A Historical Review of Earth Model Building

By Dr. Ian F. Jones¹, Dr. John Brittan¹, Johnny Chigbo¹, Dr. Gloria Awobasivwe², Christopher Osolo² and Paula Ukerun² 1: ION Geophysical;  2: Bulwark Services Nigeria

Introduction

In this review article, we consider the development of subsurface parameter estimation for use in building subsurface images for geological interpretation and reservoir evaluation using seismic migration procedures. We outline the progressive evolution form a purely linear approach wherein no reference was made for consistency between the various steps in the procedures, to the emerging approach of a closed-loop iterative workflow wherein each step is checked for internal consistency, and the parameter fields updated until all steps in the procedures are mutually consistent (Brittan and Jones, 2019).

In seismic data processing we aim to: separate ‘signal’ from ‘noise’; build an anisotropic velocity model; migrate the data, producing ‘true amplitude’ angle classes that are then used for elastic parameter estimation for reservoir characterisation. The parameter estimation techniques we have are limited in their resolution, and this restricts the accuracy and precision of the images we can produce. In general, with conventional tomographic velocity update we are limited by the ray-theory ‘scattering limit’ to a resolution of perhaps 5x the available sound-wavelength. Hence we are modest in what parameters we try to estimate tomographically, at best obtaining a smooth anisotropic velocity field suitable for migration, with features with lateral scales of about 500m.  Many excellent results have been obtained with ray methods, and developments (such as well and structural constraints) continue to improve them. Conversely, parameter estimation using ‘full waveform inversion’ (FWI) can perhaps deliver resolution of about half the available sound-wavelength, so theoretically perhaps ten-times the resolution of ray methods. FWI primarily uses the transmitted (refracted) wavefield rather than the reflected wavefield, and typically ignores density contrast, attenuation (Q), etc., (e.g. Virieux and Operto, 2009; Jones 2010, 2018).

For the majority of geological environments, building a model with FWI will not result in an image that is radically different than that obtained using tomography. The exception to this observation would be in shallow water with small-scale anomalies (e.g. over-pressured gas), or for deep subsalt reservoirs (and then only if we have low frequencies and long offsets). Along with better well-ties and potentially better images, the additional promise of FWI is in delivering high resolution interpretable attribute fields directly and quickly. 

Here, we’ll assess the development of the data processing procedures involved in obtaining subsurface parameter fields for use in migration, and consider how these methods have developed over the past thirty-odd years, and what their future development direction might be.

Figure 1. The ‘S-curve’ development profile for any technology development, in the context of tomography and FWI.

Historical Background

In the life-cycle of any technological development, there is a slow development phase when our initial understanding is poor but growing, followed by rapid development once the fundamentals of the process are fully comprehended, and finally further development levels-out as the method is then fully exploited (Figure 1).

Historically, seismic data processing workflows were purely linear. Field data were ‘processed’, a rudimentary velocity model was estimated from stacking velocity picking, using map migration to depth-locate picked time-horizons, and migration was performed. These tasks happened just once.

From about 1995 onwards, with the introduction of ray-based tomography, the model building element changed to become doubly iterative, in that repeated ray-trace modelling was utilized within an inversion scheme, so as to converge on a model that produced flat common-reflection-point (CRP) gathers, after several iterations of migration. As it is comparing data after migration, this technique is an ‘image domain’ inversion scheme, and hence it is not looking for consistency with the raw input data.

Since about 2005, FWI has been gradually introduced, modifying the tomographic solution by using wavefield-extrapolation modelling so as to iteratively match forward modelled synthetic data with measured field data. Hence, this methodology does indeed ‘refer back’ to the raw input data, but as the inversion is performed in the ‘data domain’, and still has limiting assumptions, the resulting model is not guaranteed to produce ‘flat gathers’ in the ensuant migration

What are the respective parameter resolutions available from these two methods? The resolution of ray-tomography is limited to cell-sizes of perhaps 100*100*25m, as on scale lengths smaller than this, the ray theory approximation fails. Conversely, waveform methods use a cell size of potentially less than 15*15*15m … hence we can expect much better lateral resolution in the parameters in the near surface, and overall better resolution in the deep section.

