Characterization of a shale-gas reservoir based on a seismic amplitude variation with offset inversion for transverse isotropy with vertical axis of symmetry media and quantitative seismic interpretation

The Lower Silurian shale-gas formation in the south of the Sichuan Basin represents a strong transverse isotropy with vertical axis of symmetry (VTI) feature. Successful characterization of shale-gas formation requires handling the great influence of anisotropy in the seismic wave propagation. Seismic amplitude variation with offset (AVO) inversion for VTI media using PP-waves only is a difficult issue because more than three parameters need to be estimated and such an inverse problem is highly ill posed. We have applied an AVO inversion method for VTI media based on a modified approximation of the PP-wave reflection coefficient. This approximation consists of only three model parameters: the acoustic impedance (attribute A), shear modulus proportional to the anellipticity parameter (attribute B), and the approximated horizontal P-wave velocity (attribute C), which can be well-inverted and have great interpretation capability in shale-gas reservoir characterization. A statistical-rock-physics method was then applied to the inverted attributes for quantitative interpretation of the shale-gas reservoir. A Markov random field is combined with Bayesian rule to improve the continuity and accuracy of the interpretation results. Shales can be successfully discriminated from surrounding formations by using the attribute pair A-C, and the organic-rich gas-bearing shale can be successfully identified by using the attribute pair C-B . Comparison between the prediction results and well logs demonstrates the feasibility of the inversion and quantitative interpretation approaches

Quantitative seismic interpretation of rock brittleness based on statistical rock physics

Rock brittleness is one of the important properties for fracability evaluation, and it can be represented by different physical properties. The mineralogy-based brittleness index (BIM) builds a simple relationship between mineralogy and brittleness, but it may be ambiguous for rocks with a complex microstructure; whereas the elastic moduli-based brittleness index (BIE) is applicable in the field, but BIE interpretation needs to be constrained by lithofacies information. We have developed a new workflow for quantitative seismic interpretation of rock brittleness: Lithofacies are defined by a criterion combining BIM and BIE for comprehensive brittleness evaluation; statistical rock-physics methods are applied for quantitative interpretation by using inverted elastic parameters; acoustic impedance and elastic impedance are selected as the optimized pair of attributes for lithofacies classification. To improve the continuity and accuracy of the interpreted results, a Markov random field is applied in the Bayesian rule as the spatial constraint. A 2D synthetic test demonstrates the feasibility of the Bayesian classification with a Markov random field. This new interpretation framework is also applied to a shale reservoir formation from China. Comparison analysis indicates that brittle shale sections can be efficiently discriminated from ductile shale sections and tight sand sections by using the inverted elastic parameters

Seismic Inversion and Uncertainty Analysis using Transdimensional Markov Chain Monte Carlo Method

We use a transdimensional inversion algorithm, reversible jump MCMC (rjMCMC), in the seismic waveform inversion of post-stack and prestack data to characterize reservoir properties such as seismic wave velocity, density as well as impedance and then estimate uncertainty. Each seismic trace is inverted independently based on a layered earth model. The model dimensionality is defined as the number of the layers multiplied with the number of model parameters per layer. The rjMCMC is able to infer the number of model parameters from data itself by allowing it to vary in the iterative inversion process, converge to proper parameterization and prevent underparameterization and overparameterization. We also use rjMCMC to enhance uncertainty estimation since it can transdimensionally sample different model spaces of different dimensionalities and can prevent a biased sampling in only one space which may have a different dimensionality than that of the true model space. An ensemble of solutions from difference spaces can statistically reduce the bias for parameter estimation and uncertainty quantification. Inversion uncertainty is comprised of property uncertainty and location uncertainty. Our study revealed that the inversion uncertainty is correlated with the discontinuity of property in such a way that 1) a smaller discontinuity will induce a lower uncertainty in property at the discontinuity but also a higher uncertainty of the location of that discontinuity and 2) a larger discontinuity will induce a higher uncertainty in property at the discontinuity but also a higher ``certainty'' of the location of that discontinuity. Therefore, there is a trade-off between the property uncertainty and the location uncertainty. To our surprise, there is a lot of hidden information in the uncertainty result that we can actually take advantage of due to this trade-off effect. On the basis of our study using rjMCMC, we propose to use the inversion uncertainty as a novel attribute in an optimistic way to characterize the magnitude and the location of subsurface discontinuities and reflectors

A data-driven transdimensional approach to include lateral constraints on 2D target-oriented AVA inversion

Seismic inversion aims to infer subsurface properties from processed seismic data; since these are often ill-conditioned procedures, numerous strategies can be investigated. To date currently adopted procedures assume an a priori structural knowledge of the investigated area and impose such constraints to the recovered solution. To overcome this downside we apply a transdimensional reversible jump-Markov chain Monte Carlo (Rj-McMC) algorithm to solve the interval-oriented amplitude versus angle (AVA) inversion on 2D synthetic seismic data. This approach considers the model parametrization as an unknown, together with the elastic properties of the investigated area. The algorithm samples models discretized in Voronoi cells characterized by similar AVA responses. The elastic values associated with each Voronoi cell are obtained taking the average of the elastic properties of the CDPs falling within it. This data-driven approach does, therefore, need no external assumption over the investigated area and ensures an automatically inferred strategy to include lateral variability of data inside the inversion kernel. We compare results obtained to a standard Bayesian approach for different SNR, showing how the increase of random noise contaminating the data strongly affects the linear approach, while the Rj-McMC generates model predictions in accordance with the true model, producing more reliable results

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

Characterisation of shallow marine sediments using high-resolution velocity analysis and genetic-algorithm-driven 1D elastic full-waveform inversion

