Stochastic perturbation optimization for discrete-continuous inverse problems

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. M73-M83 ◽  
Author(s):  
Leonardo Azevedo ◽  
Dario Grana ◽  
Leandro de Figueiredo
Keyword(s):  
Seismic Data ◽  
Seismic Reflection ◽  
Stochastic Perturbation ◽  
Rock Physics ◽  
Rock Properties ◽  
Petrophysical Properties ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Physics Model ◽  
Rock Physics Model

Accurate subsurface modeling and characterization require the prediction of facies and rock properties within the reservoir model. This is commonly achieved by inverting geophysical data, such as seismic reflection data, using a two-step approach either in the discrete or the continuous domain. We have adopted an iterative simultaneous method, namely, stochastic perturbation optimization, to invert seismic reflection data jointly for facies and rock properties. Facies first are simulated according to a Markov chain model, and then rock properties are generated with stochastic sequential simulation and cosimulation conditioned to each facies. Elastic and seismic data are computed by applying a rock-physics model to the realizations of petrophysical properties and a seismic convolutional model. The similarity between observed and synthetic seismic data is used to update the solution by perturbing facies and rock properties until convergence. Coupling the discrete and continuous domains ensures a consistent perturbation of the reservoir models throughout the iterations. We have evaluated the method in a 1D synthetic example for the estimation of facies and porosity from zero-offset seismic data assuming a linear rock-physics model to demonstrate the validity of the method. Then, we apply the method to a real 3D data set from the North Sea for the joint estimation of facies and petrophysical properties from prestack seismic data. The results show spatially consistent rock and fluid inverted models in which the predicted facies reproduce the vertical ordering as observed in the well data.

Seismic Reflections of Rock Properties in a Clastic Environment

2021 ◽  
Author(s):  
Vagif Suleymanov ◽  
Abdulhamid Almumtin ◽  
Guenther Glatz ◽  
Jack Dvorkin
Keyword(s):  
Rock Physics ◽  
Pore Fluid ◽  
Rock Properties ◽  
Petrophysical Properties ◽  
Sound Waves ◽  
Reservoir Properties ◽  
Field Guide ◽  
Physics Model ◽  
Rock Physics Model ◽  
Seismic Reflections

Abstract Generated by the propagation of sound waves, seismic reflections are essentially the reflections at the interface between various subsurface formations. Traditionally, these reflections are interpreted in a qualitative way by mapping subsurface geology without quantifying the rock properties inside the strata, namely the porosity, mineralogy, and pore fluid. This study aims to conduct the needed quantitative interpretation by the means of rock physics to establish the relation between rock elastic and petrophysical properties for reservoir characterization. We conduct rock physics diagnostics to find a theoretical rock physics model relevant to the data by examining the wireline data from a clastic depositional environment associated with a tight gas sandstone in the Continental US. First, we conduct the rock physics diagnostics by using theoretical fluid substitution to establish the relevant rock physics models. Once these models are determined, we theoretically vary the thickness of the intervals, the pore fluid, as well as the porosity and mineralogy to generate geologically plausible pseudo-scenarios. Finally, Zoeppritz (1919) equations are exploited to obtain the expected amplitude versus offset (AVO) and the gradient versus intercept curves of these scenarios. The relationship between elastic and petrophysical properties was established using forward seismic modeling. Several theoretical rock physics models, namely Raymer-Dvorkin, soft-sand, stiff-sand, and constant-cement models were applied to the wireline data under examination. The modeling assumes that only two minerals are present: quartz and clay. The appropriate rock physics model appears to be constant-cement model with a high coordination number. The result is a seismic reflection catalogue that can serve as a field guide for interpreting real seismic reflections, as well as to determine the seismic visibility of the variations in the reservoir geometry, the pore fluid, and the porosity. The obtained reservoir properties may be extrapolated to prospects away from the well control to consider certain what-if scenarios like plausible lithology or fluid variations. This enables building of a catalogue of synthetic seismic reflections of rock properties to be used by the interpreter as a field guide relating seismic data to volumetric reservoir properties.

