OTC 23702

High-resolution FWI: Changing the Way we Image and Interpret Seismic Spyros Lazaratos, David McAdow, Partha Routh, Ivan Chikichev, ExxonMobil Upstream Research Company

Copyright 2012, Offshore Technology Conference This paper was prepared for presentation at the Offshore Technology Conference held in Houston, Texas, USA, 30 April–3 May 2012. This paper was selected for presentation by an OTC program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material does not necessarily reflect any position of the Offshore Technology Conference, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of OTC copyright.

Abstract The emergence of Full Wavefield Inversion (FWI) methods represents a paradigm shift with the potential to revolutionize the way we image and interpret seismic. Advances in algorithms and computing technology are now making FWI practical, making it possible to construct detailed subsurface property models that adequately explain the full bandwidth of the seismic data. We recently developed new concepts and algorithms that allow us to run 3D FWI using much higher frequencies - up to 45 Hz for one of the examples we will be discussing - than what has been shown in most published FWI studies to-date (usually less than 8-10 Hz). High-resolution FWI products can be viewed as 3D volumes of well logs, and their availability creates new opportunities in the way we interpret and use seismic data. We expect FWI to impact applications at all business stages, ranging from improved structural imaging during exploration to detailed reservoir description and characterization for development and production. Introduction Seismic imaging has been advancing rapidly over the last two decades, transitioning from post-stack time migration to pre-stack depth migration and from ray-theoretic algorithms (Kirchoff migration) to one-way wave-equation solvers (wave-equation migration), and finally to more accurate reverse-time migration (RTM) methods. This progression has been motivated by the business climate, with exploration moving to more and more challenging environments (e.g. Gulf of Mexico sub-salt) and the demand for more and more accurate reservoir characterization to maximize and maintain production from discovered fields. The most recent, and perhaps ultimate, step in this evolving sequence is Full Wavefield Inversion (FWI), which has rapidly become a focal area for research and development within the geophysical community and industry. One could argue that the FWI approach represents the dream of every geoscientist: generate detailed subsurface property models of the earth that can accurately reproduce, through simulation, the seismic data used to construct them. Unlike evolution in the migration algorithms, which has been continuous and incremental, FWI represents a change in philosophy, both in the way we image the seismic data, and also in how we interpret the resulting products. Although much more research and development will be necessary to capitalize on the full potential of FWI, we feel that several of the main difficulties (primarily overcoming the computational requirements necessary to implement and apply the method) have been overcome. We are already using FWI to generate subsurface models with the resolution and quality to impact business decisions. This presentation will provide an overview of the method, some of the advances that are making it feasible, and real data examples to illustrate its potential. Full-Wavefield Inversion A generic conceptual flowchart of the Full Wavefield Inversion (FWI) approach is shown in Figure 1. The objective of the method is to generate models of subsurface rock properties (e.g. compressional and shear wave velocity, density) fully consistent with the recorded seismic data, such that the recorded real data can be reproduced through accurate forward simulation of the seismic experiment. The simulation needs to incorporate a high degree of realism, correctly representing the seismic data acquisition geometry and the physics governing seismic wave propagation in the subsurface. The level of sophistication of seismic simulation employed in FWI projects is currently evolving beyond using simple acoustic physics (subsurface supporting compressional waves only but ignoring shear strength of rocks) to more elaborate and realistic elastic

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modeling (both compressional and shear waves adequately described). Ultimately anisotropic visco-elastic simulations will provide the degree of realism required to fully match the complexity of seismic wave propagation in the earth’s subsurface. The FWI process starts with synthetic data generated from an initial subsurface model. The synthetic and real seismic data are compared and their difference used to update the model. Then new synthetic data are generated leading to new model updates and the process continues iteratively until an acceptable level of match is achieved between synthetic and real data. The iterative, simulation-based FWI method represents a drastic change in the way seismic data are analyzed and used to image the subsurface. Standard seismic processing consists of a sequence of operations, each successively “cleaning-up” and preparing the data for the ultimate imaging step (migration). As the data progress through the sequence, several recorded wave modes (e.g. multiples, converted waves) are removed (considered to be “noise’) so that they do not interfere with the image created from the primary compressional reflections. Estimation (inversion) of subsurface rock properties is done after imaging, but there is no explicit feedback loop validating such estimates based on the degree to which they can reproduce the original data. In contrast to the standard approach, FWI has the potential to use all recorded wave modes to constrain the subsurface model. The process includes an explicit validation step, checking the degree to which our subsurface representation is consistent with the data, naturally providing measures of non-uniqueness and uncertainty in our estimates. The process is largely automated, using highly accurate and expensive computer simulation to bypass the human-intensive and subjective sequence of decisions implied by the traditional approach. Speed-up Methods Although the FWI concept is very appealing and the relevant theory was developed several decades ago (Tarantola, 1984), commercial 3D application of FWI is only now becoming practical, largely driven by advances in computing technology that enable wave simulation using highly-accurate techniques such as finite differences and finite elements. Despite such advances, FWI applications are challenging even for state-of-the-art computing clusters. This is particularly true as we move from acoustic to elastic and visco-elastic simulations of large 3D seismic surveys. Simulating the full bandwidth of modern, high-resolution seismic surveys is particularly challenging: the computing cost of seismic simulation increases by a factor proportional to the 4th power of the frequency being simulated (e.g. doubling the maximum frequency by a factor of 2 increases the computing cost by a factor of 16). In most published FWI real-data studies to-date (e.g. Sirgue et al., 2009; Vigh et al., 2010), only the lowest frequency (usually less than 8-10 Hz) portion of the data was used as input for FWI, generating interesting, but very low-resolution, results. We recently developed new concepts and algorithms that are now allowing us to simulate and invert the full bandwidth of the seismic data. We can now run 3D FWI using much higher frequencies (up to 45 Hz for one of the examples we will be discussing), generating high-resolution FWI products. Below we briefly highlight two such methods. Encoded Simultaneous Source The FWI process in principle requires simulation of a very large number of independent seismic experiments, each one corresponding to a source location that was occupied in the seismic survey. This would imply calculating tens of thousands of shot simulations for medium-to-small-size 3D surveys and for each iteration of the FWI loop. Instead we have found that the cost of FWI can be significantly reduced by applying it to data formed by encoding and summing the seismograms obtained from the individual shot experiments (Figure 2). The encoding step forms a single gather from many input source gathers. This gather represents data that would have been acquired from a spatially distributed set of sources. Instead of simulating and inverting the original shots independently, we found that we can invert the encoded simultaneous source gather, without significantly reducing the accuracy of the inversion results. The technique as published in Krebs (Krebs et al, 2009) describes application for fixed-spread data, and further enhancements are described in Routh (Routh et al., 2011) for marine streamer data. Spectral Shaping The number of iterations required for convergence of FWI can often be dramatically reduced by appropriately shaping the spectrum of the seismic data and the source wavelet. The key idea behind the method is that a reasonable estimate of the frequency spectrum of the subsurface is known a-priori. When this is the case, the inversion can be conditioned to produce models with the desired frequency spectrum from the very first iteration. This implies that computational effort does not need to be spent on iterations that adjust the spectrum of the subsurface model, leading to much faster convergence rate. In addition spectral shaping provides stability for FWI, by preferentially weighting the lower frequency components of the data.

