Imaging of vertical seismic profiling data using the common-reflection-surface stack. Abbildungsverfahren für seismische Daten aus Bohrlochmessungen mit der Common-Reflection-Surface Stapelung

Diese Dissertation beschäftigt sich mit der Entwicklung eines automatisierten, datenorientierten Abbildungsverfahrens, das auf der sogenannten Common-Reflection-Surface (CRS) Stapelung basiert. Durch die Miteinbeziehung von benachbarten Experimenten bei der Rekonstruktion eines Einzelexperiments ergibt sich ein verbessertes Signal-zu-Rauschen Verhältnis und eine starke Bereinigung von Mehrdeutigkeiten. Hauptaugenmerk liegt auf der Adaption der Methode für Bohrloch- und Mehrkomponentendaten

Seismic Waves

The importance of seismic wave research lies not only in our ability to understand and predict earthquakes and tsunamis, it also reveals information on the Earth's composition and features in much the same way as it led to the discovery of Mohorovicic's discontinuity. As our theoretical understanding of the physics behind seismic waves has grown, physical and numerical modeling have greatly advanced and now augment applied seismology for better prediction and engineering practices. This has led to some novel applications such as using artificially-induced shocks for exploration of the Earth's subsurface and seismic stimulation for increasing the productivity of oil wells. This book demonstrates the latest techniques and advances in seismic wave analysis from theoretical approach, data acquisition and interpretation, to analyses and numerical simulations, as well as research applications. A review process was conducted in cooperation with sincere support by Drs. Hiroshi Takenaka, Yoshio Murai, Jun Matsushima, and Genti Toyokuni

Quantitative seismic interpretation in thin-bedded geology using full-wavefield elastic modelling