Rock-physics diagnostics of a turbidite oil reservoir offshore northwest Australia

Geophysics ◽  
2017 ◽  
Vol 82 (1) ◽  
pp. MR1-MR13 ◽  
Author(s):  
Humberto S. Arévalo-López ◽  
Jack P. Dvorkin
Keyword(s):  
Seismic Data ◽  
Rock Physics ◽  
Rock Properties ◽  
Oil Reservoir ◽  
Controlled Experiments ◽  
Seismic Modeling ◽  
Physics Model ◽  
Rock Physics Model ◽  
Offshore Oil ◽  
Northwest Australia

Interpreting seismic data for petrophysical rock properties requires a rock-physics model that links the petrophysical rock properties to the elastic properties, such as velocity and impedance. Such a model can only be established from controlled experiments in which both groups of rock properties are measured on the same samples. A prolific source of such data is wellbore measurements. We use data from four wells drilled through a clastic offshore oil reservoir to perform rock-physics diagnostics, i.e., to find a theoretical rock-physics model that quantitatively explains the measurements. Using the model, we correct questionable well curves. Moreover, a crucial purpose of rock-physics diagnostics is to go beyond the settings represented in the wells and understand the seismic signatures of rock properties varying in a wider range via forward seismic modeling. With this goal in mind, we use our model to generate synthetic seismic gathers from perturbational modeling to address “what-if” scenarios not present in the wells.

Delineating ophiolite-derived host rocks of massive sulfide Cu-Co-Zn deposits with 2D high-resolution seismic reflection data in Outokumpu, Finland

Geophysics ◽  
2012 ◽  
Vol 77 (5) ◽  
pp. WC213-WC222 ◽  
Author(s):  
I. T. Kukkonen ◽  
S. Heinonen ◽  
P. Heikkinen ◽  
P. Sorjonen-Ward
Keyword(s):  
Seismic Data ◽  
Host Rock ◽  
Seismic Reflection ◽  
Massive Sulfide ◽  
High Amplitude ◽  
Ore Deposits ◽  
Acoustic Properties ◽  
Rock Properties ◽  
Seismic Reflection Data ◽  
Reflection Data

Seismic reflection data was applied to a study of the upper crustal structures in the Outokumpu mining and exploration area in eastern Finland. The Cu-Co-Zn sulfide ore deposits of the Outokumpu area are hosted by Palaeoproterozoic ophiolite-derived altered ultrabasic rocks (serpentinite, skarn rock, and quartz rock) and black schist within turbiditic mica schist. Mining in the Outokumpu area has produced a total of 36 Mt of ore from three historical and one active mine. Seismic data comprises 2D vibroseis data surveyed along a network of local roads. The seismic sections provide a comprehensive 3D view of the reflective structures. Acoustic rock properties from downhole logging and synthetic seismograms indicate that the strongly reflective packages shown in the seismic data can be identified as the host-rock environments of the deposits. Reflectors show excellent continuity along the structural grain of the ore belt, which allows correlating reflectors with surface geology, magnetic map, and drilling sections into a broad 3D model of the ore belt. Massive ores have acoustic properties that make them directly detectable with seismic reflection methods assuming the deposit size is sufficient for applied seismic wavelengths. The seismic data revealed numerous interesting high-amplitude reflectors within the interpreted host-rock suites potentially coinciding with sulfides.

Multivariate probabilistic rock physics models using Kumaraswamy distributions

Geophysics ◽  
2021 ◽  
pp. 1-43
Author(s):  
Dario Grana
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Random Variables ◽  
Rock Physics ◽  
Petrophysical Properties ◽  
Kumaraswamy Distribution ◽  
Model Predictions ◽  
Physics Model ◽  
Rock Physics Model

Rock physics models are physical equations that map petrophysical properties into geophysical variables, such as elastic properties and density. These equations are generally used in quantitative log and seismic interpretation to estimate the properties of interest from measured well logs and seismic data. Such models are generally calibrated using core samples and well log data and result in accurate predictions of the unknown properties. Because the input data are often affected by measurement errors, the model predictions are often uncertain. Instead of applying rock physics models to deterministic measurements, I propose to apply the models to the probability density function of the measurements. This approach has been previously adopted in literature using Gaussian distributions, but for petrophysical properties of porous rocks, such as volumetric fractions of solid and fluid components, the standard probabilistic formulation based on Gaussian assumptions is not applicable due to the bounded nature of the properties, the multimodality, and the non-symmetric behavior. The proposed approach is based on the Kumaraswamy probability density function for continuous random variables, which allows modeling double bounded non-symmetric distributions and is analytically tractable, unlike the Beta or Dirichtlet distributions. I present a probabilistic rock physics model applied to double bounded continuous random variables distributed according to a Kumaraswamy distribution and derive the analytical solution of the posterior distribution of the rock physics model predictions. The method is illustrated for three rock physics models: Raymer’s equation, Dvorkin’s stiff sand model, and Kuster-Toksoz inclusion model.

