Halite solution mining and natural gas production in the west of the province of Fryslân in the Netherlands cause subsidence significantly exceeding original predictions. Subsidence at the centre of the salt subsidence bowl reached 33 cm in 2015 while only 7 cm had been predicted in the 1995 forecast. Maximum subsidence above the nearby Harlingen gas field was around 33 cm in 2015 compared to 10 cm in the 2003 forecast for the end of field life. In addition, subsidence accelerated over time. From the regulator's point of view, the development of the discrepancies was unacceptable and led to an early reassessment of the salt mining project and to suspension of the gas production by the operator in 2008. Extensive research into the causes of the exceedances was able to provide a proper explanation for both occurrences. For the salt solution mining, cavern convergence rates at the in-situ stresses and temperatures at the depth of the project are much higher than initially estimated. This leads to a different production mechanism (squeeze mining), which gives much more subsidence. After convergence and subsidence modelling were corrected for this in 1998, predicted and observed subsidence are in much better agreement. The additional and accelerating subsidence above the Harlingen gas field can only be explained by pore-collapse of the gas-bearing reservoir chalk. During the laboratory compaction tests used for the original subsidence predictions, pore collapse only occurred at stress levels beyond those possible in-situ. The explanation for the inconsistency was found to be the strong impact of loading rate on the pore-collapse stress level. The applicability of an existing rate type compaction model for the Harlingen chalk was confirmed by new variable loading rate laboratory experiments. Using the model to translate the laboratory measured pore-collapse stresses into values applicable under field conditions, a much better agreement with the observed field behaviour was obtained. The Harlingen case thus provides further evidence that the large influence of loading rate on the chalk pore collapse stress seen during laboratory experiments applies down to field loading rates and that corrections for this need to be applied in compaction and subsidence forecasts.@en

The Wadden Sea is a shallow tidal sea in the north of the Netherlands where gas production is ongoing since 1986. Due to the sensitive nature of this area, gas extraction induced subsidence must remain within the "effective subsidence capacity" for the two tidal basins (Pinkegat and Zoutkamperlaag) affected. We present a probabilistic method to monitor the "effective subsidence capacity" and ensure that subsidence is below the long term (18.6 years) volumetric rate for relative sea level rise that can be accommodated by the tidal basins without environmental harm. The role of sedimentation volume rate, relative sea level rise and subsidence volume rate due to gas depletion are taken into account including their uncertainties. The probability of exceeding the acceptable subsidence limit for the period 2012 to 2050 is 2.8% for the tidal basin called Zoutkamperlaag and 1% for the tidal basin of Pinkegat for climate scenarios that fit the current relative sea level rise observations on the Dutch coast. The values are shown to be dominated by the effect of relative sea level rise, and not due to subsidence induced by gas depletion in the Wadden Sea. To current knowledge no harm is done to nature.@en

In the Netherlands, seismicity is induced by the reactivation of faults because of the extraction of gas. The Dutch mining law requires a seismic-risk assessment as part of the license application process. For this purpose, a risk-assessment guideline has been developed over the past decade. The guideline contains three assessment levels. At the first level, a screening occurs to assess the potential of inducing seismicity. On the basis of three key parameters and an analysis of the maximum potential magnitude, each field can be classified for induced-seismicity risk prior to the onset of production. For fields with a low seismicity potential, the existing national monitoring network suffices. At the second level, for fields with medium and high seismicity potential, a qualitative assessment of hazard and risk is required based on a risk-matrix approach. The large Groningen gas field is considered a field with high seismic risk requiring a level 3 assessment. For such fields, a probabilistic seismic-risk assessment and risk-management plan are required. The risk assessment requires special attention because most of the seismic risk is associated with low-probability events that can induce large ground accelerations.@en

