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INVERSION OF STRONG MOTION DATA FOR SLIP ON EXTENDED FAULTS: THE CASE OF THE TWO M6.5 ICELAND EARTHQUAKES OF JUNE 2000
SANDRON, DENIS
2006-04-21
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Contributor(s)
PETRINI, RICCARDO
Abstract
Several attempts were undertaken to solve the inverse problem for the source of a particular earthquake that is to determine the spatial and temporal distribution of slip or slip rate over the fault area. The solution of ali these problems is far from trivial. lt is well known that this inverse problem is unstable and from the computational point of view, this instability is equivalent to the non uniqueness of the solution. Consequently, to obtain a definite solution of such a problem, one needs some physical constraints on the source process, in addition to the requirement of fitting the observed seismograms. In the first part of this thesis we introduce the inverse problem and the seismic source in their theoretical framework. After a brief historical excursus on source modelling, we present the mechanical principles of the tectonic earthquake source (Chap.2) and the kinematic approach to the inverse problem (Chap.3). The dynamic description of fractures, based on fracture mechanics, leads to the I boundary value problems of the dynamic theory of elasticity, which are unsolvable in generai form. The kinematic description in terms of the displacement jump vector on the fracture surface as a function of position and time is more advantageous from this point of view because in this case the most generai solution to the problem of radiation exists, permitting the inverse problem formulation. Using the representation theorem the displacement record at a station located on the earth surface can be expressed in terms of the slip distribution over a fault. Assuming that the fault is planar and that the slip direction is constant over the fault, the problem can be discretized, by dividing the fault into square cells and the source time function into steps, and it can be reduced to the system of linear equations Ax = b, where A is the matrix of the Green' s functions, b is the matrix of the re al data and x is the matrix of the unknowns slips or slip rates. W e use the simplex method of solving the linear programming problem. In mathematics, linear programming (LP) problems are optimization problems in which the objective function and the constraints are alllinear (Chap. 4). The simplex algorithm, developed by George Denting, solves LP problems by constructing an admissible solution (a set of values that satisfies the constraints) and then looking for successively higher values of the objective function until the optimum is reached. In our case the objective function is the vector of the residuals ( r = b - Ax) which is minimized following the approach of Das e Kostrov (Chap. 5). The study of the two M6.5 Iceland Earthquake of June 2000 has been the praticai application of the simplex algorithm. We invert observed records acquired by a local strong-motion network. We use only data from a set of rock-stations distributed uniformly around the fault. The accelerograms are filtered at 1Hz and we model about 15 sec of the signals. The phase of pre-processing has been laborious. The lack of absolute timing has been successfully overcome by estimating the propagation of P waves in a detailed structural model. After discovering that the longitudinal and transversal components as given in the ISESD database were not related to the hypocenter, we had to measure the orientation of the strong motion instruments to derive the correct rotation of horizontal components. The number of stations for one of the two events has been reduced because part of some signals was contaminated by the triggered event occurred a few seconds after the main shock. After a short geologica! description of Iceland in generai and on SISZ in particular (Chap. 6), we present the results (Chap. 7) of the inversions for the two Events. The constraints of the positivity of the slip rates on the fault are used in all cases in this study. In some cases additional physical constraints, such us preassigning the final moment, is also used. The results obtained are appreciable both for the slip distribution, which show some similarities to the ones proposed by inverting geodetic data, and for the waveform fit. As regards the 21 June event our best result shows that the maximum in moment release is located at a depth of about 7 km. An increase in moment release follows approximately the distribution of the aftershocks along the bottom of the fault. Two additional maxima are located at the top of the fault in correspondence of the observed surface ruptures. For the 17 June event on the other hand most of the moment is released on a centrally located patch. A second maximum is located at shallow depth (3 km) roughly l km south of the southem III edge of the fault and two additional peaks in momentum are also obtained near the surface. The soundness of obtained slip inversion is best tested if the inversion results are compared with the actual distribution of slip on the fault, which is impossible for natural earthquakes. In the absence of the possibility to compare the inversion to the true solution, the only way of testing the inverse algorithm is to apply it to synthetic data obtained from the solution of a forward problem based on the representation theorem (Chap. 8). In this way we can estimate the resolution of our results. In arder to complement the study of the physical process of the source with a useful hazard assessment related application, realistic ground shaking scenarios are estimated in the SISZ. The synthetic seismograms are computed using a kinematic approach considering both a constant seismic moment distribution and the seismic moment distribution obtained from the inversions (Chap. 9).
Insegnamento
Publisher
Università degli studi di Trieste
Languages
en
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