Scattering-based focusing for imaging in highly complex media from band-limited, multicomponent data

TLDR: In this article, the details of subsurface structures deep beneath complex overburden structures, such as subsalt, remains a challenge for seismic imaging, and the authors propose a method to reconstruct these details.

Abstract: Reconstructing the details of subsurface structures deep beneath complex overburden structures, such as subsalt, remains a challenge for seismic imaging. Over the past few years, the Marche...

Figures

Figure 8: (a) The directly modeled pressure for evaluation of the (b) SR-Marchenko and (c) Marchenko retrieved pressure response for a fixed virtual source xf = (4.4, 6.0) km and variable receiver position. (d) An overlay of traces demonstrates a better amplitude prediction of the scattering-driven technique (reddashed line) when compared with the R-Marchenko (blue-dashed line) against the numerically modeled solution (solid black line).

Figure 4: Different focusing functions for the virtual point located at xf = (4.4, 8.13) km. (a) corresponds to the result estimated by S-Marchenko, and (b) the conventional focusing scheme. In panel (c), a close-up view by trace comparison indicates some of the most prominent features where events are underestimated or missing. Matching traces are extracted from a receiver at 8.8 km (colored lines in the gathers).

Figure 9: Local extended images for a virtual source at xf = (4.4, 7.5) km. (a) For comparison, a benchmark, finite-difference modeled pressure field up to 40 Hz in a truncated section of the model, Figure 2, below the focusing datum at 4.4 km. (b) S-Marchenko-based reflectivity. (c) Marchenko driven reflection response. (d) corresponds to a band-limited directly modeled reflection response up to 20 Hz. (e) and (f) are reconstructed counterparts using the SR-Marchenko and R-Marchenko redatumed wavefields. Most of the major events in (a) and (d) recovered in (b) and (e) are not present in the (c) and (f). Similarly, substantial discontinuities and missing events arise in (c) and (f), contrary to (b) and (e).

Figure 13: RTM close-up sections extracted from boxes 1, 2, and 3 in Figure 11. The top row corresponds to the green box 1, the middle row coupled to the magenta box 2, and the bottom row to that of the cyan box 3. Columns (a), (b), (c) correspond to migrated images from the synthetic, SR-Marchenko, and RMarchenko virtual gathers, respectively.

Figure 12: RTM zoomed sections associated with boxes 1, 2, and 3 in Figure 10. Columns (a), (b), (c) correspond to migrated images from the synthetic, S-Marchenko, and Marchenko virtual gathers accordingly. The top row corresponds to the green box 1, the middle row linked to the magenta box 2, and the bottom row with that of the cyan box 3.

Figure 5: Comparisons between the forward modeled pressure field (a) and estimates from the S-Marchenko (b) and the original Marchenko (c). The total field is the superposition of retrieved up- and downgoing fields, given by $\mathbf{g}= \mathbf{g}^{-} + \mathbf{g}^{+}$. All panels are displayed with the same amplitude scaling. (d) displays corresponding traces from a receiver at 9.2 km, uncovering phase and amplitude differences.

Full text

Scattering-based focusing for imaging in highly complex
media from band-limited, multi-component data
David Vargas
1
, Ivan Vasconcelos
1
, Yanadet Sripanich
2
, Matteo Ravasi
3
,
1 Department of Earth Sciences, Utrecht University, 3584 CB, The
Netherlands,
2 PTT Exploration and Production Public Company Limited, Chatuchak,
Bangkok 10900 Thailand,
3 Earth Science and Engineering, King Abdullah University of Science and
Technology, Thuwal 23955, Kingdom of Saudi Arabia.
(May 20, 2021)
GEO-2020-0939
Running head: Scattering-based Marchenko
ABSTRACT
Reconstructing the details of subsurface structures deep beneath complex overburden
structures, such as sub-salt, remains a challenge for seismic imaging. Over the past years, the
Marchenko redatuming approach has proven to reliably retrieve full-wavefield information in
the presence of complex overburden effects. When used for redatuming, current practical
Marchenko schemes cannot make use of a priori subsurface models with sharp contrasts
because of their requirements regarding initial focusing functions, which for sufficiently
complex media can result in redatumed fields with significant waveform inaccuracies. Using
a scattering framework, we present an alternative form of the Marchenko representation
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This paper presented here as accepted for publication in Geophysics prior to copyediting and composition.
© 20 Society of Exploration Geophysicists21
Downloaded 05/30/21 to 109.171.207.22. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/page/policies/terms
DOI:10.1190/geo2020-0939.1

