Michael Korn

Modelling the teleseismic P coda envelope: depth dependent scattering and deterministic structure

Abstract The P-coda of teleseismic events contains information on the small-scale random structure of the near-receiver lithosphere. Various scattering theories have been suggested to model the time and frequency dependence of the coda envelopes for a given random structure. A specially simple model is the energy-flux model that describes P-coda excitation in terms of scattering attenuation of the direct P-wave front without dealing with the details of the scattering process. It is based on energy conservation and is valid for both weak and strong scattering cases. Here, the energy-flux model is extended to include a depth-dependence of the scattering structure. A variation of the depth range of the random medium manifests itself mainly in different decay rates of the coda, whereas the coda amplitudes at small lapse times behind the direct arrival are sensitive to the scattering strength of the shallow structure. Strongly heterogeneous layers at greater depths yield more complicated coda shapes which cannot be fully described by parameters like decay rate or coda Q . Full waveform simulations in random structures superimposed onto a deterministic layered model show that (1) the energy-flux model yields reliable results, and (2) the effects of deterministic layering on the coda envelopes are relatively small for waves with small incidence angles and realistic scattering strength and therefore may be neglected in coda inversions for teleseismic waves.

Seismogram Envelope Inversion Using a Multiple Isotropic Scattering Model: Application to Aftershocks of the 2001 Bhuj Earthquake

We apply the energy transfer theory of 3D multiple isotropic scattering to analyze seismogram envelopes of the 2001 Bhuj earthquake of India. We synthesized the S -wave coda envelopes by using a numerical Monte Carlo method. Our model is described by total scattering coefficient g , intrinsic absorption coefficient b , spectral source energy S , and site factors Z . Isotropic source radiation and acoustic wave propagation were assumed. We inverted the observed coda envelopes of 10 aftershocks ( M L ≥4) using the grid search for g , least-squares inversion for b , and S between 1 and 24 Hz. Parameter g does not show significant frequency dependency and averages to 0.01 1/km. This corresponds to a mean free path of 100 km. Parameter b shows weak frequency dependency, increasing with frequency. Its value ranges from 0.02 1/sec to 0.05 1/sec. Consequently, the frequency dependency of intrinsic attenuation takes the power-law form of Qi ( f ) = 280 f 0.72. The source energy is largely consistent with the well-known ω 2-source model and the seismic moment is comparable to estimates using standard empirical relations between seismic moment and local magnitude. We also inverted the envelopes for site-amplification factors Z . The values of Z range from 0.5 to 1.75 with no clear frequency dependence, which is consistent with the geology of the region, as the stations were deployed on hard- rock sites.

Envelope syntheses of cylindrical vector-waves in 2-D random elastic media based on the Markov approximation

Seismograms of microearthquakes are complex; however, their envelopes broaden as the travel distance increases. P-waves are recorded in transverse components, S-waves are recorded in the longitudinal component, and waves are observed at sites even in the nodal direction of the source radiation. These phenomena, which are typically found in short-period seismograms, can be interpreted to be the result of scattering due to lithospheric inhomogeneity. We report here our study of a simple statistical model in which the propagation of waves radiated from a point source in two-dimensional (2-D) random elastic media is characterized by a Gaussian autocorrelation function. For the case that the wavelength is shorter than the correlation distance, two methods based on the Markov approximation are introduced for the direct synthesis of vector wave envelopes. One is to analytically solve the stochastic equation for the two-frequency mutual coherence function; the validity of the solution is confirmed by using finite difference simulations. The second is to numerically solve the stochastic equation for the mutual coherence function. The two methods are equivalent, but the latter is applicable to nonisotropic source radiation. For the case of a point shear dislocation source, a peak delay from the onset and a smoothly decaying tail are found to be common to synthesized envelopes in all azimuths. Scattered waves are excited even at receivers in the nodal direction, and amplitudes become independent of the radiation pattern as lapse time increases.

Seismic tomography reveals a mid-crustal intrusive body, fluid pathways and their relation to the earthquake swarms in West Bohemia/Vogtland

S U M M A R Y The region of West Bohemia/Vogtland in the Czech–German border area is well known for the repeated occurrence of earthquake swarms, CO2 emanations and mofette fields. We present a local earthquake tomography study undertaken to image the Vp and Vp/Vs structure in the broader area of earthquake swarm activity. In comparison with previous investigations, more details of the near-surface geology, potential fluid pathways and features around and below the swarm focal zone could be revealed. In the uppermost crust, for the first time the Cheb basin and the Bublák/Hartoušov mofette fields were imaged as distinct anomalies of Vp and Vp/Vs. The well-pronounced low-Vp anomaly of the Cheb basin is not continuing into the Eger rift indicating a particular role of the basin within the rift system. A steep channel of increased Vp/Vs is interpreted as the pathway for fluids ascending from the earthquake swarm focal zone up to the Bublák/Hartoušov mofette fields. As a new feature, a mid-crustal body of high Vp and increased Vp/Vs is revealed just below and north of the earthquake swarm focal zone. It may represent a solidified intrusive body which emplaced prior or during the formation of the rift system. We speculate that enhanced fluid flow into the focal zone and triggering of earthquakes could be driven by the presence of the intrusive body if cooling is not fully completed. We consider the assumed intrusive structure as a heterogeneity leading to higher stress particularly at the junction of the rift system with the basin and prominent fault structures. This may additionally contribute to the triggering of earthquakes.

