Joost van der Neut

Passive seismic interferometry by multidimensional deconvolution

We introduce seismic interferometry of passive data by multidimensional deconvolution (MDD) as an alternative to the crosscorrelation method. Interferometry by MDD has the potential to correct for the effects of source irregularity, assuming the first arrival can be separated from the full response. MDD applications can range from reservoir imaging using microseismicity to crustal imaging with teleseismic data.

Controlled-source interferometric redatuming by crosscorrelation and multidimensional deconvolution in elastic media

Various researchers have shown that accurate redatuming of controlled seismic sources to downhole receiver locations can be achieved without requiring a velocity model. By placing receivers in a horizontal or deviated well and turning them into virtual sources, accurate images can be obtained even below a complex near-subsurface. Examples include controlled-source interferometry and the virtual-source method, both based on crosscorrelated signals at two downhole receiver locations, stacked over source locations at the surface. Because the required redatuming operators are taken directly from the data, even multiple scattered waveforms can be focused at the virtual-source location, and accurate redatuming can be achieved. To reach such precision in a solid earth, representations for elastic wave propagation that require multicomponent sources and receivers must be implemented. Wavefield decomposition prior to crosscorrelation allows us to enforce virtual sources to radiate only downward or only upward. Virtual-source focusing and undesired multiples from the overburden can be diagnosed with the interferometric point-spread function (PSF), which can be obtained directly from the data if an array of subsurface receivers is deployed. The quality of retrieved responses can be improved by filtering with the inverse of the PSF, a methodology referred to as multidimensional deconvolution.

A representation for Green’s function retrieval by multidimensional deconvolution

Greens function retrieval by crosscorrelation may suffer from irregularities in the source distribution, asymmetric illumination, intrinsic losses, etc. Multidimensional deconvolution (MDD) may overcome these limitations. A unified representation for Greens function retrieval by MDD is proposed. From this representation, it follows that the traditional crosscorrelation method gives a Greens function of which the source is smeared in space and time. This smearing is quantified by a space-time point-spread function (PSF), which can be retrieved from measurements at an array of receivers. MDD removes this PSF and thus deblurs and deghosts the source of the Greens function obtained by correlation.

Green's function retrieval from reflection data, in absence of a receiver at the virtual source position

The methodology of Greens function retrieval by cross-correlation has led to many interesting applications for passive and controlled-source acoustic measurements. In all applications, a virtual source is created at the position of a receiver. Here a method is discussed for Greens function retrieval from controlled-source reflection data, which circumvents the requirement of having an actual receiver at the position of the virtual source. The method requires, apart from the reflection data, an estimate of the direct arrival of the Greens function. A single-sided three-dimensional (3D) Marchenko equation underlies the method. This equation relates the reflection response, measured at one side of the medium, to the scattering coda of a so-called focusing function. By iteratively solving the 3D Marchenko equation, this scattering coda is retrieved from the reflection response. Once the scattering coda has been resolved, the Greens function (including all multiple scattering) can be constructed from the reflection response and the focusing function. The proposed methodology has interesting applications in acoustic imaging, properly accounting for internal multiple scattering.

Improved surface‐wave retrieval from ambient seismic noise by multi‐dimensional deconvolution

The methodology of surface?wave retrieval from ambient seismic noise by crosscorrelation relies on the assumption that the noise field is equipartitioned. Deviations from equipartitioning degrade the accuracy of the retrieved surface?wave Greens function. A point?spread function, derived from the same ambient noise field, quantifies the smearing in space and time of the virtual source of the Greens function. By multidimensionally deconvolving the retrieved Greens function by the point?spread function, the virtual source becomes better focussed in space and time and hence the accuracy of the retrieved surface?wave Greens function may improve significantly. We illustrate this at the hand of a numerical example and discuss the advantages and limitations of this new methodology.

Estimating and correcting the amplitude radiation pattern of a virtual source

In the virtual source (VS) method we crosscorrelate seismic recordings at two receivers to create a new data set as if one of these receivers were a virtual source and the other a receiver. We focus on the amplitudes and kinematics of VS data, generated by an array of active sources at the surface and recorded by an array of receivers in a borehole. The quality of the VS data depends on the radiation pattern of the virtual source, which in turn is controlled by the spatial aperture of the surface source distribution. Theory suggests that when the receivers are surrounded by multi-component sources completely filling a closed surface, then the virtual source has an isotropic radiation pattern and VS data possess true amplitudes. In practical applications, limited sourceaperture and deployment of a single source type create an anisotropic radiation pattern of the virtual source, leading to distorted amplitudes. This pattern can be estimated by autocorrelating the spatial Fourier transform of the downgoing wavefield in the special case of a laterally invariant medium. The VS data can be improved by deconvolving the VS data with the estimated amplitude radiation pattern in the frequency-wavenumber domain. This operation alters the amplitude spectrum but not the phase of the data. We can also steer the virtual source by assigning it a new desired amplitude radiation pattern, given sufficient illumination exists in the desired directions. Alternatively, time-gating the downgoing wavefield before crosscorrelation, already common practice in implementing the VS method, can improve the radiation characteristics of a virtual source.

