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The first technical discussions, held in 1958, on methods of verifying compliance with a treaty banning nuclear explosions, concluded that a monitoring system could be set up to detect and identify such explosions anywhere except underground: the difficulty with underground explosions was that there would be some earthquakes that could not be distinguished from an explosion. The development of adequate ways of discriminating between earthquakes and underground explosions proved to be difficult so that only in 1996 was a Comprehensive Nuclear Test Ban Treaty (CTBT) finally negotiated. Some of the important improvements in the detection and identification of underground tests—that is in forensic seismology—have been made by the UK through a research group at the Atomic Weapons Establishment (AWE). The paper describes some of the advances made in identification since 1958, particularly by the AWE Group, and the main features of the International Monitoring System (IMS), being set up to verify the Test Ban.Once the Treaty enters into force, then should a suspicious disturbance be detected the State under suspicion of testing will have to demonstrate that the disturbance was not a test. If this cannot be done satisfactorily the Treaty has provisions for on-site inspections (OSIs): for a suspicious seismic disturbance for example, an international team of inspectors will search the area around the estimated epicentre of the disturbance for evidence that a nuclear test really took place.Early observations made at epicentral distances out to 2,000 km from the Nevada Test Site showed that there is little to distinguish explosion seismograms from those of nearby earthquakes: for both source types the short-period (SP: ∼1 Hz) seismograms are complex showing multiple arrivals. At long range, say 3,000-10,000 km, loosely called teleseismic distances, the AWE Group noted that SP P waves-the most widely and well-recorded waves from underground explosions-were in contrast simple, comprising one or two cycles of large amplitude followed by a low-amplitude coda. Earthquake signals on the other hand were often complex with numerous arrivals of similar amplitude spread over 35 s or more. It therefore appeared that earthquakes could be recognised on complexity. Later however, complex explosion signals were observed which reduced the apparent effectiveness of complexity as a criterion for identifying earthquakes. Nevertheless, the AWE Group concluded that for many paths to teleseismic distances, Earth is transparent for P signals and this provides a window through which source differences will be most clearly seen. Much of the research by the Group has focused on understanding the influence of source type on P seismograms recorded at teleseismic distances. Consequently the paper concentrates on teleseismic methods of distinguishing between explosions and earthquakes.One of the most robust criteria for discriminating between earthquakes and explosions is the mb: Ms criterion which compares the amplitudes of the SP P waves as measured by the body-wave magnitude mb, and the long-period (LP: ∼0.05 Hz) Rayleigh-wave amplitude as measured by the surface-wave magnitude Ms; the P and Rayleigh waves being the main wave types used in forensic seismology. For a given Ms, the mb for explosions is larger than for most earthquakes. The criterion is difficult to apply however, at low magnitude (say mb < 4.5) and there are exceptions—earthquakes that look like explosions.A difficulty with identification criteria developed in the early days of forensic seismology was that they were in the main empirical—it was not known why they appeared to work and if there were test sites or earthquakes where they would fail. Consequently the AWE Group in cooperation with the University of Cambridge used seismogram modelling to try and understand what controls complexity of SP P seismograms, and to put the mb: Ms criterion on a theoretical basis. The results of this work show that the mb: Ms criterion is robust because several factors contribute to the separation of earthquakes and explosions. The principal reason for the separation however, is that for many orientations of the earthquake source there is at least one P nodal plane in the teleseismic window and this biases mb low. Only for earthquakes with near 45° dip-slip mechanisms where the antinode of P is in the source window is the mb:Ms criterion predicted to fail. The results from modelling are consistent with observation—in particular there are earthquakes, “anomalous events”, which look explosion-like on the mb:Ms criterion, that turn out to have mechanisms close to 45° dip-slip. Fortunately the P seismograms from such earthquakes usually show pP and sP, the reflections from the free surface of P and S waves radiated upwards. From the pP-P and sP-P times the focal depth can be estimated. So far the estimated depth of the anomalous events have turned out to be ∼20 km, too deep to be explosions.Studies show that the observation that P seismograms are more complex than predicted by simple