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- Volume 54, Issue 3, 2006
Geophysical Prospecting - Volume 54, Issue 3, 2006
Volume 54, Issue 3, 2006
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Enforcing smoothness and assessing uncertainty in non‐linear one‐dimensional prestack seismic inversion
Authors Omar J. Varela, Carlos Torres‐Verdín and Mrinal K. SenABSTRACTEstimation of elastic properties of rock formations from surface seismic amplitude measurements remains a subject of interest for the exploration and development of hydrocarbon reservoirs. This paper develops a global inversion technique to estimate and appraise 1D distributions of compressional‐wave velocity, shear‐wave velocity and bulk density, from normal‐moveout‐corrected PP prestack surface seismic amplitude measurements. Specific objectives are: (a) to evaluate the efficiency of the minimization algorithm (b) to appraise the impact of various data misfit functions, and (c) to assess the effect of the degree and type of smoothness criterion enforced by the inversion. Numerical experiments show that very fast simulated annealing is the most efficient minimization technique among alternative approaches considered for global inversion. It is also found that an adequate choice of data misfit function is necessary for a reliable and efficient match of noisy and sparse seismic amplitude measurements. Several procedures are considered to enforce smoothness of the estimated 1D distributions of elastic parameters, including predefined quadratic measures of length, flatness and roughness.
Based on the general analysis of global inversion techniques, we introduce a new stochastic inversion algorithm that initializes the search for the minimum with constrained random distributions of elastic parameters and enforces predefined autocorrelation functions (semivariograms). This strategy readily lends itself to the assessment of model uncertainty. The new global inversion algorithm is successfully tested on noisy synthetic amplitude data. Moreover, we present a feasibility analysis of the resolution and uncertainty of prestack seismic amplitude data to infer 1D distributions of elastic parameters measured with wireline logs in the deepwater Gulf of Mexico. The new global inversion algorithm is computationally more efficient than the alternative global inversion procedures considered here.
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Numerical modelling of complex resistivity effects on a homogenous half‐space at low frequencies
Authors T. Ingeman‐Nielsen and François BaumgartnerABSTRACTThe many different existing models describing the spectral behaviour of the resistivity of geological materials at low frequency, combined with the lack of available field data, render the interpretation of complex resistivity (CR) data very difficult. With a recent interest in CR‐measurements for environmental applications and thanks to technological progress, the use of wide‐band frequency equipment seems promising, and it is expected to shed light on the different results among the published solutions to the electromagnetic (EM) coupling problem. We review the theory of EM‐coupling over a homogeneous half‐space with CR‐effects and study some aspects of the complex coupling function. We advocate the use of the CR‐based coupling function in the interpretation process, in order to obtain a better understanding of the physical processes involved in CR‐effects. Application of the model to real field data shows systematic good agreement in two simple cases, even over wide ranges of frequencies. Interpretation with a double Cole–Cole model is applied for comparison, and in spite of good fits to the data, large differences are observed in the interpreted low‐frequency dispersion. We conclude that the use of a second Cole–Cole model to describe EM‐coupling may corrupt the interpretation of the low‐frequency dispersion, even when only the normal range of frequencies (<100 Hz) is considered, and that the use of the actual EM‐coupling expression is essential when the goal is a better understanding of interaction between CR‐effects and EM‐coupling.
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Internal structure of an alpine rock glacier based on crosshole georadar traveltimes and amplitudes
Authors Martin Musil, Hansruedi Maurer, Klaus Hollinger and Alan G. GreenABSTRACTRapid melting of permafrost in many alpine areas has increased the probability of catastrophic rock slides. In an attempt to provide critical structural information needed for the design and implementation of suitable mitigation procedures, we have acquired low frequency (22 MHz) cross‐hole radar data from within a fast‐moving rock glacier, an important form of alpine permafrost. Since the ice, rock and pockets of water and air found in the underground of high alpine areas have very different dielectric permittivities and electrical conductivities, the radar method was well‐suited for investigating the structure and state of the rock glacier. Our interpretation of the radar velocities and attenuations was constrained by geomorphological observations, borehole lithological logs and the results of a surface seismic survey. The radar data revealed the existence of a discontinuous 7–11 m thick ice‐rich zone distinguished by high velocities (0.14–0.17 m/ns) and low attenuations (0.04–0.09 m−1) and a thin underlying ice‐free zone characterized by moderate velocities (0.11–0.12 m/ns) and low attenuations (0.04–0.09 m−1). Beneath these two zones, we observed a prominent band of high velocities (0.14–0.17 m/ns) and moderately high attenuations (0.10–0.20 m−1) associated with unconsolidated glacial sediments and numerous large air‐filled voids, which in the past were probably filled with ice. At greater depths, the variably dry to water‐saturated sediments were represented by generally lower velocities (0.08–0.10 m/ns) and higher attenuations (0.16–0.24 m−1). The bedrock surface was represented by an abrupt ∼0.03 m/ns velocity increase. We speculate that the disappearance of ice, both laterally and with depth, occurred during the past one to two decades.
