J. van der Neut

Data-driven Green's function retrieval and application to imaging with multidimensional deconvolution

An iterative method is presented that allows one to retrieve the Greens function originating from a virtual source located inside a medium using reflection data measured only at the acquisition surface. In addition to the reflection response, an estimate of the travel times corresponding to the direct arrivals is required. However, no detailed information about the heterogeneities in the medium is needed. The iterative scheme generalizes the Marchenko equation for inverse scattering to the seismic reflection problem. To give insight in the mechanism of the iterative method, its steps for a simple layered medium are analyzed using physical arguments based on the stationary phase method. The retrieved Greens wavefield is shown to correctly contain the multiples due to the inhomogeneities present in the medium. Additionally, a variant of the iterative scheme enables decomposition of the retrieved wavefield into its downgoing and upgoing components. These wavefields then enable creation of a ghost-free image of the medium with either cross correlation or multidimensional deconvolution, presenting an advantage over standard prestack migration.

Unified double- and single-sided homogeneous Green’s function representations

In wave theory, the homogeneous Green’s function consists of the impulse response to a point source, minus its time-reversal. It can be represented by a closed boundary integral. In many practical situations, the closed boundary integral needs to be approximated by an open boundary integral because the medium of interest is often accessible from one side only. The inherent approximations are acceptable as long as the effects of multiple scattering are negligible. However, in case of strongly inhomogeneous media, the effects of multiple scattering can be severe. We derive double- and single-sided homogeneous Green’s function representations. The single-sided representation applies to situations where the medium can be accessed from one side only. It correctly handles multiple scattering. It employs a focusing function instead of the backward propagating Green’s function in the classical (double-sided) representation. When reflection measurements are available at the accessible boundary of the medium, the focusing function can be retrieved from these measurements. Throughout the paper, we use a unified notation which applies to acoustic, quantum-mechanical, electromagnetic and elastodynamic waves. We foresee many interesting applications of the unified single-sided homogeneous Green’s function representation in holographic imaging and inverse scattering, time-reversed wave field propagation and interferometric Green’s function retrieval.

Retrieving the Earth’s Reflection Response by Multi-dimensional Deconvolution of Ambient Seismic Noise

A major assumption for retrieving the earth’s reflection response with seismic interferometry by cross-correlation of ambient noise is that subsurface sources are uniformly distributed. It has been shown that interferometry by multi-dimensional deconvolution can cope with non-uniform source arrays, but implementation of this concept requires a separation of the incident wavefield from the free-surface multiples. For transient passive sources, this separation can be implemented by time-gating in the recorded transmission panels before cross-correlation, but such methodology cannot be applied for simultaneously acting noise sources. Here we show that time-gating can also be applied after an intermediate cross-correlation step. In cross-correlated data, we isolate events around t=0, which inhabit the illumination imprint of the subsurface sources. Next, we apply multi-dimensional deconvolution with the isolated events to the events away from t=0. In this way we can effectively correct for the effects of a non-uniform subsurface source distribution in data that is already cross-correlated. With this new approach, multi-dimensional deconvolution becomes feasible for simultaneously acting noise sources.

Deghosting, demultiple, and deblurring in controlled-source seismic interferometry

With controlled-source seismic interferometry we aim to redatum sources to downhole receiver locations without requiring a velocity model. Interferometry is generally based on a source integral over cross-correlation (CC) pairs of full, perturbed (time-gated), or decomposed wavefields. We provide an overview of ghosts, multiples, and spatial blurring effects that can occur for different types of interferometry. We show that replacing cross-correlation by multidimensional deconvolution (MDD) can deghost, demultiple, and deblur retrieved data. We derive and analyze MDD for perturbed and decomposed wavefields. An interferometric point spread function (PSF) is introduced that can be obtained directly from downhole data. Ghosts, multiples, and blurring effects that may populate the retrieved gathers can be locally diagnosed with the PSF. MDD of perturbed fields can remove ghosts and deblur retrieved data, but it leaves particular multiples in place. To remove all overburden-related effects, MDD of decomposed fields should be applied.