that aims at retrieving only the unknown perturbations to both focusing functions and
redatumed fields. From this framework, we propose a two-step practical focusing-based
redatuming scheme that first solves an inverse problem for the background focusing functions,
which are then used to estimate the perturbations to focusing functions and redatumed
fields. In our scheme, initial focusing functions are significantly different from previous
approaches since they contain complex waveforms encoding the full transmission response
of the a priori model. Our goal is the handling of not only highly complex media but
also realistic data - band-limited, unevenly sampled, free-surface-multiple contaminated
data. To that end, we combine the versatility of Rayleigh-Marchenko redatuming with
the proposed scattering-based scheme allowing an extended version of the method able to
handle single-sided band-limited multicomponent data. This Scattering-Rayleigh-Marchenko
strategy accurately retrieves wavefields while requiring minimum pre-processing of the data.
In support of the new methods, we present a comprehensive set of numerical tests using
a complex 2D subsalt model. Our numerical results show that the scattering approaches
retrieve accurate redatumed fields that appropriately account for the complexity of the a
priori model. We show that the improvements in wavefield retrieval translate into measurable
improvements in our subsalt images.
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This paper presented here as accepted for publication in Geophysics prior to copyediting and composition.
© 20 Society of Exploration Geophysicists21
Downloaded 05/30/21 to 109.171.207.22. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/page/policies/terms
DOI:10.1190/geo2020-0939.1

INTRODUCTION
Accurate estimation of the stratigraphy and properties of complex subsurface geology has
long represented a challenge for seismic imaging, especially in the presence of salt (or basalt)
formations in the overburden (Leveille et al., 2011). This is largely due to uneven illumination
of the target area arising from the complex propagation in the overburden as well as the
presence of strong reverberations in the recorded surface data (Jones and Davison, 2014).
On one hand, advances in seismic acquisition techniques, such as the adoption wide-azimuth
surveys, have played a major role in providing more even subsurface illumination, which in
turn can help reduce the ill-posed nature of the associated imaging problem. On the other
hand, it is only by incorporating better physics in the imaging process that the full potential
of the recorded seismic data can be exploited. This is for example justified by the uplift in
the quality and focusing of reflectors provided by high-end, wave equation-based migration
methods such as reverse-time migration (McMechan, 1983; Baysal et al., 1983; Farmer et al.,
2009), data or image domain least-squares migration (Nemeth et al., 1999; Fletcher et al.,
2016; Arasanipalai et al., 2019) as well as Full Waveform Inversion (Tarantola, 1984; Virieux
and Operto, 2009; Esser et al., 2016; Wang et al., 2019). Moreover, a variety of approaches,
emerged under the pursuit of imaging with multiples, have also shown their effectiveness in
such settings; these methods turn multiple reverberations originating from high impedance
contrasts around salt and basalt structures into useful signal that can complement the
illumination of primaries (Malcolm et al., 2008; Liu et al., 2015).
Alongside model-driven approaches that aim at iteratively reconstructing the velocity
(and/or reflectivity) model of the subsurface, from which a more accurate propagation of
the underlying wavefield can be numerically modeled, a great deal of research has been
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This paper presented here as accepted for publication in Geophysics prior to copyediting and composition.
© 20 Society of Exploration Geophysicists21
Downloaded 05/30/21 to 109.171.207.22. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/page/policies/terms
DOI:10.1190/geo2020-0939.1

