A numerical study on the determination of the 3-D structure of the lithosphere by linear and non-linear inversion of teleseismic travel times

Abstract

This paper gives the essential results of numerical simulations on the stability, uniqueness and reliability of the solution for the 3-D seismic inverse problem for the determination of lateral velocity heterogeneities in the lithosphere. The starting point of the investigations is the well known and widely used 3-D inverse method of Aki, Christoffersson & Husebye (ACH method) for the inversion of teleseismic travel times. There are several approximations inherent in the construction of the method which may bias considerably the inverse solution obtained. These approximations are essentially: (1) the simplified block sampling which deteriorates the spatial resolution, and (2) the neglect of the lateral refraction at the vertical block boundaries. For the examination of the inherent approximations in the ACH method an exact 3-D ray tracing program has been developed which allows the calculation of theoretical travel times in an arbitrary laterally inhomogeneous media parameterized b y rectangular blocks. The numerical computations show that approximation (1) in the ACH method does not cause a significant degradation of the quality of the model reconstructed. Nevertheless for lateral heterogeneities of about 5-6 per cent contrast a systematic underestimation of the original perturbations of about 25 per cent is encountered. For remedy a non-linear inverse method has been developed which is based on the Levenberg-Marquardt (LM) algorithm. The computations with the LM method show that the systematic underestimate in the linear ACH method can be removed substantially. For investigating the statistical errors a non-linear F-test has been used which proves to give more conservative and reliable confidence regions than the formulae generally used for the calculation of the covariance of the inverse solution. On the other hand the confidence regions demonstrate also that non-linear inversion gives only a significant improvement with 95 per cent certainty if the statistical errors in the arrival-time data do not exceed 0.1-0.2 s.

Non-linear optimization for seismic traveltime tomography

“…This view has already been taken by a number of researchers, such as Koch (1985) and Nolet (1987b). A possible approach to measure this quantity is the non-linear least-squares technique; solving the problem then amounts to minimizing the least-squares norm of the misfit.…”

Theory and Observations - Seismic Tomography and Inverse Methods

“…For regions with higher-amplitude anomalies, a nonlinear solution could be significantly different. Early efforts at nonlinear teleseismic inversion were made by Thomson and Gubbins (1982), Koch (1985), and Nakanishi and Yamaguchi (1986). More recently, Weiland et al (1995) and VanDecar et al (1995) developed nonlinear algorithms for teleseismic tomography and applied them to Long Valley Caldera, California, and eastern Brazil, respectively.…”

Simultaneous Inversion For 3-D Crustal Structure and Hypocentres Including Direct, Refracted and Reflected Phases-Iii. Application to the Southern Rhine Graben Seismic Region, Germany

“…This means that the mimima of s(x,) are sufficiently deep and narrow to allow a discrimination between perturbed models; i.e. are able to delimit approximate confidence intervals in the model space (cf Koch 1985). For most of the structurally interesting velocity anomalies of the previous section, these intervals can be quantified as about *20 per cent of the computed velocity anomaly value.…”