We estimate the elastic properties of marine sediments beneath the seabed by means of high-resolution velocity analysis and one-dimensional elastic full-waveform inversion performed on twodimensional broad-band seismic data of a well-site survey. A high-resolution velocity function is employed to exploit the broad frequency band of the data and to derive the P-wave velocity field with a high degree of accuracy. To derive a complete elastic characterisation in terms of P-wave and S-wave velocities (Vp, Vs) and density of the subsurface, and to increase the resolution of the Vp estimates, we apply a one-dimensional elastic full-waveform inversion in which the outcomes derived from the velocity analysis are used as a priori information to define the Vp search range. The one-dimensional inversion is done using genetic algorithm as the optimisation method. It is performed by considering two misfit functions: the first uses the entire waveform to compute the misfit between modelled and observed seismograms, and the second considers the envelope of the seismograms, thus relaxing the requirement of an exact estimation of the wavelet phase. The full-waveform inversion and the high-resolution velocity analysis yield comparable Vp profiles, but the full-waveform inversion reconstruction is much more detailed. Regarding the full-waveform inversion results, the final depth models of P- and S-wave velocities and density show a fine-layered structure with a significant increase in velocities and density at shallow depth, which may indicate the presence of a consolidated layer. The very similar velocities and density-depth trends obtained by employing the two different misfit functions increase our confidence in the reliability of the predicted subsurface models

Optimization Using Genetic Algorithms – Methodology with Examples from Seismic Waveform Inversion

Genetic algorithms use the survival of the fittest analogy from evolution theory to make random walks in the multiparameter model-space and find the model or the suite of models that best-fit the observation. Due to nonlinear nature, runtimes of genetic algorithms exponentially increase with increasing model-space size. A diversity-preserved genetic algorithm where each member of the population is given a measure of diversity and the models are selected in preference to both their objective and diversity values, and scaling the objectives using a suitably chosen scaling function can expedite computation and reduce runtimes. Starting from an initial model and the model-space defined as search intervals around it and using a new sampling strategy of generating smoothly varying initial set of random models within the specified search intervals; the proposed diversity-preserved method converges rapidly and estimates reliable models. The methodology and implementation of this new genetic algorithm optimization is described using examples from the prestack seismic waveform inversion problems. In geophysics, this new method can be useful for subsurface characterization where well-control is sparse

1D elastic full-waveform inversion and uncertainty estimation by means of a hybrid genetic algorithm-Gibbs sampler approach

Stochastic optimization methods, such as genetic algorithms, search for the global minimum of the misfit function within a given parameter range and do not require any calculation of the gradients of the misfit surfaces. More importantly, these methods collect a series of models and associated likelihoods that can be used to estimate the posterior probability distribution. However, because genetic algorithms are not a Markov chain Monte Carlo method, the direct use of the genetic-algorithm-sampled models and their associated likelihoods produce a biased estimation of the posterior probability distribution. In contrast, Markov chain Monte Carlo methods, such as the Metropolis-Hastings and Gibbs sampler, provide accurate posterior probability distributions but at considerable computational cost. In this paper, we use a hybrid method that combines the speed of a genetic algorithm to find an optimal solution and the accuracy of a Gibbs sampler to obtain a reliable estimation of the posterior probability distributions. First, we test this method on an analytical function and show that the genetic algorithm method cannot recover the true probability distributions and that it tends to underestimate the true uncertainties. Conversely, combining the genetic algorithm optimization with a Gibbs sampler step enables us to recover the true posterior probability distributions. Then, we demonstrate the applicability of this hybrid method by performing one-dimensional elastic full-waveform inversions on synthetic and field data. We also discuss how an appropriate genetic algorithm implementation is essential to attenuate the "genetic drift" effect and to maximize the exploration of the model space. In fact, a wide and efficient exploration of the model space is important not only to avoid entrapment in local minima during the genetic algorithm optimization but also to ensure a reliable estimation of the posterior probability distributions in the subsequent Gibbs sampler step

Joint non-linear inversion of amplitudes and travel times in a vertical transversely isotropic medium using compressional and converted shear waves

Massive shales and fractures are the main cause of seismic anisotropy in the upper-most part of the crust, caused either by sedimentary or tectonic processes. Neglecting the effect of seismic anisotropy in seismic processing algorithms may incorrectly image the seismic reflectors. This will also influence the quantitative amplitude analysis such as the acoustic or elastic impedance inversion and amplitude versus offsets analysis. Therefore it is important to obtain anisotropy parameters from seismic data. Conventional layer stripping inversion schemes and reflector based reflectivity inversion methods are solely dependent upon a specific reflector, without considering the effect of the other layers. This, on one hand, does not take the effect of transmission in reflectivity inversion into the account, and on the other hand, ignores the information from the waves travelling toward the lower layers. I provide a framework to integrate the information for each specific layer from all the rays which have travelled across this layer. To estimate anisotropy parameters I have implemented unconstrained minimization algorithms such as nonlinear conjugate gradients and variable metric methods, I also provide a nonlinear least square method, based on the Levenberg-Marquardt algorithm. In a stack of horizontal transversely isotropic layers with vertical axis of symmetry, where the layer properties are laterally invariant, we provide two different inversion schemes; traveltime and waveform inversion.Both inversion schemes utilize compressional and joint compressional and converted shear waves. A new exact traveltime equation has been formulated for a dipping transversely isotropic system of layers. These traveltimes are also parametrized by the ray parameters for each ray element. I use the Newton method of minimization to estimate the ray parameter using a random prior model from a uniform distribution. Numerical results show that with the assumption of weak anisotropy, Thomsen’s anisotropy parameters can be estimated with a high accuracy. The inversion algorithms have been implemented as a software package in a C++ object oriented environment