Reliable prediction of the induced subsidence resulting from gas production is important for a near sea level country like the Netherlands. Without the protection of dunes, dikes and pumping, large parts of the country would be flooded. The predicted sea-level rise from global warming increases the challenge to design proper mitigation measures. Water management problems from gas production induced subsidence can be prevented if measures to counter its adverse effects are taken timely. This requires reliable subsidence predictions, which is a major challenge. Since the 1960's a number of large, multi-decade gas production projects were started in the Netherlands. Extensive, well-documented subsidence prediction and monitoring technologies were applied. Nevertheless predicted subsidence at the end of the Groningen field production period (for the centre of the bowl) went from 100 cm in 1971 to 77 cm in 1973 and then to 30 cm in 1977. In 1984 the prediction went up again to 65 cm, down to 36 cm in 1990 and then via 38 cm (1995) and 42 cm (2005) to 47 cm in 2010 and 49 cm in 2013. Such changes can have large implications for the planning of water management measures. Until 1991, when the first event was registered, production induced seismicity was not observed nor expected for the Groningen field. Thereafter the number of observed events rose from 5 to 10 per year during the 1990's to well over a hundred in 2013. The anticipated maximum likely magnitude rose from an initial value of less than 3.0 to a value of 3.3 in 1993 and then to 3.9 in 2006. The strongest tremor to date occurred near the village of Huizinge in August 2012. It had a magnitude of 3.6, caused significant damage and triggered the regulator into an independent investigation. Late 2012 it became clear that significantly larger magnitudes cannot be excluded and that values up to magnitude 5.0 cannot be ruled out. As a consequence the regulator advised early 2013 to lower Groningen gas production by as much and as fast as realistically possible. Before taking such a decision, the Minister of Economic Affairs requested further studies. The results became available early 2014 and led to the government decision to lower gas production in the earthquake prone central area of the field by 80 % for the next three~years. In addition further investigations and a program to strengthen houses and infrastructure were started. Important lessons have been learned from the studies carried out to date. It is now realised that uncertainties in predicted subsidence and seismicity are much larger than previously recognised. Compaction, subsidence and seismicity are strongly interlinked and relate in a non-linear way to production and pressure drop. The latest studies by the operator suggest that seismic hazard in Groningen is largely determined by tremors with magnitudes between 4.5 and 5.0 even at an annual probability of occurrence of less than 1 %. And that subsidence in 2080 in the centre of the bowl could be anywhere between 50 and 70 cm. Initial evaluations by the regulator indicate similar numbers and suggest that the present seismic risk is comparable to Dutch flooding risks. Different models and parameters can be used to describe the subsidence and seismicity observed so far. The choice of compaction and seismicity models and their parameters has a large impact on the calculated future subsidence (rates), seismic activity and on the predicted response to changes in gas production. In addition there are considerable uncertainties in the ground motions resulting from an earthquake of a given magnitude and in the expected response of buildings and infrastructure. As a result uncertainties in subsidence and seismicity become very large for periods more than three to five years into the future. To counter this a control loop based on interactive modelling, measurements and repeated calibration will be used. Over the coming years, the effect of the production reduction in the centre of the field on subsidence and seismicity will be studied in detail in an effort to improve understanding and thereby reduce prediction uncertainties. First indications are that the reduction has led to a drop in subsidence rate and seismicity within a period of a few months. This suggests that the system can be controlled and regulated. If this is the case, the integrated loop of predicting, monitoring and updating in combination with mitigation measures can be applied to keep subsidence (rate) and induced seismicity within limits. To be able to do so, the operator has extended the field-monitoring network. It now includes PS-InSAR and GPS stations for semi-permanent subsidence monitoring in addition to a traditional network of levelling benchmarks. For the seismic monitoring 60 shallow (200 m) borehole seismometers, 60 + accelerometers and two permanent downhole seismic arrays at reservoir level will be added. Scenario's spanning the range of parameter and model uncertainties will be generated to calculate possible subsidence and seismicity outcomes. The probability of each scenario will be updated over time through confrontation with the measurements as they become available. At regular intervals the subsidence prediction and the seismic risk will be re-evaluated. Further mitigation measures, possibly including further production measures will need to be taken if probabilities indicate unacceptable risks.@en

Subsidence caused by salt mining operations is a sensitive issue in The Netherlands. An extensive legal framework is in place to ensure a high probability that such subsidence will stay within predefined limits. The key question is: how much subsidence is acceptable and at which rate? And: how can it be reliably assured that (future) subsidence will stay within these limits? In order to manage and constrain subsidence (rate) within these limits the concept of ‘effective subsidence capacity’ has been introduced. The ‘effective subsidence capacity’ is the maximum human-induced subsidence that the affected area can robustly sustain. On land limits on ‘effective subsidence capacity’ are dictated by the capabilities of the water boards to manage the water table in the subsiding area in order to prevent flooding of the polders as well as to restrain increasing salinity of shallow subsurface aquifers. For salt solution mining underneath the wetlands of the Wadden Sea area in the Netherlands, the limiting factor for the ‘effective subsidence capacity’ is the area-averaged rate of subsidence. This limit for the tidal basin system is determined by the volume of sediment that over a lunar cycle period of 18.6 years can be transported and deposited by nature into the tidal basin system where the subsidence may occur. Taking into account sea level rise and natural shallow compaction (together known as the relative sea level rise), the effective subsidence capacity is the maximum area-averaged subsidence rate available for planning of human activities without damaging the natural environment. It is obtained by subtracting the area-averaged subsidence rate ‘consumed’ by relative sea level rise from the total long-term acceptable area-averaged subsidence rate limit. Monitoring and management schemes become of increasing importance to ensure that predicted and actual subsidence (rates) stay within the limit of acceptable subsidence (rates). The schemes contain the validation of models, assessment of position relative to subsidence limits, as well as mitigation actions necessary to reduce subsidence (rate) as soon as it cannot be guaranteed anymore that the imposed limits will not be exceeded. A GPS based early warning system is used for early detection of unexpected behaviour. Regular communication keeps the authorities and the general public informed.@en

