Centroid moment tensor inversion of low-frequency seismic spectra using Green's functions for aspherical earth models

We present a new method for centroid moment tensor (CMT) inversion, in which we employ the Green's function computed for aspherical earth models using the Direct Solution Method. We apply this method to CMT inversion of low-frequency seismic spectra for the 1994 Bolivia and 1996 Flores Sea deep earthquakes. The estimated centroid locations agree well with those obtained by multiple-shock analyses using body-wave data. This shows that it is possible to obtain reliable CMT solutions by analyses of low-frequency seismic spectra using accurate Green's functions computed for present 3-D earth models.     

Recovering magnetic susceptibility from electromagnetic data over a one-dimensional earth

While the inversion of electromagnetic data to recover electrical conductivity has received much attention, the inversion of those data to recover magnetic susceptibility has not been fully studied. In this paper we invert frequency-domain electromagnetic (EM) data from a horizontal coplanar system to recover a 1-D distribution of magnetic susceptibility under the assumption that the electrical conductivity is known. The inversion is carried out by dividing the earth into layers of constant susceptibility and minimizing an objective function of the susceptibility subject to fitting the data. An adjoint Green's function solution is used in the calculation of sensitivities, and it is apparent that the sensitivity problem is driven by three sources. One of the sources is the scaled electric field in the layer of interest, and the other two, related to effective magnetic charges, are located at the upper and lower boundaries of the layer. These charges give rise to a frequency-independent term in the sensitivities. Because different frequencies penetrate to different depths in the earth, the EM data contain inherent information about the depth distribution of susceptibility. This contrasts with static field measurements, which can be reproduced by a surface layer of magnetization. We illustrate the effectiveness of the inversion algorithm on synthetic and field data and show also the importance of knowing the background conductivity. In practical circumstances, where there is no a priori information about conductivity distribution, a simultaneous inversion of EM data to recover both electrical conductivity and susceptibility will be required.     

Time-domain electromagnetic migration in the solution of inverse problems

Time-domain electromagnetic (TDEM) migration is based on downward extrapolation of the observed field in reverse time. In fact, the migrated EM field is the solution of the boundary-value problem for the adjoint Maxwell's equations. The important question is how this imaging technique can be related to the solution of the geoelectrical inverse problem. In this paper we introduce a new formulation of the inverse problem, based on the minimization of the residual-field energy flow through the surface or profile of observations. We demonstrate that TDEM migration can be interpreted as the first step in the solution of this specially formulated TDEM inverse problem. However, in many practical situations this first step produces a very efficient approximation to the geoelectrical model, which makes electromagnetic migration so attractive for practical applications. We demonstrate the effectiveness of this approach in inverting synthetic and practical TDEM data.     

Source investigation of a small event using empirical Green's functions and simulated annealing

We propose a two-step inversion of three-component seismograms that (1) recovers the far-field source time function at each station and (2) estimates the distribution of co-seismic slip on the fault plane for small earthquakes (magnitude 3 to 4). The empirical Green's function (EGF) method consists of finding a small earthquake located near the one we wish to study and then performing a deconvolution to remove the path, site, and instrumental effects from the main-event signal.
The deconvolution between the two earthquakes is an unstable procedure: we have therefore developed a simulated annealing technique to recover a stable and positive source time function (STF) in the time domain at each station with an estimation of uncertainties. Given a good azimuthal coverage, we can obtain information on the directivity effect as well as on the rupture process. We propose an inversion method by simulated annealing using the STF to recover the distribution of slip on the fault plane with a constant rupture-velocity model. This method permits estimation of physical quantities on the fault plane, as well as possible identification of the real fault plane.
We apply this two-step procedure for an event of magnitude 3 recorded in the Gulf of Corinth in August 1991. A nearby event of magnitude 2 provides us with empirical Green's functions for each station. We estimate an active fault area of 0.02 to 0.15 km² and deduce a stress-drop value of 1 to 30 bar and an average slip of 0.1 to 1.6 cm. The selected fault of the main event is in good agreement with the existence of a detachment surface inferred from the tectonics of this half-graben.     

Calculating the two-dimensional magnetotelluric Jacobian in finite elements using reciprocity

To speed up the calculation of the field Jacobian for 2-D magnetoteliuric inversion using finite elements, the principle of electromagnetic reciprocity is applied. The governing relationship for the Jacobian of the field along strike is obtained by differentiating the Helmholtz equation with respect to the resistivity of each region in the finite-element mesh. The result is a similar Helmholtz equation for the Jacobian, with new sources distributed over all nodes within the parameter medium. However, according to the principle of electromagnetic reciprocity, the roles of sources and receivers are interchangeable. Utilizing reciprocity, the field values obtained from the original forward problem and for new unit sources imposed at the receivers are then utilized in the calculation of the Jacobian by simple multiplication and summation with finite-element terms at each rectangle in the mesh. For the auxiliary (across-strike) fields, the Jacobian terms are obtained by solving source vectors loaded with parabola coefficients used in the approximation to Maxwell's equations. Jacobian terms for the apparent resistivity ( p _a), the impedance phase (φ) and the vertical magnetic field ( K _zy) are then calculated utilizing the parallel- and auxiliary-field Jacobians. Comparison of Jacobian values obtained from reciprocity calculations and by differencing two forward solutions show that the reciprocity method is accurate and can be used to decrease the number of calculations required to obtain sensitivities by one to two orders of magnitude.