A Temporary Network For Seismological Monitoring In West-Saxony: First Results

Since December 1997 a network of 10 autonomously recording digital seismic stations operates in W-Saxony to monitor microseismic activity generated by tectonic movements in the Gera-Jáchymov fault zone and induced by the flooding of the uranium mining area near Aue. Further goals to be followed with these data are the in situ verification of engineering seismological parameters and the study of the transmission properties of seismic waves across the Gera-Jáchymov fault zone to improve seismic risk evaluation.So far 19 tectonic and more than 50 induced events have been located and source parameters have been determined. Event clusters near Zwickau and within the Aue mining area could be spatially resolved with a master event technique. The cluster near Zwickau occured on a common fault plane striking parallel to the Gera-Jáchymov fault zone and dipping at an angle of about 60° towards ENE. The induced events near Aue occured within a volume of approximately 5 km3. The majority of these events were located in the granite body underneath the mining area. Fault plane solutions show a variety of focal mechanisms with no clear relation to the regional stress field.

Chapter 3 Synthesis of Vector‐Wave Envelopes in Random Elastic Media on the Basis of the Markov Approximation

Abstract High‐frequency seismograms of earthquakes are complex mainly caused by scattering due to the lithospheric inhomogeneity. Disregarding phase information, seismologists have often focused on the characteristics of seismogram envelopes. The delay time of the maximum amplitude arrival from the onset and the apparent duration time are good measures of scattering caused by random velocity inhomogeneities. There is a stochastic method to directly simulate wave envelopes in random media. The Markov approximation for the parabolic equation is known to be powerful for the direct synthesis of scalar wave envelopes when the wavelength is shorter than the correlation length of random media. It leads to the master equation for the two‐frequency mutual coherence function (TFMCF) of waves, of which the Fourier transform gives the time trace of the wave intensity. It well predicts the peak delay and the broadening of wave envelopes with increasing travel distance for an impulsive source. In this chapter, we extend this approximation to vector waves in random elastic media. When the medium inhomogeneity is weak and the wavelength is shorter than the correlation distance, P‐ and S‐waves can be separately treated by using potentials since conversion scattering between them is weak. Applying the Markov approximation to the TFMCF of potential field, we are able to synthesize vector‐wave envelopes. Vector‐wave envelopes are analytically derived for plane wavelet incidence onto random media and for wavelet radiation from a point source in random media characterized by a Gaussian autocorrelation function. For P‐waves, this approximation predicts not only the peak delay and envelope broadening in the longitudinal component but also the excitation of wave amplitude in the transverse component due to ray bending. The ratio of the mean square (MS) fractional velocity fluctuation to the correlation distance ɛ 2 / a is the key parameter characterizing these vector‐wave envelopes. The relation between the time integral of the transverse‐component MS amplitude against travel distance gives this ratio. S‐wave envelopes can be synthesized with an analogous mathematical approach. For the same randomness, the envelope broadening of S‐wavelet is larger than that of P‐wavelet by a factor of the ratio of their wave velocities. The validity of the direct envelope synthesis with the Markov approximation is confirmed by a comparison with vector‐wave envelopes calculated from finite difference simulations in two dimensions. The direct syntheses of vector‐wave envelopes developed here could serve for the mathematical interpretation of observed seismograms in terms of lithospheric inhomogeneity.

MIIC: Monitoring and Imaging Based on Interferometric Concepts

The capability of seismic interferometry to create virtual sources at receiver sites from records of ambient seismic noise is used for seismic monitoring and tomography of different targets. We present hardware developed specifically for the needs of seismic data acquisition in the context of monitoring and ambient noise tomography. Digitizers are capable of continuous recording and real time wireless data transmission in self organizing meshes to allow for robust telemetry in difficult circumstances such as cities or landslides that may cause the loss of stations. A software tool is described that implements required processing and analysis procedures for the interferometric processing. We have applied the novel 3D ambient noise surface wave tomography approach to the Issyk-Ata fault in Kyrgyzstan. It shows that seismic interferometry can successfully be used for structural investigations on length scales of only 100 m. The method uses 3D sensitivity kernels for a single-step inversion of phase velocity dispersion curves for subsurface S-wave velocity structure and incorporates topography. We recover lateral differences in sediment velocities and an offset of the bedrock depth across the fault. Applications of interferometric monitoring to the geological \(\mathrm{CO}_2\) storage test site in Ketzin (Germany) and to the Piton de la Fournaise volcano (La Reunion island) emphasize the value of this approach. At Ketzin site we identify variations of the subsurface velocities that are correlated with changes in the ground water level and mask potential signals from the reservoir depth. At Piton de la Fournaise volcano, seismic velocity changes are linked to volcanic processes as shown by comparison with surface displacement and seismicity that are typically used to characterize volcanic activity. We observe a clear distinction between phases of inflation prior to eruptions and deflation during periods of quiescence.

Acoustic and elastic radiative transfer theory in seismology

Inversion results that were obtained by applying the acoustic and elastic radiative transfer theory to seismological data will presented. Scattering of seismic wave fields within the earth is documented by the pulse broadening of direct wave trains and the appearance of coda waves following the direct waves. The pulse broadening is caused by forward‐scattered waves and the coda by wide‐angle scattering. Random media are used as models for the heterogeneities of the earth. The energy transfer equations are solved with Monte Carlo methods. The results obtained with the acoustic and elastic theory for the transport scattering coefficients and absorption coefficients are compared with each other. It shows that scattering is the main process for lower frequencies. For higher frequencies intrinsic absorption is dominant. The results for elastic and acoustic radiative transfer are the same if strong forward scattering is assumed. For lower values of anisotropy the results are different.