Refleksjonsseismikk brukes til å lage seismiske «bilder» av den øverste delen av jordskorpen, blant annet med tanke på leting etter reservoarer for olje, gass, karbonlagring og geotermisk energi. I tillegg til å gi grunnlag for en strukturell tolkning, kan de seismiske dataene brukes til å kvantifisere egenskapene til det faste materialet og væskeinnholdet i bergartene. Et viktig verktøy i slik kvantitativ seismisk tolkning er analyse av såkalt AVO: amplitudenes variasjon med avstanden mellom kilde og mottaker (offset). Tynne geologiske lag gir utfordringer for AVO-modellering og tolkning, fordi lagtykkelsen vil kunne være mindre enn oppløsningen i de seismiske dataene. En problemstilling som tas opp i denne avhandlingen er nettopp hvordan man kan gjøre nøyaktig seismisk (forover) modellering i medier med tynne lag. En konvensjonell tilnærming innen AVO- modellering og inversjon er å bruke såkalt konvolusjonsmodellering. Denne metoden tar imidlertid bare hensyn til de primære seismiske refleksjonene og er derfor unøyaktig når modellene har tynne lag. To bedre alternativer er endelig-differanse-modellering og reflektivitetsmetoden. Reflektivitetsmetoden er en delvis analytisk modelleringsmetode for horisontalt lagdelte medier og er beregningsmessig billigere enn endelig-differansemodellering, der beregningene er basert på et tett samplet rutenett (grid). Jeg viser i avhandlingen at reflektivitetsmetoden er godt egnet for AVO-modellering i lagdelte medier. Seismiske data har en båndbegrenset karakter. En konsekvens er at beregning av reservoaregenskaper fra seismiske data generelt ikke er entydig, noe som særlig kommer til uttrykk for lagdelt geologi med tynne lag. Probabilistiske inversjonsmetoder, som for eksempel bayesianske metoder, tar hensyn til denne flertydigheten ved å forutsi sannsynligheter, noe som gjør det mulig a kvantisere usikkerheten. I avhandlingen kombinerer jeg seismisk modellering med bayesiansk klassifisering og inversjon. Modelleringen er utført med reflektivitetsmetoden og er basert på det komplette elastiske bølgefeltet. Formålet er å adressere to konkrete kvantitative seismiske tolkningsproblemer: 1) kvantifisering av usikkerhet i bayesiansk porevæske-klassifisering i nærvær av tynne lag med høy impedans, forårsaket av kalsittsementering i sandstein, og 2) estimering av reservoaregenskapene til turbiditt-reservoarer karakterisert ved alternerende lag av sandstein og skifer. I den første anvendelsen viser jeg i en modelleringsstudie at kalsitt-sementerte lag kan gi en detekterbar refleksjonsrespons, noe som kan påvirke amplituden målt ved reservoartoppen og dermed forstyrre AVO-målingen. Den observerte effekten øker usikkerheten ved porevæske-klassifisering basert på AVO-attributter, som jeg har demonstrert i en case-studie. Følgelig øker sannsynligheten for en falsk hydrokarbon-indikasjon betydelig i nærvær av kalsittsementerte lag. I den andre anvendelsen presenterer jeg en bayesiansk inversjon som tar AVO-skjæringspunktet og gradienten målt på toppen av et reservoar som inngangsdata og estimerer sannsynlighetstetthetsfunksjonen til forholdstallene «net-to-gross» og «net-pay-to-net». Metoden ble anvendt på syntetiske data og AVO-attributtkart fra Jotunfeltet på norsk kontinentalsokkel. Det ble funnet at AVO-gradienten korrelerer med reservoarets net-togross forhold, mens AVO-skjæringspunktet er mest følsomt for typen porevæske. Etter inversjon genererte jeg kart over de mest sannsynlige verdiene av forholdene net-to-gross og net-pay-to-net, samt kart over net pay og usikkerhetene. Disse kartene kan bidra til å identifisere potensielle soner med høy reservoarkvalitet og hydrokarbonmetning.Reflection seismics is used to image the subsurface for the exploration of oil and gas, geothermal or carbon storage reservoirs, among others. In addition to the structural interpretation of the resulting seismic images, the seismic data can be interpreted quantitatively with the goal to obtain rock and fluid properties. An essential tool in quantitative seismic interpretation is the analysis of the amplitude variation with offset (AVO). Thin-bedded geology below the seismic resolution poses challenges for AVO modelling and interpretation. One problem addressed in this thesis is accurate seismic forward modelling in thin-bedded media. Primaries-only convolutional modelling, commonly used in conventional AVO modelling and inversion, is prone to failure in the presence of thin beds. Better alternatives are finite-difference modelling or the reflectivity method. The reflectivity method is a semi-analytic modelling method for horizontally layered media and is computationally cheaper than finite-difference modelling on densely sampled grids. I show in this thesis that the reflectivity method is well-suited for the AVO modelling of layered media. The band-limited nature of seismic data is one reason for the non-unique estimation of reservoir properties from seismic data, especially in thin-bedded geology. Probabilistic inversion methods, such as Bayesian methods, honour this non-uniqueness by predicting probabilities that allow the uncertainty to be quantified. In this thesis, I integrate full-wavefield elastic seismic modelling by the reflectivity method with Bayesian classification and inversion. The objective is to address two concrete quantitative seismic interpretation problems: 1) the uncertainty quantification of Bayesian pore-fluid classification in the presence of thin high-impedance layers caused by calcite cementation in sandstone, and 2) the estimation of reservoir properties of turbidite reservoirs characterised by sand-shale interbedding. In the first application, I show through a modelling study that calcite-cemented beds lead to detectable reflection responses that can interfere with the target reflection at the reservoir top and thereby perturb the AVO behaviour. The observed effect increases the uncertainty of pore-fluid classification based on AVO attributes, as demonstrated by a case study. Consequently, the probability of a false hydrocarbon indication is significantly increased in the presence of calcite-cemented beds. In the second application, I present a Bayesian inversion that takes the AVO intercept and gradient measured at the top of a reservoir as input and estimates the probability density function of the net-to-gross ratio and the net-pay-to-net ratio. The method was applied to synthetic data and AVO attribute maps from the Jotun field on the Norwegian Continental Shelf. It was found that the AVO gradient correlates with the net-to-gross ratio of the reservoir, while the AVO intercept is most sensitive to the type of pore fluid. After inversion, maps of the most-likely values of the net-to-gross ratio, net-pay-to-net ratio, net pay and the uncertainty could be generated. These maps help to identify potential zones of high reservoir quality and hydrocarbon saturation.Doktorgradsavhandlin

