Basis Pursuit Receiver Function

Receiver functions (RFs) are derived by deconvolution of the horizontal (radial or transverse) component of ground motion from the vertical component, which segregates the PS phases. Many methods have been proposed to employ deconvolution in frequency as well as in time domain. These methods vary in their approaches to impose regularization that addresses the stability problem. Here, we present application of a new time-domain deconvolution technique called basis pursuit deconvolution (BPD) that has recently been applied to seismic exploration data. Unlike conventional deconvolution methods, the BPD uses an L1 norm constraint on model reflectivity to impose sparsity. In addition, it uses an overcomplete wedge dictionary based on a dipole reflectivity series to define model constraints, which can achieve higher resolution than that obtained by the traditional methods. We demonstrate successful application of BPD based RF estimation from synthetic data for a crustal model with a near-surface thin layer of thickness 5, 7, 10, and 15 km. The BPD can resolve these thin layers better with much improved signal-to-noise ratio than the conventional methods. Finally, we demonstrate application of the BPD receiver function (BPRF) method to a field dataset from Kutch, India, where near-surface sedimentary layers are known to be present. The BPRFs are able to resolve reflections from these layers very well.Jackson Chair funds at the Jackson School of Geosciences, University of Texas, AustinCouncil of Scientific and Industrial Research twelfth five year plan project at the Council of Scientific and Industrial Research National Geophysical Research Institute (CSIR-NGRI), HyderabadInstitute for Geophysic

Monitoring Pressure and Saturation Changes in a Clastic Reservoir from Time-lapse Seismic Data Using the Extended Elastic Impedance Method

The Extended Elastic Impedance (EEI) concept has been used by the oil industry primarily for lithology and fluid prediction in exploration and development projects. We present a method of reservoir monitoring that identifies and maps changes in pressure and saturation in a producing reservoir by applying EEI to time-lapse seismic data. The method uses time-lapse seismic difference data rotated to specific EEI ? angles which are optimised for the changes expected in a given reservoir

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

Quantifying the Basal Conditions of a Mountain Glacier Using a Targeted Full-Waveform Inversion: Bench Glacier, Alaska, USA

Glacier dynamics are inextricably linked to the basal conditions of glaciers. Seismic reflection methods can image the glacier bed under certain conditions. However, where a seismically thin layer of material is present at the bed, traditional analyses may fail to fully characterize bed properties. We use a targeted full-waveform inversion algorithm to quantify the basal-layer parameters of a mountain glacier: thickness (d), P-wave velocity (α) and density (ρ). We simultaneously invert for the seismic quality factor (Q) of the bulk glacier ice. The inversion seeks to minimize the difference between the data and a one-dimensional reflectivity algorithm using a gradient-based search with starting values initialized from a Monte Carlo scheme. We test the inversion algorithm on four basal layer synthetic data traces with 5% added Gaussian noise. The inversion retrieved thin-layer parameters within 10% of synthetic test parameters with the exception of seismic Q. For the seismic dataset from Bench Glacier, Alaska, USA, inversion results indicate a thin basal layer of debris-rich ice within the study area having mean velocity 4000 ± 700 m s–1, density 1900 ± 200 kg m–3 and thickness 6 ± 1.5 m

Seismic Spectral Monitoring of CO2 in a Geological Reservoir

Peak frequency is a spectral seismic attribute widely used for reservoir thickness estimation and hydrocarbon detection. In this work we apply this attribute in the context of the geological storage of carbon dioxide (CO2) and analyze its reliability as a thickness estimator for the gas accumulation. To model the vertical distribution of CO2, we solve the Buckley-Leverett equation with discontinuous flux function. A matrix reflectivity algorithm then computes, in the frequency domain, the seismic reflectivity. We find that the peak frequency variability due to CO2 saturation does not alter significantly its correlation with the accumulation thickness. We then extend the applicability of the spectral attribute by examining its time-lapse response to the evolution of the injected CO2 volume within a reservoir. We find that a description of the CO2-brine contact as well as the evaluation of the reservoir’s caprock sealing capacity can be obtained from this implementation. Peak-frequency time-lapse signatures when the CO2 forms an up-going front, evolves into a growing accumulation and leaks into the caprock are identified.Fil: Gómez, Julián Luis. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas. Departamento de Geofísica Aplicada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Ravazzoli, Claudia Leonor. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas. Departamento de Geofísica Aplicada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Reflection and transmission coefficients of a thin bed