A higher than predicted annual frequency of earthquakes with a magnitude equal or above 3.0 has led to an independent assessment by State Supervision of Mines (SSM) of the available Groningen earthquake data and the applied analysis methods. The occurrence of the highest magnitude earthquake thus far, near Huizinge in August 2012, with a moment magnitude of 3.6 gave further impetus. In the re-assessment SSM has limited the analysis to the earthquake data from the Groningen field only. @en

The Roswinkel gas field in the northeastern part of the Netherlands has been in production between 1980 and 2005. Located at about 2100 m depth, it is a severely faulted anticlinal structure, constituting up to 30 reservoir compartments. Due to the complicated nature of this field, there are large uncertainties in both the fault transmissibilities and the strength of the connected aquifer. Consequently, there is a possibility of undepleted compartments in the reservoir. Pressure depletion due to gas production results in compaction of the reservoir sandstones leading to surface subsidence. The gas production in Roswinkel has induced subsidence of approximately 17 cm above the centre of the field. The subsidence at any point on the surface is a result of compaction over a large area within the reservoir. We estimated the compaction in the reservoir using subsidence data in order to reduce the uncertainties in fault transmissibility and aquifer connection. We employed a previously developed Bayesian inversion method in which prior knowledge is combined with observations. The prior knowledge on the compaction and the associated uncertainties were generated by Monte Carlo simulations of the reservoir in which the fault transmissibilities were varied. In the mean time the geological reality was maintained and the production history was honored. The average prior compaction field is a relatively smooth field extending well into the aquifer, with a typical uncertainty of 40%. Our inversion results show a reservoir in which certain large faults are dividing the reservoir in compartments containing different pressure histories. Furthermore, the aquifer activity appeared to be much weaker than the average prior knowledge suggested. The posterior uncertainty of the compaction levels was reduced to about 10%. Our study demonstrates that a carefully executed inversion exercise can considerably reduce uncertainties, thus giving scope for the identification of undepleted compartments in the reservoir.@en

Subsidence caused by extraction of hydrocarbons and solution salt mining is a sensitive issue in the Netherlands. An extensive legal, technical and organisational framework is in place to ensure a high probability that such subsidence will stay within predefined limits. The key question is: how much subsidence is acceptable and at which rate? And: how can it be reliably assured that (future) subsidence will stay within these limits? To address the issue for the Wadden Sea area, the concept of ‘effective subsidence capacity’ is used. To determine the ‘effective subsidence capacity’, the maximum volumetric rate of relative sea-level rise, that can be accommodated in the long term, without environmental harm, is established first. The volume of sediment that can be transported and deposited by nature into the tidal basin where the subsidence is expected, ultimately determines this ‘limit of acceptable average subsidence rate’. The capability of the tidal basins to ‘capture’ sediment over the lunar cycle period of 18.6 years is the overall rate-determining step. Effective subsidence capacity is then the maximum average subsidence rate available for planning of human activities. It is obtained by subtracting the subsidence volume rate ‘consumed’ by natural relative subsidence in the area (sealevel rise plus natural shallow compaction) from the total long-term acceptable subsidence volume rate limit. In the operational procedure for mining companies, six-years-average expectation values of subsidence rates are used to calculate the maximum allowable production rates. This is done under the provision that production will be reduced or halted if the expected or actual subsidence rate (natural + man induced) is likely to exceed the limit of acceptable subsidence. Monitoring and management schemes ensure that predicted (6-year average) and actual (18.6-year average) subsidence rates stay within the limit of acceptable subsidence rate and that no damage is caused to the protected nature. A GPS based early warning system is used for early detection of unexpected behaviour. In support of SSM (State Supervision of Mines, the government regulator), TNO-AGE (an independent government advisory group) applies an independent Bayesian statistical analysis of all data, as they become available, to calculate the probability of scenario's under which future subsidence will exceed the defined limits. It is external to the operator's annual measurement and control loop and ensures that preventive actions can be taken in time in case such scenarios emerge. Regular communication keeps the authorities and the general public informed on the use of the effective subsidence capacity to demonstrate that the actual average subsidence rate stays strictly within the defined bounds and that, from a scientific point of view, there is no reasonable doubt that damage to the tidal system will not occur now or in the future.@en

