A. Kurzmann

3D elastic full-waveform inversion of small-scale heterogeneities in transmission geometry

Three-dimensional elastic full-waveform inversion aims to reconstruct elastic material properties of 3D structures in the subsurface with high resolution. Here we present an implementation of 3D elastic full-waveform inversion based on the adjoint-state method. The code is optimized regarding runtime and storage costs by using a time-frequency approach. The gradient is computed from monochromatic frequency-domain particle-velocity wavefields calculated with a time-domain velocity-stress finite-difference scheme. The 3D full-waveform inversion was applied to data of a complex random medium model, which resembles a realistic crystalline rock environment. We show synthetic inversion results of P-wave and S-wave velocities for two transmission geometries: (1) a 3D acquisition geometry with planes of sources and receivers and (2) a 2D geometry with two lines of sources and receivers, resembling a realistic two-borehole geometry. The 3D inversion of data acquired with 3D source-receiver geometry is capable to reconstruct differently sized 3D structures of shear and compressional velocities with resolution of about a wavelength. The 3D random medium data recorded with 2D acquisition geometry were inverted using 3D inversion and 2D full-waveform inversion for comparison. The 2D inversion suffers from strong artefacts that are caused by 3D scattering. The multiparameter 3D inversion, by contrast, is capable to invert the 3D scattered waves and to reconstruct 3D structures up to about 1–2 wavelengths adjacent to the plane between sources and receivers. The resolution is lower compared to the 3D acquisition geometry result. Still, a 3D inversion of cross-hole data can be beneficial compared to a 2D inversion in the presence of complex 3D small-scale heterogeneities, as it is capable to resolve 3D structures next to the source-receiver plane.

2D Acoustic Full Waveform Tomography – Performance and Optimization

For better parameter estimation we develop imaging methods that can exploit the richness of full seismic waveforms. Full waveform tomography (FWT) is a powerful method to reach this goal. In this study, we demonstrate the performance of our new parallel a

The Role of Density in Acoustic Full Waveform Inversion of Marine Reflection Seismics

Full waveform inversion (FWI) is a data-fitting method that exploits the full information from the seismic data to provide high-resolution models of the subsurface. To reconstruct realistic models from field measurements the forward modeling should correctly account for wave propagation phenomena present in the recorded data. This mainly concerns the correct modeling of seismic amplitudes that are sensitive not only to the velocity variations, but also to the density, attenuation, seismic noise. The objective of this study is to investigate the role of density in the reconstruction of P-wave velocity models in the marine environment. We generated a realistic, synthetic data set with the conventional streamer geometry, and the frequency range from 3 to 20 Hz. We performed series of numerical experiments, testing various initial density models and different strategies for the density update. Our results suggest that it is important to include the realistic density information into the inversion scheme to bring improvement in the P-velocity reconstruction. Moreover, we investigated the potential benefits of multi-parameter inversion (P-velocity and density) of the noisy data, by considering random and spatially coherent noise. Density inversion has partly absorbed noise-related artefacts, which yielded better resolved P-wave models than the single-parameter inversion.

2D Elastic Full Waveform Tomography of Synthetic Marine Reflection Seismic Data

With the increasing performance of parallel supercomputers full waveform tomography (FWT) approaches can reduce the misfit between recorded and modelled data, to deduce a very detailed physical model of the underground. In recent years acoustic waveform tomography became a very popular tool to image the underground structures. However, acoustic waveform inversion has the disadvantage, that only P waves can be inverted. It can not invert for S-waves or surface waves. Here we will present the first inversion results of our elastic parallel time domain FWT code for two synthetic model examples and discuss problems which occurred during the code development like the choice of model parameters. Even though the problem is highly nonlinear and ill conditioned the elastic FWT is able to resolve very detailed images of all three elastic model parameters.

Comparison of acoustic full waveform tomography in the time - and frequency - domain

For better parameter estimation, both in active source and earthquakes seismology, we need to exploit the richness of full seismic waveforms. Full waveform tomography (FWT) is a powerful method to reach this goal. Although first implementations in the 1980s were conducted in the time-domain by Tarantola, the frequency-domain version of FWT developed in the 1990s by G. Pratt and coworkers has now emerged as an efficient imaging tool. The main advantage of the frequency-domain approach is the possibility of starting the inversion at low frequencies (large scale structures) and then moving to higher frequency compounds (smaller scale structures), thereby realizing a multiscale approach. The main advantage of the time-domain method is the efficient parallelization by domain decomposition leading to a significant speedup on parallel computers. In this study, we demonstrate the performance of our parallel acoustic time-domain code. We present the results for a very complex example - a random medium model. Last but not least, we compare our time-domain inversion results with the frequency-domain results calculated using the FULLWV code by G. Pratt et al.

