After removing the instrument response, we notice that the horizontal components of these records are generally noisy, presumably due to the moderate magnitude and normal faulting focal mechanism. Thus we limit our attention to only the vertical components. We selected six broad-band P waves, which has been bandpass filtered from 0. These waveforms are aligned by the first arriving P wave; the alignment was calibrated using the M w 5. We also selected 28 Rayleigh waves, which were bandpass filtered from 0. A representative slip model based on this seismic data set is shown in Fig. The total seismic moment of Model I is 3.
This depth discrepancy might explain the difference in total seismic moments of these two solutions. Comparison of teleseismic P waveforms black and synthetic seismograms red of Model I. The data and synthetics have been bandpass filtered from 0. The value above the beginning of each trace is the source azimuth and below is the epicentral distance in degrees. Comparison of long period 4—6 mHz Rayleigh waves and synthetic seismograms of Model I. The peak displacement of the observation in meter is indicated above the end of each trace, which is used to normalize both data and the corresponding synthetic seismogram.
The red star indicates the hypocentre. The colour and the white arrows denote the slip amplitude and direction. The contours show the rupture initiation time. Their model features two high slip regions. The second, and dominant, high-slip patch is located 8.
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Model I is consistent with their result in along strike distribution, though the two high slip patches in Model I are connected. The second high-slip patch spans a large downdip distance range from 5. This is probably caused by the fact that we have used longer durations for the strong motion records inside basin. Second, we constrain a slip model using geodetic data only. Thirty-six are daily samples at permanent GPS sites. Others were collected at campaign sites.
Radar acquisitions covering the L'Aquila region before and after the earthquake are also available. As shown in Fig. See text for details. Note that the observed LOS displacement d might be represented as the summation of the true ground deformation d g and noise n , which is caused by the unwrapped data process, inaccurate digital elevation models DEM , and error in satellite orbits and atmospheric perturbation, etc.
Here, x 0 , y 0 denotes the centre of image. We estimate these parameters simultaneously during the inversion. The least square average residual is 0. They are small in compared with original range of LOS displacements Fig. Model II has a total seismic moment of 3. It can be seen that the slip Fig.
The centroid depth inferred from this model is 6. The peak slip occurred at a depth of 5. For instance, it can be seen that the inverted slip is less than 0. The existence of discrepancies between slip models constrained with different data should not be surprising. Each data has different spatial coverage to the source. These factors lead to different spatial resolution on the fault plane. In regions where the slip cannot be fully constrained with one type of data, inversion regularization, such as the Laplace smoothing constraint mentioned above, dominate and adjust the inverted slip distribution accordingly.
Therefore, unless the spatial resolutions of different data sets are exactly same, the differences between inverted models are inevitable. For L'Aquila earthquake the coseismic deformation that excited the seismic waves is not exactly the same as the deformation that produced geodetic observations. In contrast, the GPS daily solutions included all deformations within the first day. These differences are presumably due to the post-seismic deformation. InSAR data reflects the pre-seismic deformation from April 27 and April 6 as well as the post-seismic deformation from April 6 to April While the pre-seismic deformation might not be significant, the post-seismic deformation within the first a few days could surely be one of important causes of large residuals shown in Fig.
The fact that coseismic geodetic observations are significantly contaminated by the post-seismic deformation makes it difficult to improve the existing coseismic model i. Model I by further including the geodetic data. Currently, there are two conventional strategies to conduct inversions with joint seismic and geodetic data sets. The main challenge in applying this approach is how to properly choose these weights.
In this approach the geodetic data are inverted first. The results include both the slip distribution, its variance and most importantly the spatial resolution mapped onto the fault. However, if the geodetic data include significant contributions from post-seismic deformation, the constraints on the inversion of the seismic data are not appropriate.