Subsidence can be induced by hydrocarbon production, due to the decrease in pore pressure in the reservoir which causes the reservoir to compact. The subsidence at any point on the surface is a result of the compaction over a large area of the reservoir. The properties of the reservoir and thus the compaction are uncertain. Therefore, an inversion is needed to constrain the knowledge about compaction in the reservoir with the use of subsidence data. We applied a previously developed linearized subsidence inversion method to the Roswinkel gas field. This field is situated in the northeastern part of The Netherlands. The Roswinkel field has been in production between 1980 and 2005. It is a complicated anticlinal structure with many faults in two major directions, dividing the reservoir in up to 30 reservoir compartments. Prior geomechanical modelling of the Roswinkel field revealed deviations in the measured subsidence from the predicted ideal elliptical shape of the subsidence bowl, possibly indicating partly undepleted compartments in this reservoir. The prior knowledge of the reservoir was quantified using Monte Carlo simulations. The degree of compartmentalization was varied by perturbing the fault transmissibilities. The prior knowledge, contained in the simulation models, includes the expected compaction field, the standard deviations, and the spatial and temporal correlations between the model elements. Our inversion study on Roswinkel demonstrates our ability to constrain the prior uncertainty of the reservoir model. The inversion exercise gave a clear adaptation of the prior compaction field from a smooth, extended field to a sharply bounded field with internal structure. This means that identification of gas compartments and fault properties by inversion of subsidence measurements is feasible. The prior knowledge is the critical part in the inversion exercise; the most critical steps seem to be the geological and the geodetic analysis. For the latter, new data like space-geodetic observations might help improve the analysis. However, we expect the largest improvement to come from integrating inversion steps, implying that all the different data are taken into account simultaneously.@en

In an attempt to derive more information on the parameters driving compaction, this paper explores the feasibility of a method utilizing data on compaction-induced subsidence. We commence by using a Bayesian inversion scheme to infer the reservoir compaction from subsidence observations. The method’s strength is that it incorporates all the spatial and temporal correlations imposed by the geology and reservoir data. Subsequently, the contributions of the driving parameters are unravelled. We apply the approach to a synthetic model of an upscaled gas field in the northern Netherlands. We find that the inversion procedure leads to coupling between the driving parameters, as it does not discriminate between the individual contributions to the compaction. The provisional assessment of the parameter values shows that, in order to identify adequate estimate ranges for the driving parameters, a proper parameter estimation procedure (Markov Chain Monte Carlo, data assimilation) is necessary.@en

Understanding and predicting surface movement is important both technically and for social reasons. The shallow processes contributing to subsidence include construction works, peat oxidation, clay compaction, and groundwater withdrawal; deep causes are hydrocarbon and salt production. We describe an inversion procedure we have devised to disentangle the deep and shallow causes of surface movement. It employs a Bayesian inversion scheme, using forward models and other ‘a priori’ information about shallow and deep compaction. Parameter estimation thus takes place at two different depths, thereby disentangling the deep and shallow compaction processes responsible for surface movement. The uncertainty in the surface measurements and ‘a priori’ estimates is naturally incorporated. Furthermore, spatial and temporal correlations can be taken into account through inclusion of the covariance matrix. The inversion scheme is demonstrated for two synthetic cases. The first combines a compacting gas field and a compacting shallow peat layer. We demonstrate that assumptions on the shape of the subsidence bowl are not necessary. We also show how neglecting either deep or shallow causes of subsidence can produce spurious results. The advantage of using the ‘a priori’ estimates of the compaction and the covariance matrix obtained by Monte Carlo simulations is demonstrated with a second synthetic example involving two polders and different depths of their water table. A robust solution is obtained for each polder unit, while a simpler (and faster) ‘a priori’ estimate based on the expected average clay thickness fails to reproduce the actual compaction. Monte Carlo simulations can also be applied to compaction in depleting gas reservoirs. Information on spatial correlations is often available, even when the absolute values of the ‘a priori’ compaction data are quite uncertain. Explicitly incorporating such ‘a priori’ known spatial correlations improves the result significantly.@en

