2D full-waveform modeling of seismic waves in layered karstic media

We have developed a new propagator-matrix scheme to simulate seismic-wave propagation and scattering in a multilayered medium containing karstic voids. The propagator matrices can be found using the boundary element method. The model can have irregular boundaries, including arbitrary free-surface topography. Any number of karsts can be included in the model, and each karst can be of arbitrary geometric shape. We have used the Burton-Miller formulation to tackle the numerical instability caused by the fictitious resonance due to the finite size of a karstic void. Our method was implemented in the frequency-space domain, so frequency-dependent Q can be readily incorporated. We have validated our calculation by comparing it with the analytical solution for a cylindrical void and to the spectral element method for a more complex model. This new modeling capability is useful in many important applications in seismic inverse theory, such as imaging karsts, caves, sinkholes, and clandestine tunnels

Borehole Seismic Source Radiation In Layered Isotropic And Anisotropic Media: Boundary Element Modeling

An algorithm based on the boundary element method is established for modeling seismic source radiation from open or cased boreholes in layered transversely isotropic (TI) media. The axis of symmetry of TI layers is assumed to be parallel to the borehole axis. Under this assumption, the problem is significantly simplified because the element discretization of the borehole remains one dimensional. For fluid-filled open boreholes, three equivalent sources on each element are required to represent the boundary effects on the inner fluid and the outer solid. The three boundary conditions for a f1uidsolid interface set up a system of equations for the equivalent sources on all elements. Once the sources are known, displacements in the solid and pressure in the fluid are obtained. For fluid-filled and cased boreholes, the method treats borehole fluid, casing, and cement as a cylindricaliy layered isotropic medium. In this case, the boundary conditions to be satisfied at the borehole wall are four (continuity of the normal and tangential displacements and stresses). The implementation of the method is illustrated through a few examples.United States. Dept. of Energy (Grant DE-FG02-89ERI4084

Inverse scattering of 2d photonic structures by layer-stripping

Design and reconstruction of 2d and 3d photonic structures are usually carried out by forward simulations combined with optimization or intuition. Reconstruction by means of layer-stripping has been applied in seismic processing as well as in design and characterization of 1d photonic structures such as fiber Bragg gratings. Layer-stripping is based on causality, where the earliest scattered light is used to recover the structure layer-by-layer. Our set-up is a 2d layered nonmagnetic structure probed by plane polarized harmonic waves entering normal to the layers. It is assumed that the dielectric permittivity in each layer only varies orthogonal to the polarization. Based on obtained reflectance data covering a suitable frequency interval, time-localized pulse data are synthesized and applied to reconstruct the refractive index profile in the leftmost layer by identifying the local, time-domain Fresnel reflection at each point. Once the first layer is known, its impact on the reflectance data is stripped off, and the procedure repeated for the next layer. Through numerical simulations it will be demonstrated that it is possible to reconstruct structures consisting of several layers. The impact of evanescent modes and limited bandwidth is discussed

Crustal Imaging With Bayesian Inversion of Teleseismic P Wave Coda Autocorrelation

The autocorrelation of the seismic transmission response of a layered medium(autocorrelogram), in the presence of a free surface, corresponds to the reflection response. Despite manystudies on the imaging of local structures through retrieval and forward modeling of stackedautocorrelograms, there is limited work on the inversion of these data. In this study, we demonstrate thatthe probabilistic inversion of autocorrelograms is efficientand can be used as an alternative imaging toolwhen other approaches are not applicable. Here, we calculate autocorrelograms of teleseismicPwave codarecorded on more than 1,200 permanent and temporary seismic stations across Australia and utilize aBayesian framework to invert these data for crustal imaging. The results show patterns of structuresconsistent with those seen in previous crustal models constructed from receiver function, seismicreflection, and refraction methods. The new approach can therefore image large-scale crustal structurescomparable to those from other seismological methods

A new fast multi-domain BEM to model seismic wave propagation and amplification in 3D geological structures

International audienceThe analysis of seismic wave propagation and amplification in complex geological structures raises the need for efficient and accurate numerical methods. The solution of the elastodynamic equations using traditional boundary element methods (BEMs) is greatly hindered by the fully-populated nature of the matrix equations arising from the discretization. In a previous study limited to homogeneous media, the present authors have established that the Fast Multipole (FM) method reduces the complexity of a 3-D elastodynamic BEM to $N \log N$ per GMRES iteration and demonstrated its effectiveness on 3-D canyon configurations. In this article, the frequency-domain FM-BEM methodology is extented to 3-D elastic wave propagation in piecewise-homogeneous domains in the form of a FM-accelerated multi-region BE-BE coupling approach. This new method considerably enhances the capability of the BEM for studying the propagation of seismic waves in 3-D alluvial basins of arbitrary geometry embedded in semi-infinite media. Several fully 3-D examples (oblique SV-waves) representative of such configurations validate and demonstrate the capabilities of the multi-domain fast multipole approach. They include comparisons with available (low-frequency) results for various types of incident wavefields, and time-domain results obtained by means of Fourier synthesis

A layer-stripping solution of the inverse problem for a one-dimensional elastic medium

"September, 1983."Bibliography p. 18-19.Supported by the Air Force Office of Scientific Research under Grant AFOSR-82-0135by Andrew E. Yagle, Bernard C. Levy

Anisotropic reflectivity technique

Available from British Library Document Supply Centre- DSC:D44305/83 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo

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