Determination of crystal orientation fabric from seismic wideangle data

It is known from ice core analyses that the crystal orientation fabric (COF) of ice sheets is anisotropic and changes over depth. A better understanding of these anisotropies as well as their remote detection is important to optimize flow models for ice. Here we show how seismic wideangle measurements can be used to determine the COF remotely. We demonstrate the principle formalism how observed seismic traveltimes can be related to COF properties by a forward model and then apply the formalism to field data. The eigenvalues that describe the ice fabric of the ice core EDML (Dronning Maud Land, Antarctca) are set into a relationship with the elasticity tensor. From the elasticity tensor the expected seismic velocities and reflection coefficients are calculated. Additionally we calculate the value eta from the Thomsen-parameters epsilon and delta. The value eta gives a measure of the anisotropy of vertical transverse isotropic (VTI)-media and is an important tool for the NMO-correction of anisotropic data. The approximation of reflection horizons as hyperbolas is not valid anymore in anisotropic media. The calculation of the moveout is therefore performed by a 4th order NMO-correction with the rms-velocity and the effective eta value as variables. This approach is applied to data from a wideangle survey shot at Halvfarryggen, Dronning Maud Land, Antarctica. From this data we derived rms-velocities and effective eta values. These values were than recalculated to interval velocities and interval eta values to give a hint on the measure of anisotropy of the different layers. The results give first insight into the anisotropies at Halvfarryggen

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 elasticly and viscoelasticly 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

Random-Objective Waveform Inversion of 3D-9C Shallow-Seismic Field Data

Robustness and uncertainty estimation are two challenging topics in full-waveform inversion (FWI). To overcome these challenges, we present the methodology of random-objective waveform inversion (ROWI), which adopts a multi-objective framework and a preconditioned stochastic gradient descent optimization algorithm. The use of one shot per iteration avoids using redundant data and reduces the computational cost. The Pareto solutions represent a group of most likely solutions and their differences quantifies the model uncertainty associated with the trade-off between conflicting objective functions. Due to the high dimensionality in the data and model spaces, it is prohibitively expensive to check the Pareto optimality of all solutions explicitly. Thus, we decompose the original multi-objective function into shot-related subproblems and use the Pareto solutions of the subproblems for trade-off analysis. We apply ROWI to a field multi-component shallow-seismic data set acquired in Rheinstetten, Germany. The 3D near-surface model is successfully reconstructed by ROWI and the main target, a refilled trench, is delineated. We compare the results estimated by ROWI and a conventional least squares FWI to prove the high efficiency of ROWI. We run six ROWI tests on the field data with different solution paths to prove the robustness of ROWI against the random solution path. The validity of the reconstructed model is verified by multiple 2D ground-penetrating radar profiles. We estimate 246 Pareto solutions of multi-objective subproblems for trade-off analysis. Another four ROWI tests starting from different poor initial models are performed, whose results prove the relatively high robustness of ROWI against the initial model

High-resolution characterization of near-surface structures by surface-wave inversions: From dispersion curve to full waveform

Surface waves are widely used in near-surface geophysics and provide a non-invasive way to determine near-surface structures. By extracting and inverting dispersion curves to obtain local 1D S-wave velocity profiles, multichannel analysis of surface waves (MASW) has been proven as an efficient way to analyze shallow-seismic surface waves. By directly inverting the observed waveforms, full-waveform inversion (FWI) provides another feasible way to use surface waves in reconstructing near-surface structures. This paper provides a state of the art on MASW and shallow-seismic FWI, and a comparison of both methods. A two-parameter numerical test is performed to analyze the nonlinearity of MASW and FWI, including the classical, the multiscale, the envelope-based, and the amplitude-spectrum-based FWI approaches. A checkerboard model is used to compare the resolution of MASW and FWI. These numerical examples show that classical FWI has the highest nonlinearity and resolution among these methods, while MASW has the lowest nonlinearity and resolution. The modified FWI approaches have an intermediate nonlinearity and resolution between classical FWI and MASW. These features suggest that a sequential application of MASW and FWI could provide an efficient hierarchical way to delineate near-surface structures. We apply the sequential-inversion strategy to two field data sets acquired in Olathe, Kansas, USA, and Rheinstetten, Germany, respectively. We build a 1D initial model by using MASW and then apply the multiscale FWI to the data. High-resolution 2D S-wave velocity images are obtained in both cases, whose reliabilities are proven by borehole data and a GPR profile, respectively. It demonstrates the effectiveness of combining MASW and FWI for high-resolution imaging of near-surface structures