Anisotropic Parameter Estimation from PP and PS Waves in 4-Component Data

The estimation of anisotropic parameters in the shallow subsurface becomes increasingly important for 4C seismic data processing in order to obtain accurate images in both time and depth domain. I focus on two approaches to evaluate anisotropy in seismic data: using P-wave data and PS-converted (C-wave) data. To gain better insight into the accuracy and sensitivity of anisotropic parameters to for instance layering and compaction gradients, I undertake numerical modelling studies and verify the results with full-wave modelling as well as findings from the real data from a 4C data set from the Alba field. The focus of this thesis is on vertical transverse isotropy (VTI) which widely occurs in marine sediments and cannot be neglected in seismic processing. P-wave data alone cannot constrain the vertical velocity and the depth scale of the earth model for a VTI medium. Therefore, the joint inversion of non-hyperbolic P- and converted wave (C-wave) or S-wave data from long offsets has been suggested. I carried out a detailed analysis of the resolution and accuracy of non-hyperbolic moveout inversion for P-, S- and C-waves for a single VTI layer in two parts. First, I introduce the concept of the inherited error delta inh as a measure of the possible resolution of the moveout approximations for the different wave types. The range of this error stays constant regardless of the magnitude of the anisotropic parameter for each wave type. Second, I analyse the accuracy of non-hyperbolic moveout inversion. I find that for anisotropy parameter eta the error of estimation from C-wave data is in most cases about half that from P-wave data. Inversion of non-hyperbolic S-wave moveout data does not resolve the anisotropy parameter due to the presence of cusps in the data. The study is then extended to a multilayered medium considering only P- and C-waves. The results confirm the findings from the single layer case. Furthermore, I investigate phase effects on parameter estimation for P- and C-waves. It is suggested that eta estimated from C-wave data gives a better description of the anisotropy found in a medium than the eta values picked from P-wave data. To verify the above findings near-surface effects are studied on the 4C data from the Alba field and accompanied by a full-waveform modelling study. I find that the picked eta values from P-wave data are distinctly larger than the eta values from C-wave data and also larger than the eta values from VSP data. The full-wave modelling study shows that picked eta values from P-wave data may account for influence of structure such as velocity gradients in the near-surface and are influenced by high velocity ratios and phase reversals. Finally, I have carried out an integrated analysis of the Alba 4C data to demonstrate how seismic anisotropy can be estimated from 4C seismic data and how such information can be used to improve subsurface imaging. The results are presented in two parts. The first part deals with non-hyperbolic moveout analysis for estimating anisotropic parameters to gain improved stacked sections. The second part describes migration model building and final imaging. The models are evaluated by comparison with VSP data results and with a synthetic modelling study for three events of the overburden. The evaluation confirms that the anisotropy parameter obtained from C-wave moveout corresponds better with the VSP data than the values directly estimated from P-wave data

