Maria Martinez

Inversion of Rayleigh wave phase and group velocities by simulated annealing

Abstract A joint inversion of regionalized phase and group velocities of fundamental mode Rayleigh waves is performed by means of a simulated annealing scheme which makes use of some thermodynamic analogies based on the Gibbs’ distribution. The correlations and the uncertainties on shear-wave velocities defining the elastic model are estimated by using a procedure based on the same thermodynamic analogies. As a relevant feature, the simulated annealing algorithm permits reducing the usual dependence of the solution on the sometimes arbitrary starting model. A shortcoming linked to the use of this procedure for solving an inversion problem is the necessity of a previous empirical determination of some parameters controlling the annealing process. With this aim, a simulation of a joint inversion of synthetic surface wave dispersion data has been performed. After that, path-averaged velocity dispersion curves corresponding to a Hercynian area of the Iberian Peninsula have been inverted to derive two possible crust and upper mantle elastic structures. Whereas, the first structure has been deduced by considering as unknown variables the shear velocities of the stratified Earth model, the second has been obtained also including the respective layer thicknesses. Both structures are compared with shear velocity and Qβ models derived by the stochastic inversion procedure in previous studies and from the same Rayleigh waves dataset. Finally, advantages and shortcomings of the inversion of phase and group velocity data by means of simulated annealing are discussed.

Anelastic structure of the Iberian Peninsula obtained from an automated regionalization algorithm and stochastic inversion

Abstract An automated regionalization of a reduced domain of the Earths surface, without a-priori seismotectonic information, and the corresponding anelastic structures are achieved by means of a sequential application of a principal component analysis, a clustering procedure and the stochastic inversion algorithm to anelastic attenuation coefficients of Rayleigh waves. Our database is formed by path-averaged attenuation coefficients derived from fundamental mode Rayleigh waves crossing the Iberian Peninsula. The wavetrains were recorded at the broad-band stations installed some years ago in the Iberian Peninsula for the ILIHA project. Before the sequential application of the algorithms, the area covered by the seismic paths was characterized by 22 maps of local attenuation coefficients corresponding to the 10–120 s period range. All these maps were obtained by applying Yanovskayas formulation for laterally heterogeneous media to the set of path-averaged attenuation coefficients mentioned above. After that, we divided the Iberian Peninsula into six homogeneous regions in terms of the local attenuation coefficients for 22 different periods and by means of the principal component analysis and the clustering algorithm. We then obtained, by stochastic inversion, the respective anelastic structure down to a depth of 225 km for the six homogeneous regions. The coefficients vary from 1.0 to 2.0×10−3 km−1 and the Q−1β structures, ranging from 110×10−3 to 40×10−3, suggest for five of the regions an asthenosphere with its upper and lower boundaries close to 80 and 180 km depth, respectively. A shallow beginning of the asthenosphere is detected for the sixth homogeneous region. This range is very similar to the depths deduced from previous tomographic studies of the Iberian Peninsula based on Rayleigh wave phase and group velocities. Finally, correlations obtained between the regions and some seismotectonic characteristics of the Peninsula are discussed. It is noteworthy that we cannot associate each of the six homogeneous regions with a single Hercynian, Alpine or Neogene domain.

Joint inversion of travel times and waveforms by means of annealing algorithms. Application to a seismic refraction experiment

An algorithm of annealing is applied to a joint inversion of travel times and waveforms belonging to a synthetically generated seismic refraction experiment. The medium (crust and upper mantle) is modelled by a set of plane stratified layers and a halfspace. The obtained structure (elastic parameters and depth of layers) shows that, in spite of contaminating seismic noise and poor knowledge of the seismic source, annealing methods are a good tool in these kinds of inversion problems. We think that many characteristics of the annealing process described here could be used with real data and more sophisticated media for the crust and upper mantle of the earth than the present example.

Aftershock sequences of three seismic crises at southern California, USA, simulated by a cellular automata model based on self-organized criticality

Several properties of aftershock series related to the main shocks of Landers, Northridge and Hector Mine (southern California, USA) are reproduced by the Dynamic Fiber Bundle Model, DFBM. Optimum values for the three parameters governing DFBM are determined by searching for the best agreement of real aftershock series properties and those of synthetic sequences generated by this model. The analysis of the model parameter values provides details on the underlying physical mechanism of the aftershock sequence generation. First, the ratio of seismic energy radiated as seismic waves and transferred as stress-strain to adjacent faults; second, the degree of stress heterogeneity reproducing the complex behavior of real aftershock series. Additionally, the results of simulations support the coexistence of two types of relaxation processes. One of them is associated with the well-known modified Omori’s (MO) law, which involves elapsed times between consecutive aftershocks monotonically increasing; the other is manifested by episodes of sudden stress release, with inter-event times much shorter than those predicted by MO law. These episodes are assumed to be a consequence of the complex distribution of tectonic stresses and fault geometry. The first process is associated to events designed as leading aftershocks, LA. The second process generates series of events which are designed as cascades, CA. It is worth of mention that several properties concerning CAs can be reasonably related to critical changes on stress field along the simulation process.

