Nonlinear inversion of local seismic travel times for the simultaneous determination of the 3D-velocity structure and hypocentres - application to the seismic zone Vrancea

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M. Koch


A new method for solving the full nonlinear problem of simultaneous inversion for 3D structure and hypocentres (SSH method) has been developed. In comparison with the simplified linear inversion procedure of Aki and Lee (1976), the method proposed here exhibits several extensions and improvements:
   a) The seismic forward problem is solved exactly by a newly developed 3D ray tracing method. This procedure has been conceived as a shooting method. The 3D heterogeneous medium is parametrized by rectangular blocks.
   b) The full nonlinear inverse problem is solved. The method works iteratively and was conceived in terms of the Levenberg - Marquardt (LM) algorithm. In each iteration step the seismic forward problem is solved with the ray tracing procedure and a linear inversion is performed.
   c) In order to improve the stability and uniqueness of the inverse solution, a priori information on the model space may be used in the inversion process. For example, a known crustal structure may be exploited for the retrieval of the deeper lithosphere.
The SSH method has been tested on various theoretical 1D and 3D models and its capabilities and limitations are discussed. The results demonstrate the existence of a tradeoff between hypocentral depths, origin times and seismic velocity, particularly when the horizontal dimensions of the recording network are small relative to the depths of the earthquakes.  The SSH method has been applied to real earthquake data of the Vrancea region, Romania. About 50 crustal and intermediate depth events were used in the inversion process. First, the crustal events were inverted to infer the crustal structure of the region. This crustal information was then used as an a priori constraint in the inversion of the intermediate depth events. The 3D-velocity model found for the Vrancea region reduces the RMS value of the travel-time residuals from 0.5 to 0.3 s. The most essential feature of the model is a high-velocity anomaly of about 4%-6% beneath the eastern Carpathian foredeeps, extending from about 80 to 160 km depth. This appears to be in agreement with results of teleseismic studies of other authors and may be understood in terms of the plate tectonic concept proposed for the Vrancea region. Due to lack of spatial resolution and high standard errors, the results obtained above should, nevertheless, be taken with some care and have to be substantiated by further investigations with higher quality data.

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Koch, M. (1986). Nonlinear inversion of local seismic travel times for the simultaneous determination of the 3D-velocity structure and hypocentres - application to the seismic zone Vrancea. Journal of Geophysics, 56(1), 160-173. Retrieved from


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