ALBERT

Description: Full-waveform inversion (FWI) of Rayleigh waves is attractive for shallow geotechnical investigations due to the high sensitivity of Rayleigh waves to the S-wave velocity structure of the subsurface. In shallow-seismic field data, the effects of anelastic damping are significant. Dissipation results in a low-pass effect as well as frequency-dependent decay with offset. We found this by comparing recorded waveforms with elastic and viscoelastic wave simulation. The effects of anelastic damping must be considered in FWI of shallow-seismic Rayleigh waves. FWI using elastic simulation of wave propagation failed in synthetic inversion tests in which we tried to reconstruct the S-wave velocity in a viscoelastic model. To overcome this, $$Q$$ -values can be estimated from the recordings to quantify viscoelasticity. Waveform simulation in the FWI then uses these a priori values when inferring seismic velocities and density. A source-wavelet correction, which is inevitable in FWI of field data, can compensate a significant fraction of the residuals between elastically and viscoelastically simulated data by narrowing the signals’ bandwidth. This way, elastic simulation becomes applicable in FWI of data from anelastic media. This approach, however, was not able to produce a frequency-dependent amplitude decay with offset. Reconstruction, therefore, was more accurate when using appropriate viscoelastic modeling in FWI of shallow-seismic Rayleigh waves. We found this by synthetic inversion tests using elastic forward simulation as well as viscoelastic simulation with different a priori values for $$Q$$ .

Description: The S-wave velocity of the shallow subsurface can be inferred from shallow-seismic Rayleigh waves. Traditionally, the dispersion curves of the Rayleigh waves are inverted to obtain the (local) S-wave velocity as a function of depth. Two-dimensional elastic full-waveform inversion (FWI) has the potential to also infer lateral variations. We have developed a novel workflow for the application of 2D elastic FWI to recorded surface waves. During the preprocessing, we apply a line-source simulation (spreading correction) and perform an a priori estimation of the attenuation of waves. The iterative multiscale 2D elastic FWI workflow consists of the preconditioning of the gradients in the vicinity of the sources and a source-wavelet correction. The misfit is defined by the least-squares norm of normalized wavefields. We apply our workflow to a field data set that has been acquired on a predominantly depth-dependent velocity structure, and we compare the reconstructed S-wave velocity model with the result obtained by a 1D inversion based on wavefield spectra (Fourier-Bessel expansion coefficients). The 2D S-wave velocity model obtained by FWI shows an overall depth dependency that agrees well with the 1D inversion result. Both models can explain the main characteristics of the recorded seismograms. The small lateral variations in S-wave velocity introduced by FWI additionally explain the lateral changes of the recorded Rayleigh waves. The comparison thus verifies the applicability of our 2D FWI workflow and confirms the potential of FWI to reconstruct shallow small-scale lateral changes of S-wave velocity.

Description: Full-waveform inversion (FWI) of shallow-seismic surface waves is able to reconstruct lateral variations of subsurface elastic properties. Line-source simulation for point-source data is required when applying algorithms of 2-D adjoint FWI to recorded shallow-seismic field data. The equivalent line-source response for point-source data can be obtained by convolving the waveforms with $\sqrt{t^{-1}}$ ( t : traveltime), which produces a phase shift of /4. Subsequently an amplitude correction must be applied. In this work we recommend to scale the seismograms with $\sqrt{2 r v_{\rm ph}}$ at small receiver offsets r , where v ph is the phase velocity, and gradually shift to applying a $\sqrt{t^{-1}}$ time-domain taper and scaling the waveforms with $r\sqrt{2}$ for larger receiver offsets r . We call this the hybrid transformation which is adapted for direct body and Rayleigh waves and demonstrate its outstanding performance on a 2-D heterogeneous structure. The fit of the phases as well as the amplitudes for all shot locations and components (vertical and radial) is excellent with respect to the reference line-source data. An approach for 1-D media based on Fourier–Bessel integral transformation generates strong artefacts for waves produced by 2-D structures. The theoretical background for both approaches is presented in a companion contribution. In the current contribution we study their performance when applied to waves propagating in a significantly 2-D-heterogeneous structure. We calculate synthetic seismograms for 2-D structure for line sources as well as point sources. Line-source simulations obtained from the point-source seismograms through different approaches are then compared to the corresponding line-source reference waveforms. Although being derived by approximation the hybrid transformation performs excellently except for explicitly back-scattered waves. In reconstruction tests we further invert point-source synthetic seismograms by a 2-D FWI to subsurface structure and evaluate its ability to reproduce the original structural model in comparison to the inversion of line-source synthetic data. Even when applying no explicit correction to the point-source waveforms prior to inversion only moderate artefacts appear in the results. However, the overall performance is best in terms of model reproduction and ability to reproduce the original data in a 3-D simulation if inverted waveforms are obtained by the hybrid transformation.