Robust time-domain migration velocity analysis methods for initial-model building in a full waveform tomography workflow

Full-waveform tomography (FWT) is notorious for its strong dependence on the initial model. We present a workflow for the construction of initial velocity-models for FWT methods consisting of automatic time-migration velocity analysis by means of double multi-stack migration, followed by time-to-depth conversion by image-ray wavefront propagation. Evaluation of the converted velocity model as an initial velocity model in an acoustic FWT process indicates the potential of using a combination of these methods to achieve a fully automatic tool for initial-model building in a FWT workflow. Our tests on a modified version of the Marmousi-2 model have shown that correct background velocity information can be successfully extracted from automatic time-domain migration velocity analysis even in media where time-migration cannot provide satisfactory seismic images.

3D elastic full waveform inversion-A random medium example

3D elastic full waveform inversion (FWI) has the potential to resolve complex 3D structures and to offer multiparameter images with high resolution. In this work we describe the implementation of our 3D elastic FWI code and show first results. The code is based on the adjoint method and optimized by using a combined time-frequency domain FWI. The performance is shown for a random medium model in transmission geometry, hereby inverting for the seismic velocities. Using a 3D acquisition geometry, the differently sized, complex structures of the random medium can be well resolved. In a second test, a typical borehole geometry with lines of sources and receivers was employed. Within the plane between the boreholes, it was possible to resolve the main features, however resolution and quality is less than for the 3D acquisition geometry. Nevertheless, by using a 3D FWI instead of a 2D FWI, 3D structures can be taken into account.

Viscoacoustic Full Waveform Inversion for Spatially Correlated and Uncorrelated Problems in Reflection Seismics

Seismic attenuation plays an important role in real Earth and contains valuable information about the subsurface. To recover spatial distributions of both velocity and quality factor Q, in this work we investigate the applicability of 2D viscoacoustic full waveform inversion (FWI) to synthetic marine reflection data. Viscoacoustic FWI is a multiparameter inverse problem, and suffers from the cross-talk between different parameter classes. Based on the 2D Marmousi model, we investigate the cross-talk using spatially correlated and uncorrelated models of velocity and attenuation. Our results show a good reconstruction of the velocity model and satisfactory recovery of Q only in the shallow areas. With increasing depth we observe a stronger footprint of the velocity model. Nevertheless, the fit of synthetic and recorded seismograms is excellent. This can be interpreted either as low sensitivity of the synthetic data to attenuation properties in deep parts or as cross-talk with explanation of attenuation-related data misfit by the velocity model. We find that the investigation of multiparameter inverse problems with (highly) spatially uncorrelated parameters has to be considered as a necessary step to verify the reliability of inversion strategies.

Acoustic and Elastic Full Waveform Tomography

For a better estimation of subsurface parameters we develop imaging methods that can exploit the richness of full seismic waveforms. Full waveform tomography (FWT) is a powerful imaging method and emerges as an important procedure in hydrocarbon exploration and underground construction. It is able to recover high-resolution multi-parameter subsurface images from recorded seismic data. For the reconstruction of 3D subsurface structures we apply large-scale 3D elastic and acoustic FWT, which require extensive optimization of runtime and performance. For an improvement of the gradient based optimization method we apply the inverse of a diagonal Hessian approximation for preconditioning of the gradients. However, its calculation is computationally expensive, as it requires one additional forward simulation for each receiver of the underlying seismic acquisition geometry. Therefore, we calculate it only once for an iteration subset of each stage of the multi-stage workflow considering several frequency ranges. The performance is shown for a simple transmission geometry application. Source and receiver artifacts were removed sufficiently and the inversion was successfully performed. The second application shows the effects of the number of sources – correlating with the number of simulations and, thus, mainly affecting the computational efforts – on the reconstruction of a 3D acoustic model in reflection geometry. To allow a successful inversion of the 3D structures and to avoid artifacts due to spatial aliasing, a reasonable number of sources is required. This essential amount of sources depends on the choice of seismic frequencies. Thus, we recommend to reduce simulations at early FWT stages (low frequencies) and to increase the number of sources with increasing frequencies.

2D Acoustic Full Waveform Tomography of Marine Streamer Data - Problems and Data Preprocessing

In recent years many synthetic studies showed the great resolution potential of full waveform tomography (FWT), nevertheless application to field data is not a common standard yet. This study discusses some of the problems related with the inversion of conventional single sensor marine streamer data in the 2D acoustic approximation. The lack of low frequency information makes the waveform tomography strongly depending on the initial model. In particular, density information should be considered in the inversion process to obtain reliable P-wave velocity models. The directivity of marine airguns and wave propagation effects, that cannot be reproduced by the forward modeling code require a certain amplitude calibration and scaling of amplitude with offset. Swell noise caused by time variant sea surface topography may significantly reduce the field data quality. Therefore, the noise subtraction algorithm that mutes noise and preserves the useful seismic signal must be applied. The effects of the sea surface topography can be reduced by data de-ghosting. However, this procedure may require additional measurements of pressure and particle velocities using dual-sensors.