograph Network in 1964 there were only a very few major discrepan- cies. An example of useful combination of in- strumental and macroseismic information is given by Ambraseys and Adams (1993) for a damaging earthquake of magnitude 6 in Cyprus on 10 September 1953. It was well recorded by stations world wide and given a well-determined position some 15 km off- shore to the west of the island. The macro- seismic information, however, placed highest intensities well inland. Careful scrutiny of re- ported phase arrivals then revealed that many stations reported a second arrival about 10s after the initial onset. According to distance these had been variously interpreted as P*, PP, pP or PcP. When these later arrivals were analysed separately they established the exis- tence of a second event of approximately the same size about 50 km from the first, in the area of highest reported intensity. Failure to correctly identify crustal phases in local earthquakes can also result in signifi- cant mis-locations. Figure 8 shows two solu- tions for an earthquake near the south coast of France. The first, obtained by NEIC, was cal- culated without the benefit of readings from the closest station, Cadarache, and treating arrivals from the remaining stations as simple P. Reinterpreting arrivals at the closest four stations as the crustal phase Pg and that at the most distant as P* gave a much improved so- lution at a location some 50 km away. 7. Future work An experienced analyst will learn to recognise signs that a particular solution may be in error, and to re-assess the data to give an improved result, but there is no easy way to improve early locations if the data are not ad- equate. In the earliest period each earthquake needs to be looked at individually, bearing in mind the limitations of knowledge available to the contemporary seismologists who car- ried out the original location. For the period when recordings are rou- tinely better, it may be possible to undertake routine computer re-evaluation, but this will not necessarily reveal all deficiencies. The correct assessment of macroseismic information can also be used as an additional tool to control poorly determined instrumen- tal locations and to resolve ambiguities. A combination of these techniques may be used to improve the reliability of early earth- quake catalogues for use in tectonic studies and hazard analysis. REFERENCES ADAMS, R.D. (2002): International Seismology, in Interna- tional Handbook of Earthquake and Engineering Seis- mology. Part A, edited by W.H.K. LEE, H. KANAMORI, P.C. JENNINGS and C. KISSLINGER (Academic Press, London), 29-37. ADAMS, R.D. and W.P. RICHARDSON (1996): A view of South and Central America from the International Seismological Centre, Geofís. Int., 35, 193-203. ADAMS, R.D. and D.E. WARE (1977): Sub-crustal earth- quakes beneath New Zealand, locations determined with a laterally inhomogeneous velocity model, N.Z. J. Geol. Geophys., 20, 59-83. AMBRASEYS, N.N. and R.D. ADAMS (1986): Seismicity of West Africa, Ann. Geophysicae, 4B (6), 679-702. AMBRASEYS, N.N. and R.D. ADAMS (1993): Seismicity of the Cyprus region, Terra Nova, 5, 85-94. AMBRASEYS, N.N. and R.D. ADAMS (2001): The Seismici- ty of Central America: a Descriptive Catalogue 1898- 1995 (Imperial College Press, London), pp. 309. AMBRASEYS, N.N., C.P. MELVILLE and R.D. ADAMS (1994): The Seismicity of Egypt, Arabia and the Red Sea: a Historical Review (Cambridge University Press, Cambridge), pp. 181. GEIGER, L. (1910): Herdbestimmung bei Erdbeben aus den Ankunftszeiten, Nachr. Königlichen Ges. Wiss. Göttingen, 4, 331-349. KÖVESLIGETHY, R. (1906): A makroszeizmikus rengések feldolgozása, Math. És Természettudományi Értesítõ, 24, 349-368. MALLET, R. (1858): Fourth report upon the facts and the- ory of earthquake phenomena, Report of 28th Meet- ing of British Association for the Advancement of Science (John Murray, London), 1-136 (plate XI). 871 Re-evaluation of early instrumental earthquake locations: methodology and examples MILNE, J. (1900): Fifth report of the Committee on Seismo- logical Investigations, Report of British Association for the Advancement of Science (London), plate II. MUSSON, R.M.W. and I. CECIC (2002): Macroseismology, in International Handbook of Earthquake and Engi- neering Seismology. Part A, edited by W.H.K. LEE, H. KANAMORI, P.C. JENNINGS and C. KISSLINGER (Iaspei, Academic Press, San Diego, U.S.A.), 807-822. WILLEMANN, R.J. (1999): Regional thresholds of the ISC Bulletin, Seismol. Res. Lett., 70, 313-321. ZÖPPRITZ, K. (1907): Über Erdbebenwellen II, Laufzeitkur- ven, Nachrichten der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-physi- kalische Klasse, 529-549.