The surface movement in the Krimpenerwaard polder in The Netherlands results from primary or hydrodynamic settlement/swelling, secondary or creep settlement/swelling, and peat oxidation. We used surface movement measurements in a Bayesian inversion scheme to disentangle the contribution of these three processes to the subsidence. The prior information, including spatial correlations, appeared to be crucial in our procedure. This prior information was derived from geological modeling incorporating the most important uncertainties. The inversion procedure allowed us to quantify the contributions of the three processes with unprecedented accuracy. Surface rise in the data was related to swelling of the clay layers, even though swelling was considered infeasible in the prior information. Despite this, the irreversible nature of peat oxidation was preserved. The improved subsurface description offers prospects for identification of incorrect information and for better assessments of the effects of water management.@en

One of the limitations of InSAR is that it is only capa-ble of measuring a 3D projection of a real deformation vector on the radar line of sight. Therefore it is not possi-ble to retrieve the full displacement vector from a single InSAR measurement. The optimal solution for this limi-tation is a combination of InSAR measurements from dif-ferent imaging geometries. However, this solution is not applicable in areas where InSAR data are available in one particular geometry only. In this paper, a new approach will be discussed for 3D decomposition of InSAR defor-mation measurements for the case of subsidence. We use the hypothesis of a physical relation between horizontal displacement and vertical deformation. Using this hy-pothesis, we propose an iterative strategy for 3D decom-position of InSAR subsidence measurements. The pro-posed approach is tested on the PSI results of a complex subsidence field in Friesland, the Netherlands. Finally, the results are validated by comparison with available lev-eling data.@en

We introduce a novel, time-dependent inversion scheme for resolving temporal reservoir pressure drop from surface subsidence observations (from leveling or GPS data, InSAR, tiltmeter monitoring) in a single procedure. The theory is able to accommodate both the absence of surface subsidence estimates at sites at one or more epochs as well as the introduction of new sites at any arbitrary epoch. Thus, all observation sites with measurements from at least two epochs are utilized. The method uses both the prior model covariance matrix and the data covariance matrix, which incorporates the spatial and temporal correlations between model parameters and data, respectively. The incorporation of the model covariance implicitly guarantees smoothness of the model estimate, while maintaining specific geological features like sharp boundaries. Taking these relations into account through the model covariance matrix enhances the influence of the data on the inverted model estimate. This leads to a better defined and interpretable model estimate. The time-dependent aspect of the method yields a better constrained model estimate and makes it possible to identify non-linear acceleration or delay in reservoir compaction. The method is validated by a synthetic case study based on an existing gas reservoir with a highly variable transmissibility at the free water level. The prior model covariance matrix is based on a Monte Carlo simulation of the geological uncertainty in the transmissibility.@en

Surface subsidence can have major repercussions. A classic example is the seabed above the Ekofisk field, offshore Norway, where excessive subsidence made it necessary to raise the drilling platform by 6 m in the 1980s. On land, subsidence may significantly increase the risk of damage to buildings and infrastructure. But, there is more to say about subsidence. Observations of subsidence can also give us a better handle on the subsurface processes like compaction behaviour of a reservoir, and can tell us more about the reservoir itself: about undrained compartments or the strength of the aquifer. However, to get the information from subsidence data, you have to carefully follow an inver-sion procedure. This inversion exercise is a big challenge, in which all the available knowledge has to be used to the fullest possible extent. In this article we report on the work we have recently performed in this area. @en

We have estimated the surface deformation field of the southwestern U.S. deformation zone in terms of the velocity gradient field and surface creep simultaneously by inversion of 497 geodetic velocities. The model shows aseismic fault motion consistent with aseismic creep measurements and a sense of motion consistent with geological observations. We deduce that our surface deformation field shows distributed deformation in a zone around the faults containing shear strains and rotations. The eastern California shear zone acts as a distinct fault zone bounded by more rigid blocks. The faults within the zone partition the shear motion, while right-lateral shear strain rates and clockwise rotations are concentrated between the bounding faults. In the same way, the San Jacinto and southern San Andreas faults act as bounding faults of a fault zone. The Mojave Desert is dominated by right-lateral shear, whereas the western Transverse Ranges (WTR) is subjected to contraction. We find significant localization of deformation east of the San Andreas fault between the Transverse Ranges and the San Francisco Bay. We attribute this to a relative rigidity contrast across the fault of ∼1.8. Finally, a moment deficit analysis shows an accumulation of moment deficit between 1973 and 2000 corresponding to a Mw = 6.1–6.3 earthquake along the San Andreas fault just north of the Big Bend, around the Imperial and southern San Andreas faults, and in the San Francisco Bay area along the Hayward and southern Calaveras faults.@en

