Subsurface Grid Point Research Articles

Utilization of multiple scattering: the next big step forward in seismic imaging

Surface removal and internal multiple removal are explained by recursively separating the primary and multiple responses at each depth level with the aid of wavefield prediction error filtering. This causal removal process is referred to as “data linearization.” The linearized output (primaries only) is suitable for linear migration algorithms. Next, a summary is given on the migration of full wavefields (primaries multiples) by using the concept of secondary sources in each subsurface gridpoint. These secondary sources are two-way and contain the gridpoint reflection and the gridpoint transmission properties. In full wavefield migration, a local inversion process replaces the traditional linear imaging conditions. Finally, Marchenko redatuming is explained by iteratively separating the full wavefield response from above a new datum and the full wavefield response from below a new datum. The redatuming output is available for linear migration (Marchenko imaging) or, even better, for full wavefield migration. Linear migration, full wavefield migration, and Marchenko imaging are compared with each other. The principal conclusion of this essay is that multiples should not be removed, but they should be utilized, yielding two major advantages: (i) illumination is enhanced, particularly in the situation of low signal-to-noise primaries; and (ii) both the upper side and the lower side of reflectors are imaged. It is also concluded that multiple scattering algorithms are more transparent if they are formulated in a recursive depth manner. In addition to transparency, a recursive depth algorithm has the flexibility to enrich the imaging process by inserting prior geological knowledge or by removing numerical artefacts at each depth level. Finally, it is concluded that nonlinear migration algorithms must have a closed-loop architecture to allow successful imaging of incomplete seismic data volumes (reality of field data).

Enriched seismic imaging by using multiple scattering

The migration of full wavefields (primaries + multiples) by using the concept of secondary sources at each subsurface grid point is summarized. These secondary sources are two way and contain the grid-point reflection as well as the grid-point transmission properties. They “assist” the primary sources in illumination of the subsurface. Full-wavefield migration is implemented as a closed-loop process in which the estimated reflectivity properties are used to generate all higher-order scattering (multiples and transmission effects), such that the modeled full-wavefield response matches the observed measurements. In addition, velocities can be updated simultaneously. Theoretical considerations and examples lead to the principal conclusion that multiples should be used, not removed.

Extending illumination using all multiples: application to 3D acquisition geometry analysis

Recent advances in survey design have led to conventional common‐midpoint‐based analysis being replaced by subsurface‐based seismic acquisition analysis, with emphasis on advanced techniques of illumination analysis. Among them is the so‐called focal beam method, which is a wave‐equation‐based seismic illumination analysis method. The objective of the focal beam method is to provide a quantitative insight into the combined influence of acquisition geometry, overburden structure, and migration operators on the resolution and angle‐dependent amplitude fidelity of the image. The method distinguishes between illumination and sensing capability of a particular acquisition geometry by computing the focal source beam and the focal detector beam, respectively. Sensing is related to the detection properties of a detector configuration, whereas illumination is related to the emission properties of a source configuration. The focal source beam analyses the incident wavefield at a specific subsurface grid point from all available sources, whereas the focal detector beam analyses the sensing wavefield reaching at the detector locations from the same subsurface grid point. In the past, this method could only address illumination by primary reflections. In this paper, we will extend the concept of the focal beam method to incorporate the illumination due to the surface and internal multiples. This in fact complies with the trend of including multiples in the imaging process. Multiple reflections can illuminate a target location from other angles compared with primary reflections, resulting in a higher resolution and an improved illumination. We demonstrate how an acquisition‐related footprint can be corrected using both the surface and the internal multiples.

2D frequency-domain elastic full-waveform inversion using time-domain modeling and a multistep-length gradient approach

To decouple the parameters in elastic full-waveform inversion (FWI), we evaluated a new multistep-length gradient approach to assign individual weights separately for each parameter gradient and search for an optimal step length along the composite gradient direction. To perform wavefield extrapolations for the inversion, we used parallelized high-precision finite-element (FE) modeling in the time domain. The inversion was implemented in the frequency domain; the data were obtained at every subsurface grid point using the discrete Fourier transform at each time-domain extrapolation step. We also used frequency selection to reduce cycle skipping, time windowing to remove the artifacts associated with different source spatial patterns between the test and predicted data, and source wavelet estimation at the receivers over the full frequency spectrum by using a fast Fourier transform. In the inversion, the velocity and density reconstructions behaved differently; as a low-wavenumber tomography (for velocities) and as a high-wavenumber migration (for density). Because velocities and density were coupled to some extent, variations were usually underestimated (smoothed) for [Formula: see text] and [Formula: see text] and correspondingly overestimated (sharpened) for [Formula: see text]. The impedances [Formula: see text] and [Formula: see text] from the products of the velocity and density results compensated for the under- or overestimations of their variations, so the recovered impedances were closer to the correct ones than [Formula: see text], [Formula: see text], and [Formula: see text] were separately. Simultaneous reconstruction of [Formula: see text], [Formula: see text], and [Formula: see text] was robust on the FE and finite-difference synthetic data (without surface waves) from the elastic Marmousi-2 model; satisfactory results are obtained for [Formula: see text], [Formula: see text], [Formula: see text], and the recovered [Formula: see text] and [Formula: see text] from their products. Convergence is fast, needing only a few tens of iterations, rather than a few hundreds of iterations that are typical in most other elastic FWI algorithms.