recently devoted to target-oriented methods. By targeting a specific area of the subsurface,
these methods promise to provide reservoir-characterisation-ready models of the subsurface
(da Costa et al., 2019; Cui et al., 2020; Guo and Alkhalifah, 2020). The reduced computational
domain and size of the model to invert for, can allow for the inclusions of higher frequencies
and even more complex physics (e.g., elastic, attenuation) in the modeling operator used to
describe the data. Nevertheless, the quality of the final image and/or inverted properties
is strongly dependent on the ability to accurately redatum surface data at the target level
of interest. To this regard, novel wavefield extrapolation techniques that go beyond the
single-scattering (i.e., Born) approximation open up new ways to create such target data.
Marchenko redatuming (Wapenaar et al., 2014b; van der Neut et al., 2015b) has recently
been demonstrated to be a reliable method for retrieving full-wavefield subsurface responses
in a variety of geological settings which can accommodate moderately complex overburden
geology. The Marchenko method makes use of the recorded reflection response and an
estimate of the direct transmission response in the medium to estimate so-called focusing
functions, that serve as operators to focus energy at specific points in the subsurface. Once
the redatuming step has been performed, the resulting subsurface wavefields can be used to
to create artefact-free images of the subsurface (Wapenaar et al., 2014b) or estimate local
properties (Cui et al., 2020) by naturally including all order of multiples present in seismic
reflection data. From this perspective, Marchenko redatuming represents an ideal platform
for creating subsurface wavefield suitable for target-oriented imaging and inversion beneath
complex structures such as salt, but also other environments including sub-basalt or other
highly complex tectonic settings.
To that end, however, the original Marchenko scheme has strict requirements with regards
to the reflection response. Namely, it requires large aperture acquisition geometries, it should
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This paper presented here as accepted for publication in Geophysics prior to copyediting and composition.
© 20 Society of Exploration Geophysicists21
Downloaded 05/30/21 to 109.171.207.22. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/page/policies/terms
DOI:10.1190/geo2020-0939.1

represent data from a surface-multiple-free survey, and have flat, very broadband frequency
content. When it comes to practical implementation of the method, the requirement for
an accurate deconvolution of the source wavelet, removal of surface-related multiples, and
source/receiver co-location hinders its application to real data sets. Moreover, treating
surface-related multiples as noise that must be removed from the data is not only technically
challenging and time consuming, but it may also not be beneficial in complex media. Surface
multiples can carry complementary information compared to primaries since, when compared
to surface-multiple-free data, they are exposed to longer propagation times and possibly
different propagation paths in the subsurface as a consequence of the natural interactions
of finite-aperture data with a free surface in a highly complex medium. Furthermore, on
the subject of data pre-processing for Marchenko redatuming, source deconvolution with an
erroneously estimated source wavelet leads to strong coherent artefacts in the local images
(Mildner et al., 2019b). In many ways, the success of single-sided Green’s functions retrieval
depends upon the availability of accurate focusing functions. Dukalski et al. (2019) describe
how to correct for the effect of short-period multiples in the Marchenko framework, by adding
energy conservation constraints to the focusing problem. To relax on the originally strict
acquisition requirements, Rayleigh-Marchenko redatuming (R-Marchenko) was introduced
by Ravasi (2017) and Slob and Wapenaar (2017). The main advantage of R-Marchenko is
the use of a band-limited operator defined in terms of vertical particle velocity rather than a
broadband reflection response, as is the case in standard Marchenko implementations. Such
consideration significantly reduces the need for most preprocessing steps.
More importantly in the context of this work, previous versions of the Marchenko scheme
could not accommodate highly complex media such as subsalt - particularly in the presence of
an a priori model containing sharp contrasts. This is because currently available Marchenko
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This paper presented here as accepted for publication in Geophysics prior to copyediting and composition.
© 20 Society of Exploration Geophysicists21
Downloaded 05/30/21 to 109.171.207.22. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/page/policies/terms
DOI:10.1190/geo2020-0939.1

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Scattering-based focusing for imaging in highly complex media from band-limited, multi-component data" ?

Using a scattering framework, the authors present an alternative form of the Marchenko representation 1 Page 1 of 62 GEOPHYSICS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 This paper presented here as accepted for publication in Geophysics prior to copyediting and composition. From this framework, the authors propose a two-step practical focusing-based redatuming scheme that first solves an inverse problem for the background focusing functions, which are then used to estimate the perturbations to focusing functions and redatumed fields. In their scheme, initial focusing functions are significantly different from previous approaches since they contain complex waveforms encoding the full transmission response of the a priori model. To that end, the authors combine the versatility of Rayleigh-Marchenko redatuming with the proposed scattering-based scheme allowing an extended version of the method able to handle single-sided band-limited multicomponent data. In support of the new methods, the authors present a comprehensive set of numerical tests using a complex 2D subsalt model. Their numerical results show that the scattering approaches retrieve accurate redatumed fields that appropriately account for the complexity of the a priori model. The authors show that the improvements in wavefield retrieval translate into measurable improvements in their subsalt images. This paper presented here as accepted for publication in Geophysics prior to copyediting and composition. 