The first approach, however, could be used after adopting a special inverse strategy as discussed next. Note that our goal is to improve the inverted coseismic model on the fault areas where additional geodetic data are consistent with seismic data but to limit the influence of geodetic data on the fault areas where seismic and geodetic data in conflict. Here we have assumed that the contamination to the geodetic data due to the crustal deformation occurring before the earthquake is not significant. We further assume that the deformation associated with the coseismic and post-seismic periods is caused by slip on the same fault plane.
During the inversion, our target model is then composed of the slip on two identical fault planes. So this slip is the one, which generates the seismic waves as well as some part of the static deformation. It does not generate seismic waves but affects the static measurements. We invert the slip distribution on these two planes simultaneously using both seismic and geodetic data. To stabilize the inversion, we apply the same Laplace smoothing constraint to the slip on both fault planes. However, we impose no a priori correlations between the slip on the two faults. There is also no constraint on the total seismic moment.
We have applied this approach to study the L'Aquila earthquake. A noise-free check-board test is given in Fig. But the spatial resolution becomes poorer for the deeper subfaults. It is important to note that the non-uniqueness of the non-linear inversion can be an issue particularly if we add even more degrees of freedom. Although we increase the number of data by combining seismic and static data sets, the non-uniqueness of the problem remains. Thus one has to be careful about overinterpreting results. Slip distributions and moment rate function of Model III.
The colour and the white arrows denote the slip amplitude and slip direction. Numbers on contours in a show the rupture initiation time. In each snapshot, the black circle denotes the location of rupture front at end of time window if the rupture velocity is 2. The dashed white ovals roughly indicate the regions with over 0. The least square average residuals are 0. So it is not surprising that the slip distributions of Model II Fig. The fits to the strong motion waveforms become negligibly worse than Model I.
Considering the fact that InSAR and GPS measurements locate above this fault patch and there is no close strong motion station, the fault slip then might be less well constrained by seismic data than by geodetic data. As the slip of this fault patch shall be constrained by either the geodetic data right above or the nearby five above-fault strong motion stations, the discrepancy between Model I and II reflects the conflict between seismic and geodetic data.
The inverted peak slip in this asperity is 0. Most of seismic moment occurred during the failure of this asperity. The inverted peak slip is 0. The accumulated area of subfaults with more than 0. The average slip within this region is 0. The red line in Fig. The moment rate function starts with minor amount of moment release in the first 0. We identify three local maximums in the moment rate at 2. As the snapshots shown in Fig. This rupture produced the first pulse in moment rate function and apparently ceased at about 3. Rupture then propagated along the strike when at about 3.
This period corresponds to the second pulse in the moment rate function Fig. The second and larger asperity failed at about 4. They speculated that this difference can be partially accounted by the velocity structure, i. However, as described above, the apparently slower rupture velocity in along strike direction was more likely caused by the spatial heterogeneity of fault dynamic properties, that is, the rupture propagation is slowed down when the front encounters the boundaries of asperities.
The cause of this heterogeneity is not clear yet. They then argued that a rheological barrier delayed the rupture propagation along the strike direction. However, other mechanisms, such as fault segmentation, could produce same kinematic effect. Its centroid depth of 7. The latter is defined as the ratio between the slip and rise time, which might be related with the local dynamic stress drop e. It is of interest to note that the radiated seismic energy of the L'Aquila earthquake is abnormally low. K is a function of local P and S wave velocities. Using the S -wave speed of 3.
It is not clear yet whether this is a unique characteristic associated with the L'Aquila main shock or a general feature for the normal fault earthquakes in central Apennines.
Our solution features two high slip patches with no resolvable slip in between. One of them locates on the updip and northwest sides of the hypocentre. Another patch with up to 0. The afterslip is highly concentrated. Large post-seismic deformation following the L'Aquila earthquake had been widely noticed e. However, due to the observational limitations, most previous studies focused on the afterslip occurred at least one day after this earthquake. They found that the observed time-series of post-seismic displacements can be fitted by an exponential function with best-fitting decay constants in the range of 20—40 d.