Illumination properties and imaging promises of blended, multiple‐scattering seismic data: a tutorial

ABSTRACTIn traditional seismic surveys the firing time between shots is such that the shot records do not interfere in time. In the concept of blended acquisition, however, shot records do overlap, allowing denser source sampling and wider azimuths in an economic way. A denser shot sampling and wider azimuths make that each subsurface gridpoint is illuminated from a larger number of angles and will therefore improve the image quality in terms of signal‐to‐noise ratio and spatial resolution. In this tutorial, we show that, even with very simple blending parameters like time delays, the incident wavefield at a specific subsurface gridpoint represents a dispersed time series with a complex code. For shot record migration purposes, this time series should be designed such that it facilitates a stable inversion process. In a next step, we explain how the illumination property of the incident wavefield can be further improved by utilizing the surface‐related multiples. This means that these multiples can be exploited to improve the incident wavefield by filling angle gaps in the illumination and/or by extending the range of angles (‘natural blending’). In this way the energy contained in the multiples now contributes to the image, rather than decreasing its quality. One remarkable consequence of this property is that the benefits to be obtained from the improved illumination depend on the detector locations in acquisition geometries as well. We explain how to quantify the contribution of the blended surface multiples to the incident wavefield for a blended source configuration. In addition, we explain how blended measurements can be directly used in an angle‐dependent migration process with a bifocal, least‐squares imaging condition. The result is a densely sampled reflectivity function in the ray parameter domain, also improving the capability of velocity estimation. We will show examples to illustrate the theory.

Multiscattering illumination in blended acquisition

In traditional seismic surveys, the firing time between shots is such that the shot records do not interfere in time. However, in the concept of blended acquisition, the records do overlap, allowing denser source sampling and wider azimuths in an economic way. A denser shot sampling and wider azimuths make that each subsurface gridpoint is illuminated from a larger number of angles and will therefore improve the image quality in terms of signal-to-noise ratio and spatial resolution. We show that — even with very simple blending parameters like time delays — the incident wavefield at a specific subsurface gridpoint represents a dispersed time series with a “complex code”. For shot-record migration purposes, this time series must have a stable inverse. In a next step, we show that the illumination can be further improved by utilizing the surface-related multiples. This means that these multiples can be exploited to improve the incident wavefield by filling angle gaps in the illumination and/or by extending the range of angles. In this way, the energy contained in the multiples now contributes to the image, rather than decreasing its quality. One remarkable consequence of this property is that the benefits to be obtained from the improved illumination depend on the detector locations in acquisition geometries as well. We show how to quantify the contribution of the blended surface multiples to the illuminating wavefield for a blended source configuration. Results confirm that the combination of blending and multiple scattering increases the illumination energy and, therefore, will improve the quality of shot-record migration results beyond today’s capability.

Key Issues in integrated seismic exploration

Full seismic inversion, i.e. transforming seismic shot records into geologically oriented subsurface parameters, may be performed by three separate processing modules. In the first module the surface information, i.e. the source input signal and the detector output signals, respectively, are transformed into the downgoing source wavefield and the upgoing reflected wavefield at the surface. Next, the influence of the source wavelet and the surface reflectivity are removed from the wavefields. In the second inversion module, the source wavefield and the reflected wavefield are extrapolated from the surface into the subsurface, and for each subsurface grid point (depth point) the reflectivity is computed. Finally, in the third module, the reflectivity information is transformed into velocity and density maps, and, optionally, into rock and pore parameters. The last step is only feasible if a significant amount of non-seismic information is available. This means that, particularly in the last inversion module, an integrated approach is required. An outline is given of the requirements of an exploration and production (E&P) information management system. It is argued that a fast, single-model database is a prerequisite for management of all related exploration and production data.