Porosity estimation based on rock skeleton general formula and comprehensive pore structure parameter – An application to a tight-sand reservoir

2021 ◽  
pp. 1-59
Author(s):  
Kai Lin ◽  
Xilei He ◽  
Bo Zhang ◽  
Xiaotao Wen ◽  
Zhenhua He ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Pore Structure ◽  
Seismic Data ◽  
Rock Physics ◽  
Structure Parameters ◽  
Pore Structure Parameter ◽  
Elastic Parameters ◽  
Physics Model ◽  
Rock Physics Model ◽  
Porosity Estimation

Most of current 3D reservoir’s porosity estimation methods are based on analyzing the elastic parameters inverted from seismic data. It is well-known that elastic parameters vary with pore structure parameters such as pore aspect ratio, consolidate coefficient, critical porosity, etc. Thus, we may obtain inaccurate 3D porosity estimation if the chosen rock physics model fails properly address the effects of pore structure parameters on the elastic parameters. However, most of current rock physics models only consider one pore structure parameter such as pore aspect ratio or consolidation coefficient. To consider the effect of multiple pore structure parameters on the elastic parameters, we propose a comprehensive pore structure (CPS) parameter set that is generalized from the current popular rock physics models. The new CPS set is based on the first order approximation of current rock physics models that consider the effect of pore aspect ratio on elastic parameters. The new CPS set can accurately simulate the behavior of current rock physics models that consider the effect of pore structure parameters on elastic parameters. To demonstrate the effectiveness of proposed parameters in porosity estimation, we use a theoretical model to demonstrate that the proposed CPS parameter set properly addresses the effect of pore aspect ratio on elastic parameters such as velocity and porosity. Then, we obtain a 3D porosity estimation for a tight sand reservoir by applying it seismic data. We also predict the porosity of the tight sand reservoir by using neural network algorithm and a rock physics model that is commonly used in porosity estimation. The comparison demonstrates that predicted porosity has higher correlation with the porosity logs at the blind well locations.

scholarly journals Improved Interpretation of Deep Seismic Reflection Data in Areas of Complex Geology Through Integration With Passive Seismic Data Sets

2018 ◽  
Vol 123 (12) ◽  
pp. 10,810-10,830
Author(s):  
Michael Dentith ◽  
Huaiyu Yuan ◽  
Ruth Elaine Murdie ◽  
Perla Pina-Varas ◽  
Simon P. Johnson ◽  
...  
Keyword(s):  
Seismic Data ◽  
Seismic Reflection ◽  
Data Sets ◽  
Seismic Reflection Data ◽  
Deep Seismic Reflection ◽  
Reflection Data ◽  
Passive Seismic ◽  
Complex Geology

Late Cretaceous – Cenozoic history of the transition zone between the East European Craton and the Paleozoic Platform, Polish sector of the Baltic Sea, revealed by new offshore regional seismic reflection data (BALTEC project)

2021 ◽  
Author(s):  
Piotr Krzywiec ◽  
Łukasz Słonka ◽  
Quang Nguyen ◽  
Michał Malinowski ◽  
Mateusz Kufrasa ◽  
...  
Keyword(s):  
High Resolution ◽  
Late Cretaceous ◽  
Seismic Data ◽  
Seismic Reflection ◽  
Upper Cretaceous ◽  
Seismic Reflection Data ◽  
East European ◽  
Reflection Data ◽  
Multichannel Seismic Reflection ◽  
Multichannel Seismic Reflection Data

<p>In 2016, approximately 850 km of high-resolution multichannel seismic reflection data of the BALTEC survey have been acquired offshore Poland within the transition zone between the East European Craton and the Paleozoic Platform. Data processing, focused on removal of multiples, strongly overprinting geological information at shallower intervals, included SRME, TAU-P domain deconvolution, high resolution parabolic Radon demultiple and SWDM (Shallow Water De-Multiple). Entire dataset was Kirchhoff pre-stack time migrated. Additionally, legacy shallow high-resolution multichannel seismic reflection data acquired in this zone in 1997 was also used. All this data provided new information on various aspects of the Phanerozoic evolution of this area, including Late Cretaceous to Cenozoic tectonics and sedimentation. This phase of geological evolution could be until now hardly resolved by analysis of industry seismic data as, due to limited shallow seismic imaging and very strong overprint of multiples, essentially no information could have been retrieved from this data for first 200-300 m. Western part of the BALTEC dataset is located above the offshore segment of the Mid-Polish Swell (MPS) – large anticlinorium formed due to inversion of the axial part of the Polish Basin. BALTEC seismic data proved that Late Cretaceous inversion of the Koszalin – Chojnice fault zone located along the NE border of the MPS was thick-skinned in nature and was associated with substantial syn-inversion sedimentation. Subtle thickness variations and progressive unconformities imaged by BALTEC seismic data within the Upper Cretaceous succession in vicinity of the Kamień-Adler and the Trzebiatów fault zones located within the MPS documented complex interplay of Late Cretaceous basin inversion, erosion and re-deposition. Precambrian basement of the Eastern, cratonic part of the study area is overlain by Cambro-Silurian sedimentary cover. It is dissected by a system of steep, mostly reverse faults rooted in most cases in the deep basement. This fault system has been regarded so far as having been formed mostly in Paleozoic times, due to the Caledonian orogeny. As a consequence, Upper Cretaceous succession, locally present in this area, has been vaguely defined as a post-tectonic cover, locally onlapping uplifted Paleozoic blocks. New seismic data, because of its reliable imaging of the shallowest substratum, confirmed that at least some of these deeply-rooted faults were active as a reverse faults in latest Cretaceous – earliest Paleogene. Consequently, it can be unequivocally proved that large offshore blocks of Silurian and older rocks presently located directly beneath the Cenozoic veneer must have been at least partly covered by the Upper Cretaceous succession; then, they were uplifted during the widespread inversion that affected most of Europe. Ensuing regional erosion might have at least partly provided sediments that formed Upper Cretaceous progradational wedges recently imaged within the onshore Baltic Basin by high-end PolandSPAN regional seismic data. New seismic data imaged also Paleogene and younger post-inversion cover. All these results prove that Late Cretaceous tectonics substantially affected large areas located much farther towards the East than previously assumed.</p><p>This study was funded by the Polish National Science Centre (NCN) grant no UMO-2017/27/B/ST10/02316.</p>