2D multi-parameter viscoelastic shallow-seismic full waveform inversion: reconstruction tests and first field-data application

2D full-waveform inversion (FWI) of shallow-seismic wavefields has recently become a novel way to reconstruct S-wave velocity models of the shallow subsurface with high vertical and lateral resolution. In most applications, seismic wave attenuation is ignored or considered as a passive modelling parameter only. In this study, we explore the feasibility and performance of multi-parameter viscoelastic 2D FWI in which seismic velocities and attenuation of P- and S-waves, respectively, and mass density are inverted simultaneously. Synthetic reconstruction experiments reveal that multiple crosstalks between all viscoelastic material parameters may occur. The reconstruction of S-wave velocity is always robust and of high quality. The parameters P-wave velocity and density exhibit weaker sensitivity and can be reconstructed more reliably by multi-parameter viscoelastic FWI. Anomalies in S-wave attenuation can be recovered but with limited resolution. In a field data application, a small-scale refilled trench is nicely delineated as a low P- and S-wave velocity anomaly. The reconstruction of P-wave velocity is improved by the simultaneous inversion of attenuation. The reconstructed S-wave attenuation reveals higher attenuation in the shallow weathering zone and weaker attenuation below. The variations in the reconstructed P- and S-wave velocity models are consistent with the reflectivity observed in a GPR profile

Full-waveform inversion of ground-penetrating radar data in frequency-dependent media involving permittivity attenuation

Full-waveform inversion (FWI) of ground-penetrating radar (GPR) data has received particular attention in the past decade because it can provide high-resolution subsurface models of dielectric permittivity and electrical conductivity. In most GPR FWIs, these two parameters are regarded as frequency independent, which may lead to false estimates if they strongly depend on frequency, such as in shallow weathered zones. In this study, we develop frequency-dependent GPR FWI to solve this problem. Using the τ-method introduced in the research of viscoelastic waves, we define the permittivity attenuation parameter to quantify the attenuation resulting from the complex permittivity and to modify time-domain Maxwell’s equations. The new equations are self-adjoint so that we can use the same forward engine to back-propagate the adjoint sources and easily derive model gradients in GPR FWI. Frequency dependence analysis shows that permittivity attenuation acts as a low-pass filter, distorting the waveform and decaying the amplitude of the electromagnetic waves. The 2-D synthetic examples illustrate that permittivity attenuation has low sensitivity to the surface multioffset GPR data but is necessary for a good reconstruction of permittivity and conductivity models in frequency-dependent GPR FWI. As a comparison, frequency-independent GPR FWI produces more model artefacts and hardly reconstructs conductivity models dominated by permittivity attenuation. The 2-D field example shows that both FWIs reveal a triangle permittivity anomaly which proves to be a refilled trench. However, frequency-dependent GPR FWI provides a better fit to the observed data and a more robust conductivity reconstruction in a high permittivity attenuation environment. Our GPR FWI results are consistent with previous GPR and shallow-seismic measurements. This research greatly expands the application of GPR FWI in more complicated media

Realistic FD modeling of the tunnel environment for seismic tomography

To improve the safety both of the tunnel constructions and buildings at the surface, seismic tomography methods can be used to detect possible safety threads behind the tunnel wall (e.g. cavities, water bearing zones, fractures). Basis for such a tomography is a profound understanding of the seismic wave propagation in the complex surrounding of a tunnel which can be gained from seismic modeling We, therefore, created a realistic tunnel model that accounts for typical features encountered during tunnel construction, e.g. heterogeneous host rock, excavation damaged zone (EDZ) and topography of the tunnel wall. This model is used for the 3-D elastic wave field simulations. Data from multiple shot positions will be later on used for a seismic tomography, either by standard travel time tomography or full waveform tomography. Main objective is the accurate seismic modeling using optimal discretization parameters and an implicit free surface boundary with topography

Detection of geological structures ahead of the tunnel construction using tunnel surface-waves

To improve the performance and safety of tunnel constructions, seismic predictions methods can be used to detect relevant geological structures ahead of the tunnel face (e.g. faults, lithological boundaries). We present a simple and robust processing method that can automatically calculate the distance of such a geological inhomogeneity from the seismic response of only a few receivers mounted on the tunnel wall. The method works fully automatic and does need much computational resources which is ideal under tunneling conditions. Our approach has been develop on 3D synthetic finite difference and tested on real tunneling data. In both cases, the distance of a fault zone has been determined accurately and without any a priori information