An integrated method for resolving the seismic complex near‐surface problem

ABSTRACTWe describe an integrated method for solving the complex near‐surface problem in land seismic imaging. This solution is based on an imaging approach and is obtained without deriving a complex near‐surface velocity model. We start by obtaining from the data the kinematics of the one‐way focusing operators (i.e. time‐reversed Green's functions) that describe propagation between the acquisition surface and a chosen datum reflector using the common‐focus‐point technology. The conventional statics solutions obtained from prior information about the near surface are integrated in the initial estimates of the focusing operators. The focusing operators are updated iteratively until the imaging principle of equal traveltime is fulfilled for each subsurface gridpoint of the datum reflector. Therefore, the seismic data is left intact without any application of time shifts, which makes this method an uncommitted statics solution. The focusing operators can be used directly for wave‐equation redatuming to the respective reflector or for prestack imaging if determined for multiple reflecting boundaries. The underlying velocity model is determined by tomographic inversion of the focusing operators while also integrating any hard prior information (e.g. well information). This velocity model can be used to perform prestack depth imaging or to calculate the depth of the new datum level. We demonstrate this approach on 2D seismic data acquired in Saudi Arabia in an area characterized by rugged topography and complex near‐surface geology.

Pushing the limits of seismic imaging, Part II: Integration of prestack migration, velocity estimation, and AVO analysis

The author proposes an operator‐driven prestack migration scheme that is based on the synthesis of common focus‐point (CFP) gathers. Each CFP gather represents the response of a synthesized source array that aims at the illumination of one subsurface gridpoint (focus point). The involved synthesis operator is referred to as the focusing operator. If the time‐reversed focusing operator and its related focus‐point response have equal traveltimes, then the underlying macro velocity model is correct and the focus‐point response in the CFP gather is stacked by weighted addition along the common traveltime curve (CFP‐stacking), yielding the prestack migration result at the subsurface grid point under consideration. If the time‐reversed focusing operator and its related focus‐point response have different traveltimes, then the underlying macro velocity model is incorrect and the correct focusing operator can be derived from the two traveltime curves. A simple updating procedure is proposed. The total CFP migration process of synthesis, updating, and stacking is repeated for all subsurface grid points of interest, leading to the prestack migration result in one‐way image time together with a distribution of updated focusing operators. In a postprocessing step, all operator traveltime information can be used to derive a velocity model for the time‐to‐depth conversion process. Hence, in the presented “CFP technology” the author proposes to estimate the velocity model from the correct focusing operators by a global inversion process after the migration process has been carried out (“beyond depth migration”). For each subsurface grid point, the amplitudes along the pairs of updated traveltime curves provide amplitude‐versus‐offset (AVO) information. In addition, by introducing the grid‐point gather with the aid of an extension of the second focusing process, the author shows that this gather leads to the extraction of pre‐ and postcritical amplitude‐versus‐ray parameter (AVP) information at each grid point. Finally, just as a velocity model can be estimated from all grid‐point‐oriented traveltime information, a lithology model can be estimated from all grid‐point—oriented amplitude information by a postimaging global inversion process.

Pushing the limits of seismic imaging, Part I: Prestack migration in terms of double dynamic focusing

In this paper, the author proposes to extend the synthesis of areal sources (controlled emission) to the synthesis of areal detectors (controlled detection) such that the concept of numerical focusing can be formulated as a special version of target‐oriented synthesis. As a consequence, the insight in the complex prestack migration process can be improved significantly by making use of the concepts “focusing in emission” and “focusing in detection.” Focusing in emission transforms shot records into so‐called common focus‐point (CFP) gathers. Focusing in detection transforms CFP gathers into the prestack migration result. If structural information is sought, the focus point in emission is chosen equal to the focus point in detection: confocal version of CFP migration. If rock and pore information is required as well, the focus point in emission is chosen different from the focus point in detection: bifocal version of CFP migration. Errors in the underlying macro velocity model can be better analysed than before by using CFP gathers as an intermediate migration output. The error analysis involves a comparison between each CFP gather and its related focusing operator. The quality (amplitude accuracy, noise content, resolution) of prestack migration results can be evaluated effectively at each subsurface grid point by analysing the two focused beams involved (pre‐evaluation) and by analyzing the so‐called grid‐point gather (post‐evaluation). The proposed pre‐evaluation method may lead to an improved way of coping with “acquisition footprints” of relatively sparse source and receiver coverage.

An integrated approach to lithologic inversion—Part I: Theory

For the complex problem of lithologic inversion a new formalism is proposed, using a spatial distribution of seismic velocities ([Formula: see text]) and densities (ρ) as input. At each subsurface grid point, the inversion result consists of the most likely lithotype (gas, sand, shale, etc.) together with its related litho parameters (frame strength, porosity, etc.). The inversion method is based on the Bayesian theory of parameter estimation, allowing specification of inaccuracies in the input and the incorporation of geological knowledge. An important advantage of the proposed inversion method is that for each practical situation the necessary accuracy of [Formula: see text], [Formula: see text] and ρ can be predetermined to distinguish between specific lithotypes or to estimate a specific litho parameter with a prespecified accuracy. For instance, inversion results show that water saturation can only be estimated for an unrealistic accurate input. On the other hand, for the estimation of porosities it is generally sufficient to have compressional velocities available with a realistic accuracy.