Ivan Stekl

Accurate viscoelastic modeling by frequency-domain finite differences using rotated operators

The viscoelastic wave equation is an integro‐differential equation that requires special methods when using time‐domain numerical finite‐difference methods. In the frequency domain, the integral terms are easily represented by complex valued elastic media properties. There are further significant advantages to using the frequency domain if the forward or the inverse problem requires modeling or inverting a large number of prestack source gathers. Numerical modeling is expensive for seismic data because of the large number of wavelenghths typically separating sources from receivers, which results in a need for a large number of grid points. A major obstacle to using frequency‐domain methods is the consequent storage requirements. To reduce these, we maximize the accuracy and simultaneously minimize the spatial extent of the numerical operators. We achieve this by extending earlier published methods introduced for the viscoacoustic case to the viscoelastic case. This requires the formulation of two new nume...

Full waveform inversion: A North Sea OBC case study

Full Waveform Inversion (FWI) aims to obtain superior velocity models by minimizing the difference between observed and modelled seismic waveforms. We apply FWI to a North Sea OBC field data set with wide azimuths and more than 10 km long offsets. We discuss the methodology used and the associated practical issues. Our FWI result has revealed detailed velocity features associated with thin, gas-charged layers and faulting in the shallow sections of the model. We demonstrate that this velocity update has improved the imaging of the deeper structures.

3D full-wavefield tomography: imaging beneath heterogeneous overburden

We have developed computer codes and work-flows for 3D acoustic waveform inversion in both the frequency and time domains. We have applied these methods to several 3D field datasets with a variety of acquisition geometries and target depths. In each case, wavefield tomography was able to obtain a high-resolution high-fidelity velocity model of the heterogeneous overburden, and consequently to improve subsequent depth imaging of an underlying target.

A Strategy for Waveform Inversion without an Accurate Starting Model

SUMMARY A key limitation of waveform inversion as currently implemented is the need for a starting model of high accuracy or field data with low frequencies. Here we present a new approach - staged waveform inversion - designed to mitigate this need and thereby permit the application of waveform inversion to a much wider range of datasets.

Which Physics for Full-wavefield Seismic Inversion?

Full waveform seismic inversion, as currently commercially available in 3D, uses the acoustic approximation to the wave equation, and generally ignores the effects of elasticity, attenuation and anomalous density variations. We examine the consequences of these practical compromises by inverting 3D synthetic seismic data using different approximations to the physics of wave propagation in the forward and inverse modelling. We also invert using different portions of the data, and examine the effects of data amplitudes. We conclude that current FWI practice works well if amplitudes and reflected energy are suppressed in the inversion, but that a more-complete description of the physics is required in order to extract quantitative physical properties from amplitudes and reflections.

3D Frequency Domain Waveform Inversion – Synthetic Shallow Channel Example

C026 3D Frequency Domain Waveform Inversion – Synthetic Shallow Channel Example I. Stekl* (Imperial College London) M.R. Warner (Imperial College) & A.P. Umpleby (Imperial College) SUMMARY We are presenting a first example of 3D frequency domain acoustic inversion applied to a synthetics data over a shallow channel. High resolution images are obtained in less than a day CPU time using inexpensive hardware by utilizing a point iterative solver for wave equation modelling part of the code and multi shot approach. Tests have shown that it is possible to combine multiple shot positions and reduce time required for computation dramatically. Final

Waveform inversion of surface seismic data without the need for low frequencies

Summary Waveform inversion is a technique with capability of generating velocity models with unprecedented resolution and clarity from seismic data. However it often requires unrealistically low frequencies in the data to achieve this. We propose a scheme designed to mitigate this need ‐ a necessary key step for realising the potential of the technique in a far wider range of datasets and targets than currently possible. The scheme operates by preceding the inversion of the field data by inversion of intermediate datasets ‐ synthesised by extracting the irrotational component of the phase mismatch at the lowest useable frequency. We demonstrate its effectiveness over the corresponding conventional approach by inverting data from the Marmousi model with a minimum frequency of 5Hz.

Full-waveform Seismic Inversion at Reservoir Depths

We apply 3D anisotropic acoustic full-waveform tomographic seismic inversion to a North Sea wide-angle OBC dataset, and demonstrate that our recovered velocity model is realistic within the chalk reservoir sequence to depths of up to 4000 m. Because we use predominantly wide-angle refracted arrivals in the inversion, we are able to undershoot and image within the otherwise seismic obscured area beneath a shallow gas cloud that overlies the reservoir. Wide-angle FWI techniques using similar datasets have not previously been used to image successfully at these depths.

Full Wavefield Seismic Tomography – Iterative Forward Modelling in 3D

C025 Full Wavefield Seismic Tomography – Iterative Forward Modelling in 3D M. Warner* (Imperial College London) I. Stekl (Imperial College London) & A. Umpleby (Imperial College London) SUMMARY We have developed an efficient iterative solver for the 3D two-way acoustic wave equation and demonstrate its use for 3D wavefield tomography on a synthetic seismic model. Using composite shots for the tomography the method is sufficiently fast that it can be used to image realistic-sized field datasets. EAGE 69 th Conference & Exhibition — London UK 11 - 14 June 2007 Conventional seismic tomography seeks to recover an earth model that

Time vs frequency for 3D wavefield tomography

Unlike the situation in two-dimensions, where direct factorisation of the matrix equations makes frequency-domain methods much faster than explicit solution in the time-domain, the computational resources required for practical wavefield tomography in 3D can be rather similar in the two domains. We have developed and optimised schemes that undertake wavefield tomography using explicit time stepping in the time domain and that iteratively solve the matrix equations of the implicit problem in the frequency domain. We have applied these two methods systematically to the same suite of problems. In the frequency domain, the principal advantages are that the initial tomographic updates for lowest frequencies are often seen more quickly, and spatial resolution can be better at the highest frequencies. In the time domain, one of the principal advantages is that it is possible to mute and/or weight the field data in time, and consequently the method can be made to work more effectively with difficult datasets. In practice, both approaches are useful, and both should be available within a comprehensive suite of inversion tools.