Johana Brokešová

On strong ground motion synthesis with k−2 slip distributions

This study deals with the methodical aspects of k−2(Bernard et al., 1996) kinematic strong motions modelling: (1) it is shown how to incorporate the k-dependent rise time for 2D fault geometry in the strong motion synthesis according to the representation theorem, (2) it is suggested how to produce realistic k−2 slip models including asperity(ies), (3) modifications are introduced concerning the typeof used slip velocity function and the corner wave number in the slip distribution. High frequency effects of these generalized models are discussed.It is shown that, assuming the rise time proportional to the spatial slip wavelength at high wave numbers, the spectral decay of displacement at frequencies higher than the corner frequency is given just by the decay ofthe slip distribution spectrum, regardless of the type of slip velocity function. It is shown numerically that this model provides ο-squared source spectrum even in a vicinity of a 2D normal fault buried in 1D structure, which is an agreement with previous studies.

New portable sensor system for rotational seismic motion measurements.

A new mechanical sensor system for recording the rotation of ground velocity has been constructed. It is based on measurements of differential motions between paired sensors mounted along the perimeter of a rigid (undeformable) disk. The elementary sensors creating the pairs are sensitive low-frequency geophones currently used in seismic exploration to record translational motions. The main features of the new rotational seismic sensor system are flat characteristics in the wide frequency range from 1 to 200 Hz and sensitivity limit of the order of 10(-8) rad/s. Notable advantages are small dimensions, portability, easy installation and operation in the field, and the possibility of calibrating the geophones in situ simultaneously with the measurement. An important feature of the instrument is that it provides records of translational seismic motions together with rotations, which allows many important seismological applications. We have used the new sensor system to record the vertical rotation velocity due to a small earthquake of M(L)=2.2, which occurred within the earthquake swarm in Western Bohemia in autumn 2008. We found good agreement of the rotation record with the transverse acceleration as predicted by theory. This measurement demonstrates that this device has a much wider application than just to prospecting measurements, for which it was originally designed.

Note: rotaphone, a new self-calibrated six-degree-of-freedom seismic sensor.

We have developed and tested (calibration, linearity, and cross-axis errors) a new six-degree-of-freedom mechanical seismic sensor for collocated measurements of three translational and three rotational ground motion velocity components. The device consists of standard geophones arranged in parallel pairs to detect spatial gradients. The instrument operates in a high-frequency range (above the natural frequency of the geophones, 4.5 Hz). Its theoretical sensitivity limit in this range is 10(-9) m/s in ground velocity and 10(-9) rad/s in rotation rate. Small size and weight, and easy installation and maintenance make the instrument useful for local-earthquake recording and seismic prospecting.

Six-degree-of-freedom near-source seismic motions II: examples of real seismogram analysis and S-wave velocity retrieval

Near-source records obtained by the mechanical seismic sensor Rotaphone are presented. The Rotaphone can measure six components of seismic movements, three translational and three rotational. The apparent S-wave phase velocity is determined and the possibility to obtain the wavepath S-wave velocity directly under the receiver is discussed. Rotation-to-translation ratios (RTRs) characterize the strength of rotations compared to translations. The Rotaphone records of local microearthquakes were obtained in various European seismoactive regions over the last few years. Three case studies, analyzed in detail, include various geological structures and seismograms recorded at various epicentral distances from 0.7 to 14.9 km. Also, the source depth varies from 4.8 to 10.4 km. The first case is an event from the West Bohemia intraplate seismic swarm region. The seismogram was recorded only 0.7 km from the epicenter. This case shows the complexity of rotation-to-translational relations near the epicenter. The second case is from the Corinthian Gulf active-rift region. The study confirms the expectation of the theory concerning rotations connected with the direct S wave; however, difficulties follow from a very complex 3D geological structure in the vicinity of the station, complicated by a distinctive topography with steep slopes of the hills. The third example is from South Iceland, near the active Katla volcano. The data in this case satisfy the rotation-to-translation relations very well, which is probably caused by the relatively simple geological setting and appropriate source-to-receiver configuration. The RTRs are computed for all three cases, and their frequency dependence is discussed.