Numerical solutions of differential equations on FPGA-enhanced computers

Conventionally, to speed up scientific or engineering (S&E) computation programs on general-purpose computers, one may elect to use faster CPUs, more memory, systems with more efficient (though complicated) architecture, better software compilers, or even coding with assembly languages. With the emergence of Field Programmable Gate Array (FPGA) based Reconfigurable Computing (RC) technology, numerical scientists and engineers now have another option using FPGA devices as core components to address their computational problems. The hardware-programmable, low-cost, but powerful “FPGA-enhanced computer” has now become an attractive approach for many S&E applications. A new computer architecture model for FPGA-enhanced computer systems and its detailed hardware implementation are proposed for accelerating the solutions of computationally demanding and data intensive numerical PDE problems. New FPGAoptimized algorithms/methods for rapid executions of representative numerical methods such as Finite Difference Methods (FDM) and Finite Element Methods (FEM) are designed, analyzed, and implemented on it. Linear wave equations based on seismic data processing applications are adopted as the targeting PDE problems to demonstrate the effectiveness of this new computer model. Their sustained computational performances are compared with pure software programs operating on commodity CPUbased general-purpose computers. Quantitative analysis is performed from a hierarchical set of aspects as customized/extraordinary computer arithmetic or function units, compact but flexible system architecture and memory hierarchy, and hardwareoptimized numerical algorithms or methods that may be inappropriate for conventional general-purpose computers. The preferable property of in-system hardware reconfigurability of the new system is emphasized aiming at effectively accelerating the execution of complex multi-stage numerical applications. Methodologies for accelerating the targeting PDE problems as well as other numerical PDE problems, such as heat equations and Laplace equations utilizing programmable hardware resources are concluded, which imply the broad usage of the proposed FPGA-enhanced computers

Full waveform inversion procedures with irregular topography

Full waveform inversion (FWI) is a form of seismic inversion that uses data residual, found as the misfit, between the whole waveform of field acquired and synthesized seismic data, to iteratively update a model estimate until such misfit is sufficiently reduced, indicating synthetic data is generated from a relatively accurate model. The aim of the thesis is to review FWI and provide a simplified explanation of the techniques involved to those who are not familiar with FWI. In FWI the local minima problem causes the misfit to decrease to its nearest minimum and not the global minimum, meaning the model cannot be accurately updated. Numerous objective functions were proposed to tackle different sources of local minima. The ‘joint deconvoluted envelope and phase residual’ misfit function proposed in this thesis aims to combine features of these objective functions for a comprehensive inversion. The adjoint state method is used to generate an updated gradient for the search direction and is followed by a step-length estimation to produce a scalar value that could be applied to the search direction to reduce the misfit more efficiently. Synthetic data are derived from forward modelling involving simulating and recording propagating waves influenced by the mediums’ properties. The ‘generalised viscoelastic wave equation in porous media’ was proposed by the author in sub-chapter 3.2.5 to consider these properties. Boundary layers and conditions are employed to mitigate artificial reflections arising from computational simulations. Linear algebra solvers are an efficient tool that produces wavefield vectors for frequency domain synthetic data. Regions with topography require a grid generation scheme to adjust a mesh of nodes to fit into its non-quadrilateral shaped body. Computational co-ordinate terms are implemented within wave equations throughout topographic models where a single point in the model in physical domain are represented by cartesian nodes in the computational domains. This helps to generate an accurate and appropriate synthetic data, without complex modelling computations. Advanced FWI takes a different approach to conventional FWI, where they relax upon the use of misfit function, however none of their proponents claims the former can supplant the latter but suggest that they can be implemented together to recover the true model.Open Acces

Development and application of the phase-screen seismic modelling code

As a consequence of the aims of this project, this thesis is divided into two distinct sections. Initially, the computationally efficient phase-screen forward modelling technique is extended to allow investigation of non-normal ray paths. The code is developed to accommodate all diffracted and converted phases up to critical angle, building on a geometrical construction method previously developed with a narrow-angle approximation. The new approach relies upon pre-scanning the model space to assess the complexity of each screen. The propagating wavefields are then divided as a function of horizontal wavenumber, and each subset is transformed to the spatial domain separately, carrying with it angular information. This allows both locally accurate 3D phase corrections and Zoeppritz reflection and transmission coefficients to be applied. The phase-screen code is further developed to handle simple anisotropic media. During phase-screen modelling, propagation is undertaken in the wavenumber domain where exact expressions for anisotropic phase velocities are incorporated. Extensive testing of the enhanced phase-screen technique includes simple analytical models to justify the inclusion of multiple energy alongside synthetic examples from models commonly used to test numerical modelling techniques. Additionally the code is tested with real models from a producing field in a marine sedimentary location where an exhaustive range of geophysical techniques were used to constrain the VTI parameters. Secondly within this thesis, the narrow angle version of the phase-screen method is used to generate a comprehensive pre-stack seismic reflection dataset for our industrial partners. Current exploration within the European oil and gas community is heavily focused on regions where the targets for production are positioned beneath plateau basalts oh the north west European margin. These environments produce a complex seismic response due to the scattering generated by the internal composition of the basalt flows. This study generates a large subsurface volume, derived from geological mapping projects in the Hold-with-Hope region of north east Greenland, and synthetically acquires a realistic 3-D reflection study across it. The basalt is uniquely generated as a single random volume with distinct correlation lengths in each orthogonal direction and a novel approach to determine seismic attenuation through basalts is developed. Initial results from this data set are presented after careful optimisation of the modelling code and parameters