The high afterslip regions determined by these two studies are consistent. Most of the inverted afterslip occurred within ellipses A and B. In fact, as shown in Fig. The high slip patch near the peak coseismic slip is northwest of the ellipse B without any significant overlap.
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They found that the deformation after about 1. However, the hours immediately following the earthquake, the strain observation excludes the possibility that such a mechanism is the dominant one. They showed that the preceding few-hour-long transient is fully consistent with km-long unilateral diffusive slip propagation from the region with the highest coseismic slip obliquely toward the shallower portion of the fault. Their estimate of total afterslip during this period is 2. Although we did not recognize this interesting characteristic until nearly finishing the writing of this manuscript, it is the best quantitative evidence to support our solution.
Note that the first half of diffusive slip region falls in the same location as the aforementioned high afterslip patch near the region with the peak coseismic motion Fig. If assuming the rake of the diffusive direction is o as the black arrow shown in Fig. Further extending along this direction, the afterslip becomes significantly smaller Fig. As both of them are longer than the longest period used in this study s , the existence of such a rupture shall not significantly affect the fits to the long period Rayleigh waves. Hence, regardless the poor spatial resolution, our result is consistent with the slip distribution of Amoruso and Crescentini's diffusive afterslip model.
However, the strain observations are insensitive to the afterslip near hypocentre see Fig. We applied a new inversion strategy to constrain the coseismic rupture model and early post-seismic afterslip model of the L'Aquila earthquake simultaneously from the joint inversion of near-source strong ground motion recordings, P teleseismic body waves, Long period Rayleigh waves, GPS displacement vectors, and InSAR LOS displacement image. The inverted slip history reveals that the energetic rupture starting 0.
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Our estimate of coseismic scalar moment is 3. The average slip during this period is 0. The peak slip reaches about 0. The weighted average rise time and slip rate are 0. The initial updip rupture has a rupture velocity about 2. The propagation along the strike is slower on average. Our result suggests that there was significant on-fault afterslip during this period with accumulated moment about 6.
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The afterslip distribution features two high slip patches with no resolvable slip in between. One of them is relative shallower, extending from the vicinity of the region with the highest coseismic slip to the fault shallow tip. The other is deeper, locating near the hypocentre region.
Thus, the shallow slip is robust and stable; the shallow afterslip is possibly the same diffusive afterslip inferred from the strain observations. We end this article by evaluating the new inversion approach. The difference between models inferred from different data sets static and seismic can be due to the non-uniqueness of the source inversion itself.
However, in the new inversion approach, we take an advantage of this difference which can be a result of the complexity of the deformation at different time scales. In comparison with the conventional method of inverting for the parameters mixing data with different time periods to constrain the slip on a single coseismic fault, this new approach has four advantages: As we mentioned above, the fits to the geodetic data are as good as those from a model based solely on geodetic data. Using this approach, we can always obtain a model that is not only consistent with seismic data but also partially, if not fully, in agreement with geodetic data.
This then satisfies the goal to develop the coseismic slip model defined in a sense of seismic observations. Besides the post-seismic deformation, other factors, such as inaccurate velocity structure, inaccurate fault geometry, and the observational errors in seismic and geodetic data, might lead to the conflicts between two data sets as well. On the other hand, these uncertainties should become more and more manageable with the advance in seismology, for instance, high resolution local 3-D velocity structures.
We thank the valuable discussions with Professor Toshiro Tanimoto. We have conducted a series synthetic check-board tests to explore the spatial resolution of the proposed joint inversion. The result of one test is shown in Fig. We let slip amplitudes on all these patches be 0. List of publication on International Journals since Roasting and chlorine leaching of gold-bearing refractory concentrate: International Journal of Mining Science and Technology in press. Recovery of rare earths and base metals from spent nickel-metal hydride batteries by sequential sulphuric acid leaching and selective precipitations.
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