Six-degree-of-freedom near-source seismic motions I: rotation-to-translation relations and synthetic examples

The paper deals with theoretical aspects of rotation-to-translation relations in six-degree-of-freedom short-period seismic records at close hypocentral distances. Rotation-to-translation ratios are introduced as the ratios relating peak amplitudes of the relevant rotational and translational components. Their frequency dependence is analyzed in simple models. The relations between translations and rotations are expressed by equations derived under the assumption of a spherical S wave radiated from a shallow point source in a homogeneous medium. A set of numerical experiments is performed to examine these relations for a double-couple source buried in simplified structure models. These experiments indicate that at local distances (up to several km), at lower frequencies (up to a few Hz), and at locations with rapid amplitude changes due to the radiation pattern (e.g., in the vicinity of nodal planes), the rotational components are a linear combination of terms proportional to translational velocity and acceleration, and none of the terms can be, in general, neglected. We also focus on the possibility to retrieve the S-wave phase velocity along the wavepath. The applicability of the equations is tested also in a layered velocity model. It has been found that, under certain conditions, the equations allow us to find correct values of wavepath velocity even in vertically inhomogeneous structures. The depth-range sensitivity is examined for a specific 1D model containing a thin surficial low-velocity layer. Based on these experiments, we have concluded that the retrieved velocity is representative down to the depth not exceeding one wavelength.

Construction of Ray Synthetic Seismograms Using Interpolation of Travel Times and Ray Amplitudes

The seismic wave field, in its high-frequency asymptotic approximation, can be interpolated from a low- to a high-resolution spatial grid of receivers and, possibly, point sources by interpolating the eikonal (travel time) and the amplitude. These quantities can be considered as functions of position only. The travel time and the amplitude are assumed to vary in space only slowly, otherwise the validity conditions of the theory behind would be violated. Relatively coarse spatial sampling is then usually sufficient to obtain their reasonable interpolation. The interpolation is performed in 2-D models of different complexity. The interpolation geometry is either 1-D, 2-D, or 3-D according to the source-receiver distribution. Several interpolation methods are applied: the Fourier interpolation based on the sampling theorem, the linear interpolation, and the interpolation by means of the paraxial approximation. These techniques, based on completely different concepts, are tested by comparing their results with a reference ray-theory solution computed for gathers and grids with fine sampling. The paraxial method holds up as the most efficient and accurate in evaluating travel times from all investigated techniques. However, it is not suitable for approximation of amplitudes, for which the linear interpolation has proved to be universal and accurate enough to provide results acceptable for many seismological applications.

Ray and finite-difference modelling of CDP seismic sections for shallow lignite deposits

Abstract A numerical experiment carried out to investigate the structural model of the Domenico lignite site is discussed. The model is a 2D structure containing several lignite layers at different depths, and a low-velocity layer at the top of the model. The experiment consists in simulating a measured CDP section by two independent techniques, based on completely different concepts: the finite-difference method and the ray method. Due to the incompleteness of the ray synthetic wave field, as well as to numerical problems of the finite differences at higher frequencies, the agreement between the synthetic seismogram sections for the individual shot points is poor. However, the CDP stacked sections modelled by the ray and finite-difference methods agree rather well. This is because the main differences between the wave fields computed by the two methods are due to the presence of the low-velocity layer (ground roll, head waves, etc.), and just these parts of the wave field can be suppressed by routine data processing such as f–k filtration. Synthetic ray and finite-difference CDP stacks agree relatively well with the observed data. They confirm three lignite seams and a fault in the shallower one. The synthetic data also indicate that many apparent horizons of the measured section may be due to the multiple reflections within the subsurface low-velocity layer.