Retrieval of Reflections from Ambient Noise Using the Incident Fields (Point-spread Function) as a Diagnostic Tool

Seismic interferometry (SI) enables the retrieval of virtual-shot records at the location of receivers. SI with ambient noise allows the retrieval of the reflection response of the subsurface without the need of any active source. The quality of the retrieved response is dependent on the illumination characteristics of the ambient noise. For the exploration frequency band of interest, in low-seismicity regions most of the energy in the recorded noise comes from sources at or near the surface. Such sources would mainly contribute to retrieval of surface waves, which would show up as the most energetic arrivals in the retrieved results. Because of that, the generally weaker retrieved reflections would be buried by the retrieved surface waves. Aiming at improving SI retrieved reflections, we propose a diagnostic tool applied after cross-correlation that separates the correlated noise panels into surface-wave dominated and body-wave dominated. We show results of the application of the tool to modelled data for noise sources acting separately in time and for noise sources overlapping in time. Finally, we show results from the application of the diagnostic tool to ambient noise recorded in Northern Netherlands.

A Marchenko equation for acoustic inverse source problems

From acoustics to medical imaging and seismology, one strives to make inferences about the structure of complex media from acoustic wave observations. This study proposes a solution that is derived from the multidimensional Marchenko equation, to learn about the acoustic source distribution inside a volume, given a set of observations outside the volume. Traditionally, this problem has been solved by backpropagation of the recorded signals. However, to achieve accurate results through backpropagation, a detailed model of the medium should be known and observations should be collected along a boundary that completely encloses the volume of excitation. In practice, these requirements are often not fulfilled and artifacts can emerge, especially in the presence of strong contrasts in the medium. On the contrary, the proposed methodology can be applied with a single observation boundary only, without the need of a detailed model. In order to achieve this, additional multi-offset ultrasound reflection data must be acquired at the observation boundary. The methodology is illustrated with one-dimensional synthetics of a photoacoustic imaging experiment. A distribution of simultaneously acting sources is recovered in the presence of sharp density perturbations both below and above the embedded sources, which result in significant scattering that complicates the use of conventional methods.

Turning One-sided Illumination into Two-sided Illumination by Target-enclosing Interferometric Redatuming

We present a novel method to transform seismic data with sources at the surface and receivers above and below a selected target zone in the subsurface into virtual data with sources and receivers located at the initial receiver locations. The method is based on inverting a series of multidimensional equations of the convolution- and the correlation-type. The required input data can be computed from surface seismic data with a new iterative scheme that is currently being developed. The output data contains virtual sources that illuminate the target not only from above (as in the original data), but also from below, facilitating the needs of seismic imaging and inversion in an optimal way. The method is nonlinear in the sense that all internal multiples are correctly accounted for and true amplitude in the sense that the virtual sources are forced to inherit uniform radiation patterns even though the overburden is strongly heterogeneous.

Inversion of the multidimensional marchenko equation

Focusing functions are defined as wavefields that focus at a specified location in a heterogeneous subsurface. These functions can be directly related to Greens functions and hence they can be used for seismic imaging of complete wavefields, including not only primary reflections but all orders of internal multiples. Recently, it has been shown that focusing functions can be retrieved from single-sided reflection data and an initial operator (which can be computed in a smooth background velocity model of the subsurface) by iterative substitution of the multidimensional Marchenko equation. In this work, we show that the Marchenko equation can also be inverted directly for the focusing functions. Although this approach is computationally more expensive than iterative substitution, additional constraints can easily be imposed. Such a flexibility might be beneficial in specific cases, for instance when the recorded data are incomplete or when additional measurements (e.g. from downhole receivers) are available.

Controlled-source Elastodynamic Interferometry by Cross-correlation of Decomposed Wavefields

Controlled-source interferometry can be applied to redatum source locations to downhole receiver locations by cross-correlation and summation over sources. The methodology does not require a velocity model between sources and receivers. Starting with a re

Monitoring Effective Stress Changes in Fault Zones from Time-Lapse Seismic Reflection Data – A Model Study

P061 Monitoring Effective Stress Changes in Fault Zones from Time-Lapse Seismic Reflection Data – A Model Study J.R. van der Neut* (Delft University of Technology) M.K. Sen (University of Texas Institute for Geophysics) & K. Wapenaar (Delft University of Technology) SUMMARY A fault can be interpreted as a non-welded interface causing a discontinuity of displacement in a reflecting wave field that can be described with a linear slip boundary condition. We represent a fault as a layer of cracks; its thickness being small compared to the seismic wavelength. An increase of effective stress can be induced by a drop of