However, none of these approaches and subsequent migrations attempted to compensate for the underlying ‘bad physics’ or ‘bad data’ that we were employing. For example, using a one-way acoustic wave equation, and with field data that are poorly and/or irregularly sampled, and containing remnant multiples and possibly mode-converted energy. Hence, the least-squares migration technique was introduced to attempt to compensate for some of these issues, in that another iterative inversion loop is introduced so as to form an image (and/or gathers) consistent with the input field data (Schuster, 1997). However, this does not simultaneously try to modify the subsurface model, and still assumes that data are multiple-free.

Figure 2. Flow chart representation of: a) the historical ‘linear’ approach to imaging, b) image-domain ray-based tomography, c) data-domain FWI, d) least-squares update (which can be applied in either the image or the data domain). (Adapted from Vershuur and Berkhout, 2015).

Figure 2 outlines the above methods in a series of flow-charts, and indicates a gradual transition from incremental modification of existing ‘open loop’ solutions, to more transformational and fully ‘closed loop’ solutions. A ‘closed loop’ solution would use a two-way elastic description of sound propagation, iteratively referring back to the field data, iteratively updating the model, and at each step iteratively constraining image gathers to be flat. And ultimately, evolving into inversion for high frequency elastic Earth parameter models, having made use of the full wavefield (including multiples and elastic mode conversion effects).

What are the main differences between incremental and transformational developments? Conventional methods, and their associated incremental developments, primarily are non-iterative over the entire workflow: some bits may be iterative (such as tomographic model update, or LS image enhancement), but the overall flow, from input data to final elastic parameters, is dealt with as a more or less a linear single-pass approach. Conversely, the transformational routes offer adaptive iteration over a larger part of the entire workflow, with the possibility of exploiting the full wavefield (multiples, conversions, etc.).

What is the motivation for moving beyond current ‘best-practice’? Ultimately, resolving a number of reservoir attributes to the extent that they can directly influence drilling decisions and further reduce risk. And, to exploit the full wavefield to the maximum extent possible (exploit multiples, elastic effects, etc., to make full use of all energy in the recorded data).

At present, the limiting assumptions we make in waveform inversion limit what we can achieve: we can currently forward model with a priori parameters for: anisotropic Vp, density, attenuation, (and perhaps Vs), but generally we invert only for P-wave anisotropic velocity. However, if we can push the frequency range of the inversion (which is very expensive), and invert for: anisotropic Vp, density, attenuation, (and perhaps Vs). Then we can directly output the desired elastic parameter volumes, rather than resorting to the intermediate step of migrated gathers which would then be used to perform very approximate reservoir parameter estimation.

What technologies are required to fulfil these ambitions? It is well known that low frequencies are required to facilitate the convergence of FWI (typically with less than perhaps 1.5 Hz). This requirement has led to a recent surge in development of low frequency (or enhanced frequency) sources (Brenders et al., 2018; Brittan et al., 2019). Long offsets are also of benefit, hence ocean bottom recordings are beneficial (Brittan et al. 2013). And, elastic modelling and associated parameter estimation will also be beneficial, and perhaps crucial for land data, were elastic effects severely affect sound propagation.

The Road Ahead

Currently, migration algorithms assume that all multiple energy (reverberation within layers) has been removed from the input data. Removing this restriction would enable us to make use of virtually

all the recorded energy in the field data. One method to achieve this goal is referred to as ‘full wavefield migration’ (FWM), outlined in Figure 3 (Verschuur and Berkhout, 2015). Adding a simultaneous update of the velocity field to this work-flow produces the ‘joint migration inversion’ scheme (JMI – Figure 3b). But ultimately, the objective would be to input the field data (with all its various arrival events) into an inversion scheme, and then directly output all requisite elastic parameters at a resolution sufficient to facilitate direct interpretation (Figure 3d): this was the goal originally envisaged by Tarantola (1984). However, this latter route is still beyond the reach of application as a routine process, but has been demonstrated in a few examples (e.g. Routh et al., 2018).