implications for the subduction channel and the seismogenic coupling zone

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Seismic ray fields and ray field maps : theory and algorithms

The research described in this thesis covers various aspects of the forward calculation of seismic ray fields and ray field maps. The central theme is the solution of problems encountered in smooth but complex media, i.e., media that give rise to wave front folding and associated multi-pathing of rays. The ultimate aim of the presented material is to enhance the efficiency of seismic inverse methods, by enhancing the efficiency of the forward calculations. Particular emphasis is placed on the applicability of the ray tracing results to seismic inverse methods. After an overview of seismic ray theory in Chapter 2, a novel approach to the calculation and representation of ray field maps is introduced in Chapter 3. The approach is particularly useful in cases where ray field maps are needed for a dense distribution of sources at an acquisition surface, as in reflection seismics and borehole tomography. For such source distributions it is suggested to construct a single ray field map in an extended space of spatial coordinates and angles, rather than a number of maps in the spatial domain for a range of acquisition coordinates. The ray field map in the position/angle domain is single-valued, regardless of the complexity of the medium and the ray field information is organised by angles at depth rather than by points of emergence at the surface, which makes the maps particularly suitable for use in modern seismic imaging methods. An important result is that, in contrast to what is commonly assumed, obtaining this information does not require the tracing of rays up towards the acquisition surface. Instead, existing algorithms that trace downwards can be adapted to work in the position/angle domain, leading to a considerable gain in efficiency. Interpolation is an important tool in both the construction and the application of ray field maps. A new technique for accurate interpolation using derivative information is presented in Chapter 4. It is a hybrid of extrapolation to arbitrary order and linear interpolation, and combines the advantages of both methods. Through a modification of the coefficients of the Taylor expansion, extrapolations from a number of locations can be combined to obtain a polynomial order of accuracy that is one higher than that of a single conventional Taylor expansion. In Chapter 5 a ray field construction and mapping algorithm is developed that extends and refines existing wave front construction methods. For ray field mapping in the spatial domain two refinements are proposed that enhance the accuracy and the completeness of the maps. The applicability in the position/angle domain is investigated as well, with the unfortunate conclusion is that ray field construction in its current form is not suitable for that domain, due to the type of deformation in the geometrical structure of the ray field. A successful algorithm for the calculation of ray field maps in the position/angle domain is developed in Chapter 6. It is based on the observation that in the position/angle domain the ray field maps are single-valued and that the geometrical spreading is very limited. This implies that the two most important reasons for developing wave front construction methods in the spatial domain are absent in the position/angle domain. Instead, it is possible to use the more primitive - but more efficient - paraxial ray methods. The one-to-one mapping between position/angle coordinates and ray field coordinates can be exploited in practical applications. Calculations that are typically performed in terms of ray field coordinates can now be performed in terms of position/angle coordinates and the other way around. Appendices A and B show that this may be advantageous in tomography and the and the forward calculation of ray fields maps directly on a grid in the position/angle domain. Finally, Appendix C presents an algorithm for the calculation of ray fields in smooth 2-D media, using a pseudo-spectral expansion of the wave front. This line of research was abandoned in favour of the ray field map methods described above. Nevertheless, it is presented in the thesis because its development provided useful insights for the ray field map approach and some of its features may be useful in other applications