Thomas Forbriger

On the Effects of Geometrical Spreading Corrections for a 2D Full Waveform Inversion of Recorded Shallow Seismic Surface Waves

Elastic full waveform inversion (FWI) of shallow seismic surface waves has the potential to reconstruct lateral variations of the shallow subsurface which is important e.g. for geotechnical site characterization. In order to make a 2D full waveform inversion algorithm applicable, shallow seismic field recordings excited by a point source (usually a hammer blow) must be transformed to mimic equivalent wavefields excited by a line source. Waves excited by a point source differ in geometrical spreading, i.e. amplitude decay and phase delay of Pi/4 in the far field from waves excited by a line source. When using the L2 norm as a measure of misfit a correction for the different decay of amplitudes is mandatory but not sufficient to obtain reliable results. In addition the signal phase must also be corrected which can be done by a convolution with 1/sqrt(t) or a Fourier-Bessel-expansion. Both spreading corrections work quite well for surface waves.

Guidelines for the good practice of surface wave analysis: a product of the InterPACIFIC project

Surface wave methods gained in the past decades a primary role in many seismic projects. Specifically, they are often used to retrieve a 1D shear wave velocity model or to estimate the VS,30 at a site. The complexity of the interpretation process and the variety of possible approaches to surface wave analysis make it very hard to set a fixed standard to assure quality and reliability of the results. The present guidelines provide practical information on the acquisition and analysis of surface wave data by giving some basic principles and specific suggestions related to the most common situations. They are primarily targeted to non-expert users approaching surface wave testing, but can be useful to specialists in the field as a general reference. The guidelines are based on the experience gained within the InterPACIFIC project and on the expertise of the participants in acquisition and analysis of surface wave data.

About the Nonunique Sensitivity of Pendulum Seismometers to Translational, Angular, and Centripetal Acceleration

Abstract The displacement of each part of a seismometer’s frame is identical for a purely translational motion. However, in the presence of rotary motion the different parts of a seismometer’s frame will undergo different displacements. The definition of the sensitivity of the seismometer then requires the selection of a reference location on the seismometer’s frame to which the sensitivity is attributed. This location does not necessarily coincide with the hinge and can be selected arbitrarily. The appropriate choice is to attribute the output signal to the location of the point mass of the equivalent simple pendulum (or reduced pendulum), which usually lies within the seismometer’s casing. Rotations of the sensor about this location produce no output signal due to angular or centripetal acceleration. The sensor then appears sensitive to linear acceleration only.

Recommendations for seismometer deployment and shielding

Temporary field installations for short period observations may put other demands on seismometer installation than permanent installations for broadband observations. For sensitive shortperiod observations you will primarily seek sites without local vibrational sources. High-resolution broadband observations on the other hand require careful thermal shielding and protection against air-pressure variations, since forces due to unwanted sensitivities to temperature and pressure decrease not as rapidly with increasing signal-period as the inertial forces due to ground motion do. For permanent installations you might be able to build a seismometer vault, while you have to make compromises regarding sites for temporary installations. Use the guidelines below when seeking the best solution for your specific case.

Toolbox for Applied Seismic Tomography (TOAST)

TOAST (Toolbox for Applied Seismic Tomography) makes methods of full-waveform inversion of elastic waves available for the practitioner. The inversion of complete seismograms is an utmost ambitious and powerful technology. One of its strengths is the enormously increased imaging-resolution since it is able to resolve structures smaller than the seismic wave length. Further it is sensitive to material properties like density and dissipation which are hardly accessible through conventional techniques. Within the TOAST project algorithms available in academia were collected, improved, and prepared for application to field recordings. Different inversion strategies were implemented (global search, conjugate gradient, waveform sensitivity kernels) and computer programs for imaging the subsurface in 1D, 2D, and 3D were developed. The underlying algorithms for the correct numerical simulation of physical wave propagation have thoroughly been tested for artefacts. In parallel these techniques were tested in application to waveform data. They proved their potential in application to synthetic data, shallow-seismic surface waves from field recordings, and microseismic and ultrasonic data from material testing. This provided valuable insight to the demands on seismic observation equipment (repeatability, waveform reproduction, survey layout) and inversion strategies (initial models, regularization, alternative misfit definitions, etc.). The developed software programs, results of benchmark tests, and field-cases are published online by the OpenTOAST.de initiative.

On the Significance of Viscoelasticity in a 2D Full Waveform Inversion of Shallow Seismic Surface Waves

We perform two tests to investigate to which degree viscoelastic modeling is relevant during a full waveform inversion of shallow seismic surface waves. Firstly, we compare field data with synthetic elastic and viscoelastic data. We show that the optimized source time function acts as a low pass filter in the case of elastic wavefields and can compensate a significant fraction of the residuals between elastically and viscoelastically modeled data. However, the viscoelastic data can explain the recorded data better in some aspects like the amplitude decay with offset of the fundamental mode and the near offset traces. Secondly, we run inversion tests for simulated viscoelastic observations (Q=20) using both elastic as well as viscoelastic forward modeling with Q=20, 25, and 10 during the inversion. The results show that it is not possible to infer the steep gradient in the shear wave velocity model in the topmost meter using an elastic inversion. Using a slightly wrong Q factor in the inversion produces very similar results compared to the results obtained by an inversion using the correct Q factor. If we use Q factors that are too far away from the Q factor of the observed data the inversion result becomes worse.

Locating wind farms by seismic interferometry and migration

We present a case study on the detection and quantification of seismic signals induced by operating wind turbines (WTs). We spatially locate the sources of such signals in data which were recorded at 11 seismic stations in 2011 and 2012 during the TIMO project (Deep Structure of the Central Upper Rhine Graben). During this time period, four wind farms with altogether 12 WTs were in operation near the town of Landau, Southwest Germany. We locate WTs as sources of continuous seismic signals by application of seismic interferometry and migration of the energy found in cross-correlograms. A clear increase of emitted seismic energy with rotor speed confirms that the observed signal is induced by WTs. We can clearly distinguish wind farms consisting of different types of WTs (different hub height and rotor diameter) corresponding to different stable frequency bands (1.3–1.6 Hz, 1.75–1.95 Hz and 2.0–2.2 Hz) which do not depend on wind speed. The peak frequency apparently is controlled by the elastic eigenmodes of the structure rather than the passing of blades at the tower. From this we conclude that vibrations are coupled into the ground at the foundation and propagate as Rayleigh waves (and not as infrasound). The migration velocity of 320 m/s corresponds to their group velocity. The applied migration method can contribute to the assessment of local sources of seismic noise. This topic gets growing attention in the seismological community. In particular, the recent boost of newly installed wind farms is a threat to seismological observatories such as the Black Forest Observatory (BFO) and the Gräfenberg array (GRF) or gravitational wave observatories (e.g. LIGO, VIRGO) in terms of a sensitivity degradation of such observatories.