Simulated annealing in 3-D seismic modelling and elastic structure of the mediterranean basin

Abstract 3-D elastic structures images of the Mediterranean basin are obtained by solving a tomographic problem by means of a simulated annealing algorithm. The database consists of local Rayleigh wave group velocities determined for the fundamental mode in the 10–90s period range. These local velocities were obtained from surface wavetrains recorded at very broad band stations of MEDNET network. From a methodological point of view, the characteristics of the annealing algorithm and the amount of time required for computation suggest the implementation of parallel computational procedures to shorten the computational time. According to the thermodynamic analogies used in the annealing algorithm, we propose an alternative procedure to estimate uncertainties and correlations for variables defining the elastic model (shear velocities and layer thicknesses) without necessity of computing partial derivatives. From an applied point of view, the 3-D elastic model obtained shows, as main results, relevant differences for the eastern and western pans of the Mediterranean basin, specially down to 60 km. The changes in the position of the top and bottom asthenosphere surfaces can also be followed throughout the Mediterranean basin; remarkably, these changes are in agreement with some tectonic features.

Annealing Algorithms in Computing Stress Tensors: A Set of Numerical Simulations for Local Stress Tensor Recovery

The determination of a local lithospheric stress pattern from low magnitude seismic activity recorded at a loca array is attempted by means of numerical simulations that include waveform inversion and annealing inversion techniques. A set of flat stratified layers are assumed for the propagating medium. The tests show that the annealing algorithm is a useful tool in this kind of study where collected seismic activity at local arrays could help us better understand local stress distributions in the lithosphere. Although real data recorded at local seismic arrays should be processed, assuming more realistic crust and upper mantle models, many characteristics of the annealing process described here could be used when studying real problems.

Some elements of mathematical information theory and total inversion algorithm applied to travel time inversion

The total inversion algorithm and some elements of Mathematical Information Theory are used in the treatment of travel-time data belonging to a seismic refraction experiment from the southern segment (Sardinia Channel) of the European Geotraverse Project. The inversion algorithm allows us to improve a preliminary propagating model obtained by means of usual trial and error procedure and to quantify the resolution degree of parameters defining the crust and upper mantle of such a model. Concepts related to Mathematical Information Theory detect some seismic profiles of the refraction experiment which give the most homogeneous coverage of the model in terms of number of trajectories crossing it. Finally, the efficiency of the inversion procedure is quantified and the uncertainties regarding knowledge of different parts of the model are also evaluated.

Fractal analysis and statistics of seismic generation rates: the example of the southern California

The seismic generation rate, SGR, at southern California along the 1981–2007 recording period is analysed with the main purpose of finding out whether there exist some correlations between seismic activity before, after and along aftershock sequences triggered by mainshocks of high magnitude. The possibility that a mainshock could be triggered by another neighbouring mainshock and its aftershock sequence is also investigated. The analyses are based on monthly SGR series, obtained as the number of events detected every month along the recording period considered. These monthly SGR series are derived for three aftershock areas associated with Landers (June 28, 1992, Mw = 7.3), Northridge (January 17, 1994, Mw = 6.7) and Hector Mine (October 16, 1999, Mw = 7.1) mainshocks. The most relevant features of SGR series are investigated through various techniques: 1) the rescaled range analysis and the interpretation of the Hurst exponent in terms of persistence, anti-persistence and randomness; 2) time trend estimation by the Kendall-tau algorithm and assessment of their statistical significance by the Mann-Kendall test; 3) the self-affine character, derived from semivariograms, and the Hausdorff measure; 4) autocorrelation and power spectra; 5) cross-correlation and cross-power spectra; 6) the search for the statistical distribution best reproducing the empirical probability of SGR series. Additionally, a close look at plots of epicenters within the aftershock areas, distinguishing between periods of background and aftershock activity, permits detecting some features of the seismicity. Changes on spatial patterns of seismicity suggest that the effects of tectonic stress redistribution could persist beyond an aftershock period, at short and medium distances of the mainshock. This possibility would be also in agreement with cross-correlation results for SGR series.