Seismic interferometry: a comparison of approaches

We discuss three approaches to seismic interferometry and compare their underlying assumptions. In the first approach the reflection response is reconstructed by cross-correlating the responses of many uncorrelated noise sources. In the second approach a depth image is obtained from the response of a single source, recorded by many receivers. In the third approach the Green’s function is reconstructed by cross-correlating the recordings of two receivers in a diffuse field.

Review paper: Virtual sources and their responses, Part II: data-driven single-sided focusing

ABSTRACT In Part I of this paper, we defined a focusing wave field as the time reversal of an observed point‐source response. We showed that emitting a time‐reversed field from a closed boundary yields a focal spot that acts as an isotropic virtual source. However, when emitting the field from an open boundary, the virtual source is highly directional and significant artefacts occur related to multiple scattering. The aim of this paper is to discuss a focusing wave field, which, when emitted into the medium from an open boundary, yields an isotropic virtual source and does not give rise to artefacts. We start the discussion from a horizontally layered medium and introduce the single‐sided focusing wave field in an intuitive way as an inverse filter. Next, we discuss single‐sided focusing in two‐dimensional and three‐dimensional inhomogeneous media and support the discussion with mathematical derivations. The focusing functions needed for single‐sided focusing can be retrieved from the single‐sided reflection response and an estimate of the direct arrivals between the focal point and the accessible boundary. The focal spot, obtained with this single‐sided data‐driven focusing method, acts as an isotropic virtual source, similar to that obtained by emitting a time‐reversed point‐source response from a closed boundary.

Unified multi‐depth‐level field decomposition

Wavefield decomposition forms an important ingredient of various geophysical methods. An example of wavefield decomposition is the decomposition into upgoing and downgoing wavefields and simultaneous decomposition into different wave/field types. The multi-component field decomposition scheme makes use of the recordings of different field quantities (such as particle velocity and pressure). In practice, different recordings can be obscured by different sensor characteristics, requiring calibration with an unknown calibration factor. Not all field quantities required for multi-component field decomposition might be available, or they can suffer from different noise levels. The multi-depth-level decomposition approach makes use of field quantities recorded at multiple depth levels, e.g., two horizontal boreholes closely separated from each other, a combination of a single receiver array combined with free-surface boundary conditions, or acquisition geometries with a high-density of vertical boreholes. We theoretically describe the multi-depth-level decomposition approach in a unified form, showing that it can be applied to different kinds of fields in dissipative, inhomogeneous, anisotropic media, e.g., acoustic, electromagnetic, elastodynamic, poroelastic, and seismoelectric fields. We express the one-way fields at one depth level in terms of the observed fields at multiple depth levels, using extrapolation operators that are dependent on the medium parameters between the two depth levels. Lateral invariance at the depth level of decomposition allows us to carry out the multi-depth-level decomposition in the horizontal wavenumber–frequency domain. We illustrate the multi-depth-level decomposition scheme using two synthetic elastodynamic examples. The first example uses particle velocity recordings at two depth levels, whereas the second example combines recordings at one depth level with the Dirichlet free-surface boundary condition of zero traction. Comparison with multicomponent decomposed fields shows a perfect match in both amplitude and phase for both cases. The multi-depth-level decomposition scheme is fully customizable to the desired acquisition geometry. The decomposition problem is in principle an inverse problem. Notches may occur at certain frequencies, causing the multi-depth-level composition matrix to become uninvertible, requiring additional notch filters. We can add multi-depth-level free-surface boundary conditions as extra equations to the multi-component composition matrix, thereby overdetermining this inverse problem. The combined multi-component–multi-depth-level decomposition on a land data set clearly shows improvements in the decomposition results, compared with the performance of the multi-component decomposition scheme.

Retrieval of Reflections From Ambient-noise Field Data Using Illumination Diagnostics

Seismic interferometry (SI) enables the retrieval of virtual-shot records at the location of receivers. In the case of passive SI, no active sources are required for the retrieval of the reflection response of the subsurface, but ambient-noise recording only. It is the illumination features of the recorded ambient noise that determine the resulting retrieved response. Such characteristics, like geometry and signature of the noise sources, together with the complexity of the medium, are responsible for the quality of the retrieved virtual-shot events and the length of the recorded noise. To retrieve body-wave reflections, one would need to correlate body-wave noise from relatively deeper sources. A source of such noise might be the regional seismicity. In regions with noticeable human presence, the dominant noise sources will be located at or close to the surface. In the later case, the noise will be dominated by surface waves and consequently also the retrieved virtualshot records will contain retrieved surface waves drowning retrieved reflections. We present a method for carrying out an illumination diagnostics of the recorded ambient noise using the correlation results from the recorded noise. We explain the method using an example from a passive dataset recorded at Annerveen, Northern Netherlands, and show how this diagnostic tool helps improve the retrieval of reflections.