From a joint analysis of GPS and InSAR data we have determined the kinematic coseismic surface deformation of the 1999 August 17, Izmit (Turkey) earthquake in terms of strain, rotation and fault slip. The fault slip contribution shows two distinct peaks: one of ∼4 m of slip at Gölcük, and a second of ∼2.9 m slip near Sapanca Lake. The strain field portrays four distinct quadrants reflecting the earthquake focal mechanism. The transition between the quadrants is not centred on the epicentre of the event, but shifted eastwards north of the fault and westwards south of the fault. This shift is the result of a two-stage source rupture process caused by the step-over features in the fault geometry. This rupture process also induced a distinct asymmetry in the displacement field across the fault. We obtain left-lateral shear strains along the Sakarya segment that is the result of a subsequent source nucleating at the Akyazi Gap inducing failure on the easternmost segments. Strong interaction is also observed from a consecutive source near Hersek. Finally, we deduce that the Izmit earthquake has released most of the strain that has accmulated since the last main event on this stretch of the North Anatolian fault in 1719.@en

We have determined the present-day surface deformation of Taiwan by computing the velocity gradient field and fault slip from 143 GPS velocity vectors. In southern Taiwan the derived strain and rotation rates and fault slips are indicative of lateral extrusion toward the south. In northern Taiwan we infer the onset of gravitational collapse which is induced by the on-land extension of the Okinawa Trough. In the eastern Central Range the observed inverted NW-SE extension is consistent with geological observations and high heat flow measurements. This could be the result of exhumation of crustal material. The model further shows a significant decrease in slip rate northward along the Longitudinal Valley fault at 23.7°N. The northern Coastal Range shows high strain rates and two oppositely rotating blocks. By combining the surface deformation model with seismicity data and seismic tomography we are able to propose a coherent model for the present-day tectonic activity. Both seismicity and tomography show further evidence for active, southward propagating exhumation of a crustal slice in the eastern Central Range. Offshore east Taiwan we deduce strong evidence of a southward propagating crustal tear fault, accommodating most of the Philippine Sea Plate-Eurasian Plate convergence. The tear is the crustal response to incipient northwestward subduction of the Philippine Sea Plate. Thus the Ryukyu Trench is bending southward becoming almost perpendicular to the convergence direction, while subduction of the Philippine Sea Plate continues. In this setting a sudden rapid southward propagation of the afore mentioned tear is conceivable.@en

The spatial slip distribution of the August 17, 1999, Izmit (Turkey) earthquake has previously been determined from both geodetic and seismological data. Though the models derived agree on a broad scale, they are significantly different in detail. These differences could be due to the inversion techniques applied and/or additional constraints implemented and/or be due to poor resolution. It is also conceivable that the relative agreement at larger scales results in part from a resolution artifact common to all models. To investigate this we perform a resolution analysis of fault slip models based on the inversion of surface displacement data. Assuming the theory of elastic dislocations in a half-space and adopting a parameterization for which model predictions are capable of fitting the spatial variations of the data, the inverse problem proves to be intrinsically ill-conditioned.@en

The duration of each subevent of 48 earthquakes with magnitude larger than 5.5 and depth greater than 100 km was determined from stacked traces of broadband records of Global Seismograph Network stations. We fitted the source time function by one or more triangles convolved with attenuation. We found that global stacks of displacement seismograms yield reliable estimates of the rupture duration. The durations, scaled to a moment of 1019 N m, of both the subevents and the entire earthquake show a slight decrease with depth from 9 s for events at 100 km depth to about 7 s for events at 600 km depth. Assuming that the rupture velocity is a constant fraction of the shear wave speed, this decrease can be completely explained by the increase in shear velocity of 20%. In this sense, deep earthquakes are comparable to intermediate ones. For some intermediate-depth events, Vidale and Houston [1993] found durations up to twice as long. We find that almost all of their slow events have been recorded at large epicentral distances. At these distances, we conjecture that the end of the P wave train may be extended by the arrival of reflections from the D” layer.@en