As an intermediate solution, we can employ the velocity field from FWI to better constrain conventional post-migration impedance inversion: this approach was first suggested by Cobo et al. (2019), and is outlined as a flow-chart in Figure 3c. Below we show an example of their approach (Jones et al., 2018), comparing a impedance inversion using a ‘conventional-constraint’ employing well-logs and interpreted horizons, with an FWI-only-

Figure 3. Flow chart representation of: a) full wavefield migration, b) joint migration inversion, c) impedance inversion constrained using FWI, d) full elastic FWI for direct multi-parameter estimation. (Adapted from Vershuur and Berkhout, 2015).

constraint, that uses no wells nor any picked horizons. Figure 4 shows results from Ophir’s Fortuna field (offshore Equatorial Guinea). This compares the result of a blind-test at the location of well-log which was not used to build the conventional constraints. Here, we are away from the location where the conventional result’s constraints were built, and as seen in the well-log comparison, use of the FWI constraint has resulted in a better match than the more conventional approach.

Conclusions

The evolution of FWI as a tool to improve velocity models for migration, and the move towards using such models for more direct reservoir characterization, has transformed and continues to transform the application of closed-loop’ transformational processes within exploration and production imaging projects. There remain, however, some key challenges to further successful exploitation of such methodologies: namely developing a better understanding of elastic wave propagation effects, and in obtaining the computer power to implement numerical schemes based on such an enhanced understanding.

Figure 4. In the blind-test, the FWI constrained results match the well more closely than the conventional result (courtesy of Ophir Energy and Jones et al., 2018).

Acknowledgements

The authors would like to thank the ION and Bulwark teams that have contributed to this work:  Tristram Burley, Carlos Calderón, Shihong Chi, Yannick Cobo, Paul Farmer, Juergen Fruehn, Stuart Greenwood, Claudia Hagen, Gary Martin, Ross O’Driscoll, Jeet Singh, Chao Wang and David Yingst. 

References

Brenders, A., Dellinger, J., Kanu, C., Li, Q., Michell, S., [2018].  The Wolfspar© field trial: Results from a low-frequency survey designed for FWI.  Expanded abstracts for the 88^th SEG meeting, FWI 2.1

Brittan, J., Bai, J., Delome, H., Wang, C. and Yingst, D., [2013]. Full waveform inversion – the state of the art. First Break, 31, 75-81.

Brittan, J., and Jones, I.F, [2019]. FWI evolution – from a monolith to a toolkit, The Leading Edge, 38, no.3, 179-184.

Brittan, J., Farmer, P., Bernitsas, N., and Dudley, T., [2019]. Enhanced low frequency signal to noise characteristics of an airgun technology based source. Workshop 9, 89^th SEG meeting,

Cobo, Y., Calderón-Macías, C. and Chi, S., [2018].  Improving model resolution with FWI for imaging and interpretation in a Gulf of Mexico data set. Expanded abstracts for the 88^th SEG meeting, FWI 2.2

Jones, I.F., [2018]. Velocities, Imaging, and Waveform Inversion (The evolution of characterizing the Earth’s subsurface), EET 13, EAGE, 234 pages.

Jones, I.F., Singh, J., Greenwood, S., Chigbo, J., Cox, P. and Hawke, C., [2018].  High-resolution impedance estimation using refraction and reflection FWI constraints: the Fortuna region, offshore Equatorial Guinea. First Break, 36, November, 39-44.

Jones, I.F., [2010]. An introduction to velocity model building, EAGE, ISBN 978-90-73781-84-9, 296 pages.

Routh , P., Neelamani , R., Lu , R., Lazaratos , S., Braaksma , H., Hughes , S., Saltzer, R.,  Stewart , J., Naidu , K., Averill , H., Gottumukkula ,V.,  Homonko , P., Reilly , J., and Leslie, D., [2017]. Impact of high-resolution FWI in the Western Black Sea: Revealing overburden and reservoir complexity. The Leading Edge, 36(1), 60–66.

Schuster, G., [1997]. Acquisition footprint removal by least square migration: 1997 Annual UTAM Report, 73-99.

Tarantola, A., [1984]. Inversion of Seismic Reflection Data in the Acoustic Approximation, Geophysics, 49, 1259-1266.

Verschuur, D.J. and Berkhout, A.J., [2015]. From removing to using multiples in closed-loop imaging. The Leading Edge, 34 (7), 744–759.

Virieux, J. and Operto, S., [2009]. An overview of full-waveform inversion in exploration geophysics.  Geophysics, 74, WCC1-WCC26.