The study of thin-bed seismic response is an important part in lithologic and methane reservoir modeling, critical for predicting their physical attributes and/or elastic parameters. The complex propagator matrix for the exact reflections and transmissions of thin beds limits their application in thin-bed inversion. Therefore, approximation formulas with a high accuracy and a relatively simple form are needed for thin-bed seismic analysis and inversion. We have derived thin-bed reflection and transmission coefficients, defined in terms of displacements, and approximated them to be in a quasi-Zoeppritz matrix form under the assumption that the middle layer has a very thin thickness. We have verified the approximation accuracy through numerical calculation and concluded that the errors in PP-wave reflection coefficients RPP are generally smaller than 10% when the thin-bed thicknesses are smaller than one-eighth of the PP-wavelength. The PS-wave reflection coefficients RPS have lower approximation accuracy than RPP for the same ratios of thicknesses to their respective wavelengths, and the RPS approximation is not acceptable for incident angles approaching the critical angles (when they exist) except in the case of extremely strong impedance difference. Errors in phase for the RPP and RPS approximation are less than 10% for the cases of thicknesses less than one-tenth of the wavelengths. As expected, a thinner middle layer and a weaker impedance difference would result in higher approximation accuracy

3D Post-stack Seismic Inversion using Global Optimization Techniques: Gulf of Mexico Example

Seismic inversion using a global optimization algorithm is a non-linear, model-driven process. It yields an optimal solution of the cost function – reflectivity/acoustic impedance, when prior information is sparse. The inversion result offers detailed interpretations of thin layers, internal stratigraphy, and lateral continuity and connectivity of sand bodies. This study compared two stable and robust global optimization techniques, Simulated Annealing (SA) and Basis Pursuit Inversion (BPI) as applied to post-stack seismic data from the Gulf of Mexico. Both methods use different routines and constraints to search for the minimum error energy function. Estimation of inversion parameters in SA is rigorous and more reliable because it depends on prior knowledge of subsurface geology. The BPI algorithm is a more robust deterministic process. It was developed as an alternative method to incorporating a priori information. Results for the Gulf of Mexico show that BPI gives a better stratigraphic and structural actualization due to its capacity to delineate layers thinner than the tuning thickness. The SA algorithm generates both absolute and relative impedances, which provide both qualitative and quantitative characterization of thin-bed reservoirs

3D Post-stack Seismic Inversion using Global Optimization Techniques: Gulf of Mexico Example

Seismic inversion using a global optimization algorithm is a non-linear, model-driven process. It yields an optimal solution of the cost function – reflectivity/acoustic impedance, when prior information is sparse. The inversion result offers detailed interpretations of thin layers, internal stratigraphy, and lateral continuity and connectivity of sand bodies. This study compared two stable and robust global optimization techniques, Simulated Annealing (SA) and Basis Pursuit Inversion (BPI) as applied to post-stack seismic data from the Gulf of Mexico. Both methods use different routines and constraints to search for the minimum error energy function. Estimation of inversion parameters in SA is rigorous and more reliable because it depends on prior knowledge of subsurface geology. The BPI algorithm is a more robust deterministic process. It was developed as an alternative method to incorporating a priori information. Results for the Gulf of Mexico show that BPI gives a better stratigraphic and structural actualization due to its capacity to delineate layers thinner than the tuning thickness. The SA algorithm generates both absolute and relative impedances, which provide both qualitative and quantitative characterization of thin-bed reservoirs