models can be explained on the weak-signal hypothesis: the standard phases, direct P and the surface reflections, are weak because of amongst other things, the effects of the radiation pattern or obstacles on the source-to-receiver path; other non-standard arrivals then appear relatively large on the seismograms.What has come out of the modelling of P seismograms is a criterion for recognising suspicious disturbances based on simplicity rather than complexity. Simple P seismograms for earthquakes at depths of more than a few kilometres are likely to be radiated only to stations that lie in a confined range of azimuths and distances. If then, simple seismograms are recorded over a wide range of distances and particularly azimuths, it is unlikely the source is an earthquake at depth. It is possible to test this using the relative amplitudes of direct P and later arrivals that might be surface reflections. The procedure is to use only the simple P seismograms on the assumption that whereas the propagation through Earth may make a signal more complex it is unlikely to make it simpler. From the amplitude of the coda of these seismograms, bounds can be placed on the size of possible pP and sP. The relative-amplitude method is then used to search for orientations of the earthquake source that are compatible with the observations. If no such orientations are found the source must be shallow so that any surface reflections merge with direct P, and hence could be an explosion.The IMS when completed will be a global network of 321 monitoring stations, including 170 seismological stations principally to detect the seismic waves from earthquakes and underground explosions. The IMS will also have stations with hydrophones, microbarographs and radionuclide detectors to detect explosions in the oceans and the atmosphere and any isotopes in the air characteristic of a nuclear test. The Global Communications Infrastructure provides communications between the IMS stations and the International Data Centre (IDC), Vienna, where the recordings from the monitoring stations is collected, collated, and analysed. The IDC issues bulletins listing geophysical disturbances, to States Signatories to the CTBT.The assessment of the disturbances to decide whether any are possible explosions, is a task for State Signatories. For each Signatory to do a detailed analysis of all disturbances would be expensive and time consuming. Fortunately many disturbances can be readily identified as earthquakes and removed from consideration-a process referred to as “event screening”. For example, many earthquakes with epicentres over the oceans can be distinguished from underwater explosions, because an explosion signal is of much higher frequency than that of earthquakes that occur below the ocean bed. Further, many earthquakes could clearly be identified at the IDC on the mb: Ms criterion, but there is a difficulty-how to set the decision line. The possibility has to be very small that an explosion will be classed by mistake, as an earthquake. The decision line has therefore to be set conservatively, consequently with routine application of current screening criteria, only about 50% of earthquakes can be positively identified as such.Various methods have been proposed whereby a “determined violator” could avoid the provisions of a CTBT and carry out a test that would be either undetected or detected but not identified as an explosion. The increase in complexity and cost of such a test should discourage any State from attempting it. In addition, there is always the possibility of some stations detecting the test, the test being identified as suspicious, and so subject to an OSI. With time as the IMS becomes more efficient and effective it will act increasingly to deter anyone contemplating a clandestine test, from going ahead.What has emerged is several robust criteria. The criteria include: location, which when combined with hydro-acoustic data can identify earthquakes under the sea; mb: Ms; and depth of focus. More detailed study is required of any remaining seismic disturbance that is regarded as suspicious: for example, is close to a site where nuclear tests have been carried out in the past. Any disturbance that is shown to be explosion-like, may be the subject of an OSI.One surprise is how little plate tectonics has contributed to resolving problems in forensic seismology. Much of the evidence for plate tectonics comes from seismological studies so it would be expected that the implications for Earth structure arising from forensic seismology would be consistent with plate-tectonic models. So far the AWE Group have found little synergy between plate tectonics and forensic seismology.It is to be hoped that the large volume of seismological data of high quality now being collected by the IMS and the increasing number of digital stations, will result in a revised Earth model that is consistent with the findings of forensic seismology, so that a future review of progress will show that the forensic seismologist can draw on this model in attempting to interpret apparently anomalous seismograms.