Q2. What future works have the authors mentioned in the paper "Scattering-based focusing for imaging in highly complex media from band-limited, multi-component data" ?

O rg /p ag e/ po lic ie s/ te rm s D O I:1 0. 11 90 /g eo 20 20 -0 93 9. 1 wavefield redatuming accuracy to a level of waveform fidelity in redatuming far beyond that of conventional imaging, resulting on extended image gathers and target-oriented images that are consequently highly accurate - thus realising the potential of the Marchenko framework for imaging of complex subsurface environments. To facilitate the deployment of their scheme to band-limited data, with realistic acquisition and free-surface conditions, the authors combine their scattering approach with the Rayleigh-Marchenko scheme into a new method that can produce accurate wavefields and images from offshore or ocean-bottom four-component datasets. Given their robust theoretical and numerical constructs, the authors expect that their approaches will be useful for imaging and monitoring in challenging subsurface geological conditions. 

Q3. How many sources are used to simulate the full reflection response in the true medium?

To simulate the full reflection response R in the true medium, the authors use a finite-difference acoustic solver and sequentially inject 201 sources on the model surface. 

Q4. What is the advantage of considering vertical particle velocities?

(10)The advantage of considering vertical particle velocities is that they naturally contain the effects of surface-related multiples while preserving the band-limited character of observed seismic fields. 

Q5. What is the way to decompose the vertical particle velocity?

Provided availability of dual-sensor data, one can use the recorded pressure p(xr,xs; t) to decompose the vertical particle velocity vz(xr,xs; t) into its up- and downgoing constituents v±z (xr,xs; t) (Wapenaar, 1998). 

Q6. How do the authors reconstruct pressure fields from the surface?

The authors start by reconstructing up- and downgoing pressure fields - by means of their Marchenko schemes - from the surface to an array of 151 virtual points spanning 3 km from 6.0 to 9.0 km horizontally, at a depth of 4.4 km. 

Q7. What is the main reason for the difficulty in estimating the stratigraphy of complex geology?

Accurate estimation of the stratigraphy and properties of complex subsurface geology has long represented a challenge for seismic imaging, especially in the presence of salt (or basalt) formations in the overburden (Leveille et al., 2011). 

Q8. What is the main advantage of the Marchenko scheme?

To better reproduce seismic subsurface responses in such conditions, Vasconcelos and Sripanich (2019) propose a modified Marchenko scheme that can incorporate available information from previously estimated, complex subsurface models by introducing an auxiliary Marchenko system of equations for a reference model as a constraint to the solution in the true medium. 

Q9. How can the authors obtain f + d from the truncated reference medium?

Td is available, f + d can be obtained from the focusing condition, i = Tdf + d , by direct inversion (van der Neut et al., 2015b). 

Q10. What is the reflection response of a truncated medium?

In theory, the reflection response R(xr,x ′ r; t) is a full-bandwidth field that does not include surface-related multiple effects and is, in general, assumed to be known. 

Q11. What are the constraints needed to solve the Marchenko system?

Given that equations 1 and 2 represent an underdetermined system of two equations with four unknown functions (g−, g+, f− and f+), additional constraints need to be introduced in order to solve such a system. 

Q12. What is the focusing function in a truncated medium?

On the other hand, the up- and downgoing focusing functions, f±, are defined in a truncated version of the medium designed to be reflection free outside the region between levels ∂D0 and ∂Di. 

Q13. What is the new strategy for analyzing field multicomponent data?

The new strategy naturally accounts for the compatibility between real and modelled data in the perturbation operator, which in turn allows for rather direct application on field multicomponent data sets. 

Q14. What is the way to circumvent the heavy toll of preprocessing?

in the context of Marchenko redatuming, a natural way to circumvent the heavy toll of preprocessing consists in transforming the up- and downgoing Green’s functions (equations 1 and 2), with a band-limited aerial source via multidimensional convolution (equation 9). 

Q15. What are the main reasons for the use of multiples in seismic imaging?

a variety of approaches, emerged under the pursuit of imaging with multiples, have also shown their effectiveness in such settings; these methods turn multiple reverberations originating from high impedance contrasts around salt and basalt structures into useful signal that can complement the illumination of primaries (Malcolm et al., 2008; Liu et al., 2015).