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This method has very wide applicability and extends to FWI the concepts developed through the work of Lancaster and Whitcombe (2000) and Lazaratos and David (2009). These prior publications introduced the idea that the model generated by inversion should have a frequency spectrum that, on average, is similar to the spectrum of the earth’s subsurface, as measured by well logs (Figure 3). For any given area, this target spectrum can be derived by averaging the spectra of log curves recorded in local wells. In practice, it has been observed that typical well-log spectra are fairly similar for a very large variety of geographic locations, depths and depositional environments, so that the general form of inversion target spectra is robust and well defined. Using the spectral shaping method we have been able to reduce the number of iterations required to achieve convergence for typical FWI applications from several hundreds to 10-20 iterations (Lazaratos et al., 2011). Summary FWI represents a change of philosophy in the way we analyze and image seismic data and the types of products we use for interpretation. Instead of imaging boundaries (reflectivity), we now focus on building models of subsurface rock properties. Instead of a human-intensive sequence of processing steps, that successively attenuate portions of the data (as “noise’), we use an iterative feedback loop, converging to models that can explain (through detailed simulation) more of the recorded wavefield. The FWI process is computationally very expensive, but with a combination of hardware improvements and new algorithms, such as simultaneous source and spectral shaping, we are getting to a point where we can invert the full recorded bandwidth to generate high-resolution FWI products. Computing and algorithmic improvements will remain necessary as we use more and more complex simulation physics, but the benefits of the process are already becoming apparent. At the presentation we will show examples demonstrating the benefits FWI is already providing for improved imaging and reservoir characterization. References Krebs, J., Anderson, J., Hinkley, D., Neelamani, R., Lee, S., Baumstein, A., and Lacasse, M., 2009, Fast full-wavefield seismic inversion using encoded sources, Geophysics, 74, no. 6, WCC177-188. Lancaster, S., and Whitcombe, D., 2000, Fast track “coloured” inversion, Expanded Abstracts, 70th SEG Annual Meeting, Calgary, 1672-1575. Lazaratos, S., and David, R., 2009, Inversion by pre-migration spectral shaping, Expanded Abstracts, 79th SEG Annual Meeting, Houston. Lazaratos, S., Chikichev, I., and Wang, K., 2011, Improving the convergence rate of full wavefield inversion using spectral shaping, Expanded Abstracts, 81st SEG Annual Meeting, San Antonio. Routh, P., Krebs, J., Lazaratos, S., Baumstein, A., Chikichev, I., Lee, S., Downey, N., Hinkley, D., Anderson, J., 2011, Application of encoded simultaneous source full-wavefield inversion to marine streamer data, Expanded Abstracts, 81st SEG Annual Meeting, San Antonio. Sirgue, L., Barkved, O., Van Gestel, J., Askim, O., and Kommedal, J., 2009, 3D waveform inversion on Valhall wide-azimuth OBS, Expanded Abstracts, 71st EAGE Conference & Exhibition, Amsterdam, U038. Tarantola, A., 1984, Inversion of seismic reflection data in the acoustic approximation, Geophysics, 49, 1259-1266. Vigh, D., Starr, B., Kapoor, J., and Li, H., 2010, 3D full waveform inversion of a Gulf of Mexico WAZ data set, Expanded Abstracts, 80th Annual SEG Meeting, Denver, 957-961.

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Figure 1: FWI generic flowchart.

Figure 2: Encoded simultaneous source method. Shots are encoded and simulated simultaneously with minimal loss of information. Measured seismic data are also encoded and blended to simulate simultaneous acquisition

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Figure 3: Typical seismic (red) and well log (impedance in blue; reflectivity in pink) spectra, as shown in Lazaratos and David (2009). Lancaster and Whitcombe (2000) and Lazaratos and David (2009) demonstrate that the spectrum of inversion results should match the well log impedance spectrum. This constraint can be incorporated into FWI to dramatically reduce the number of iterations required for convergence.