scholarly journals Monte Carlo reservoir analysis combining seismic reflection data and informed priors

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. R31-R41 ◽  
Author(s):  
Andrea Zunino ◽  
Klaus Mosegaard ◽  
Katrine Lange ◽  
Yulia Melnikova ◽  
Thomas Mejer Hansen
Keyword(s):  
Monte Carlo ◽  
Seismic Data ◽  
Seismic Reflection ◽  
Probabilistic Approach ◽  
Multiple Point ◽  
Petroleum Reservoir ◽  
Inversion Algorithm ◽  
Reservoir Properties ◽  
Seismic Reflection Data ◽  
Reflection Data

Determination of a petroleum reservoir structure and rock bulk properties relies extensively on inference from reflection seismology. However, classic deterministic methods to invert seismic data for reservoir properties suffer from some limitations, among which are the difficulty of handling complex, possibly nonlinear forward models, and the lack of robust uncertainty estimations. To overcome these limitations, we studied a methodology to invert seismic reflection data in the framework of the probabilistic approach to inverse problems, using a Markov chain Monte Carlo (McMC) algorithm with the goal to directly infer the rock facies and porosity of a target reservoir zone. We thus combined a rock-physics model with seismic data in a single inversion algorithm. For large data sets, the McMC method may become computationally impractical, so we relied on multiple-point-based a priori information to quantify geologically plausible models. We tested this methodology on a synthetic reservoir model. The solution of the inverse problem was then represented by a collection of facies and porosity reservoir models, which were samples of the posterior distribution. The final product included probability maps of the reservoir properties in obtained by performing statistical analysis on the collection of solutions.

Using instantaneous frequency and colored inversion attributes to distinguish and determine the sandstones facies of the Late Ordovician Mamuniyat reservoir, R-field in Murzuq Basin, Libya

2016 ◽  
Vol 4 (4) ◽  
pp. T507-T519 ◽  
Author(s):  
Yousf Abushalah ◽  
Laura Serpa
Keyword(s):  
Instantaneous Frequency ◽  
Seismic Data ◽  
Acoustic Impedance ◽  
Rock Physics ◽  
Side Lobe ◽  
Petroleum Reservoir ◽  
Seismic Reflection Data ◽  
Frequency Bands ◽  
Reflection Data ◽  
Sandstone Facies

The Mamuniyat petroleum reservoir in southwestern Libya is comprised of clean sandstones and intercalated shale and sand facies that are characterized by spatial porosity variations. Seismic reflection data from the field exhibit relatively low vertical seismic resolution, side lobes of reflection wavelets, reflection interference, and low acoustic impedance contrast between the reservoir and the units underneath the reservoir, which make mapping those facies a difficult task. In the absence of broadband seismic data, optimizing frequency bands of bandlimited data can be used to suppress pseudoreflectors resulting from side-lobe effects and help to separate the clean sandstone facies of the reservoir. We have optimized the data based on our investigation of seismic frequency bands and used instantaneous frequency analysis to reveal the reflection discontinuity that is mainly associated with the reservoir boundary of the sandstone facies of the clean Mamuniyat reservoir. We also preformed rock-physics diagnostic modeling and inverted the seismic data using spectral-based colored inversion into relative acoustic impedance. The inverted impedance matches the up-scaled impedance from the well data and the inversion of relative acoustic impedance confirms the conclusion that was drawn from the instantaneous frequency results. The interpretation of facies distributions based on the instantaneous frequency was supported by the inversion results and the rock-physics models.

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