Description: Equivalent line-source seismograms can be obtained from shallow seismic field recordings by (1) convolving the waveforms with $\sqrt{t^{-1}}$ , (2) applying a $\sqrt{t^{-1}}$ time-domain taper, where t is traveltime and (3) scaling the waveform with $r_{{\rm offset}}\sqrt{2}$ , where r offset is source-to-receiver offset. We require such a procedure when applying algorithms of 2-D adjoint full-waveform inversion (FWI) to shallow-seismic data. Although derived from solutions for acoustic waves in homogeneous full space this simple procedure performs surprisingly well when applied to vertical and radial components of shallow-seismic recordings from hammer blows or explosions. This is the case even in the near field of the force, although the procedure is derived from a far-field approximation. Similar approximative procedures recommended in literature are optimized for reflected waves and do not convert the amplitudes of all shallow seismic wavefield constituents equally well. We demonstrate the suitability of the proposed method for the viscoelastic case by numerical examples as well as analytical considerations. In contrast to the proposed single-trace procedure, integral-transform approaches are exact for all viscoelastic wavefield constituents of the near- and far-field in unknown 1-D-heterogeneous structure. Unfortunately, integral-transform approaches suffer from artefacts in applications to data sampled on 2-D structures. Here, we use the Fourier–Bessel integral transformation as a reference in 1-D heterogeneous structures. We unroll the wave-theoretical background of both approaches in order to demonstrate, why the simplistic single-trace simulation approach derived from the asymptotic acoustic case can perform so well when applied to the shallow elastic wavefield. Further we give recommendations for practical implementation and application to field data of the proposed simulation method and compare to the results of alternative conversion rules. The performance of the conversion procedure to data recorded on 2-D heterogeneous structures is presented in a companion study by FWI reconstruction tests.

Description: 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.

Description: Two types of dispersive seismic waves have been acquired in different geological settings to investigate the potential to reveal the elastic parameters of the shallow marine subsurface. Scholte waves as well as acoustic guided waves are excited by a near-surface towed airgun, and recorded using two acquisition methods: (1) the towed-acquisition system using a hydrophone streamer towed close to the sea floor, and (2) the stationary-receiver method using Ocean-Bottom Seismometers and/or Hydrophones (OBS/OBH). Our diverse data sets reveal that the spatial sampling of the wavefield required to avoid aliasing may vary significantly for different geological settings. Scholte waves are characterised by a few distinct modes observed at low frequencies and low phase velocities. Their dispersion is mainly controlled by the depth profile of the shear-wave velocity. Acoustic guided waves show profound amplitude variations of numerous higher modes over a broad frequency range. These are sensitive to shear-wave velocity, but more sensitive to compressional-wave velocity than Scholte waves are. To avoid the identification of distinct modes we infer 1-D models of elastic parameters of the subsurface from the inversion of the full wavefield spectra of acoustic guided waves. In the Siberian Laptev Sea we infer the presence of a soft sediment layer (8-10 m) with a well resolved strong S-velocity gradient (150-450 m/s). In the Baltic Sea a low P-velocity layer with a strong vertical gradient (1250-1440 m/s) corresponding to a post-glacial gassy mud layer could be resolved, which agrees well with the sediment stratigraphy derived from a gravity core.

Description: SUMMARY Tilting of the ground due to loading by the variable atmosphere is known to corrupt very long period horizontal seismic records (below 10 mHz) even at the quietest stations. At BFO (Black Forest Observatory, SW-Germany), the opportunity arose to study these disturbances on a variety of simultaneously operated state-of-the-art broad-band sensors. A series of time windows with clear atmospherically caused effects was selected and attempts were made to model these ‘signals’ in a deterministic way. This was done by simultaneously least-squares fitting the locally recorded barometric pressure and its Hilbert transform to the ground accelerations in a bandpass between 100 and 3600 s periods. Variance reductions of up to 97 per cent were obtained. We show our results by combining the ‘specific pressure induced accelerations’ for the two horizontal components of the same sensor as vectors on a horizontal plane, one for direct pressure and one for its Hilbert transform. It turned out that at BFO the direct pressure effects are large, strongly position dependent and largely independent of atmospheric events for instruments installed on piers, while three post-hole sensors are only slightly affected. The infamous ‘cavity effects’ are invoked to be responsible for these large effects on the pier sensors. On the other hand, in the majority of cases all sensors showed very similar magnitudes and directions for the vectors obtained for the regression with the Hilbert transform, but highly variable from event to event especially in direction. Therefore, this direction most certainly has to do with the gradient of the pressure field moving over the station which causes a larger scale deformation of the crust. The observations are very consistent with these two fundamental mechanisms of how fluctuations of atmospheric surface pressure causes tilt noise. The results provide a sound basis for further improvements of the models for these mechanisms. The methods used here can already help to reduce atmospherically induced noise in long-period horizontal seismic records.