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Inversion of 2D spectral induced polarization imaging data
Authors M.H. Loke, J.E. Chambers and R.D. OgilvyABSTRACTLaboratory measurements of various materials suggest that more information can be obtained by measuring the in‐phase and out‐of‐phase potentials at a number of frequencies. One common model used to describe the variation of the electrical properties with frequency is the Cole‐Cole model. Apart from the DC resistivity (ρ) and chargeability (m) parameters used in conventional induced‐polarization (IP) surveys, the Cole‐Cole model has two additional parameters, i.e. the time (τ) and relaxation (c) constants. Much research has been conducted on the use of the additional Cole‐Cole parameters to distinguish between different IP sources. Here, we propose a modified inversion method to recover the Cole‐Cole parameters from a 2D spectral IP (SIP) survey. In this method, an approximate inversion method is initially used to construct a non‐homogeneous starting model for the resistivity and chargeability values. The 2D model consists of a number of rectangular cells with constant resistivity (ρ), chargeability (m), time (τ) and relaxation (c) constant values in each cell. A regularized least‐squares optimization method is then used to recover the time and relaxation constant parameters as well as to refine the chargeability values in the 2D model. We present results from tests carried out with the proposed method for a synthetic data set as well as from a laboratory tank experiment.
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Going quantitative with 4D seismic analysis
Authors Colin MacBeth, Mariano Floricich and Juan SoldoABSTRACTIt is demonstrated that time‐lapse seismic signatures can be directly calibrated with historical data from producing and injecting wells via a reservoir simulator, material balance calculation or simply using the hard data. When this procedure is applied to a field over which two or more repeat surveys have been shot at different calendar times, the correlation coefficients that link the seismic difference signatures to the reservoir's pressure and saturation variations are determined. By utilizing several seismic attributes that respond differently to reservoir perturbations, pressure and saturation changes are then independently estimated. The approach is tested on synthetic data and then on data from the Schiehallion Field on the UK continental shelf, with favourable results.
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A field investigation of fracture compliance
Authors R. Lubbe and M.H. WorthingtonABSTRACTA field measurement of fracture compliance is described. The aim was to determine how compliance scales with fracture size and, specifically, how laboratory measurements of fracture compliance compared with field estimates from sonic and seismic data. A test site was constructed, consisting of three 40 m vertical boreholes drilled in the floor of a Carboniferous Limestone quarry. Detailed knowledge of the rocks in the test area was obtained from core analysis, wireline logging and local area fracture mapping. Seismic cross‐hole surveys were performed using a sparker source with a dominant frequency of 2000 Hz and hydrophone receivers. The rocks had a compressional‐wave velocity anisotropy of 10%, which was attributed to the presence of predominantly horizontal, partially open fractures. Estimates of normal fracture compliance within a range from 2.5 × 10−13 m/Pa to 3.5 × 10−12 m/Pa were obtained from both the cross‐hole data and the sonic‐log data. This is an order of magnitude greater than values obtained from laboratory experiments which are reported elsewhere.
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Extraction of permeability from time‐lapse seismic data
Authors Colin MacBeth and Yahya Al‐MaskeriABSTRACTTwo formulae are developed for estimating horizontal permeability directly from maps of 4D seismic signatures. The choice of the formula used depends on whether the seismic is dominated by changes of pressure or saturation. However, pressure derived from time‐lapse seismic, or seismic amplitudes controlled predominantly by pressure are to be preferred for optimal ‘illumination’ of the reservoir. The permeability is predicted to be dependent on porosity but weighted by a 4D term related to the magnitude and spatial gradient of the 4D signature. Tests performed on model‐based synthetic seismic data affirm the validity and accuracy of this approach. Application to field data from the UK continental shelf reveals a large‐scale permeability variation similar to the existing simulation model, but with additional fine‐scale detail. The technique thus has the potential of providing extra information with which to update the simulation model. The resultant permeability estimates have been successfully ground‐truthed against the results of two well tests. As non‐repeatable noise in the time‐lapse seismic data diminishes with improved 4D‐related acquisition, it will become increasingly possible to make robust permeability estimates using this approach.
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Modelling the DC electrical response of fully and partially saturated Permo‐Triassic sandstone
Authors Steve Taylor and Ron BarkerABSTRACTResults from a laboratory investigation into the electrical properties of fully and partially saturated Wildmoor Triassic Sandstone have been modelled using the Archie, Waxman–Smits and Hanai–Bruggeman equations. The results demonstrate the limitation of using simple relationships to describe samples when the matrix resistivity ρr is not significantly greater than the saturating electrolyte resistivity ρw. In these situations Archie's parameters m and n are not accurately determined. Conversely, the more sophisticated Waxman–Smits and Hanai–Bruggeman models provide parameters that better describe the electrical properties of the rock and are able to identify heterogeneity between samples that would otherwise be missed. The ranges of values for matrix resistivity (49 < ρr < 161 Ωm) and cementation factor (1.6 < m < 2.1) obtained from the Hanai–Bruggeman model indicate significant variation between samples. Comparison of laboratory‐determined values for cation exchange capacity (0.06 < Qv < 0.51 meq/mL) and those obtained from the Waxman–Smits model (0.09 < Qv < 0.55 meq/mL) indicates a very strong correlation, suggesting this model is appropriate for describing the rock. There is good agreement between parameters modelled using fully and partially saturated versions of both the Hanai–Bruggeman and Waxman–Smits equations, indicating that the data are consistent with these models and that the assumptions made are appropriate.
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Sensitivity of time‐lapse seismic to reservoir stress path
More LessABSTRACTThe change in reservoir pore pressure due to the production of hydrocarbons leads to anisotropic changes in the stress field acting on the reservoir. Reservoir stress path is defined as the ratio of the change in effective horizontal stress to the change in effective vertical stress from the initial reservoir conditions, and strongly influences the depletion‐induced compaction behaviour of the reservoir. Seismic velocities in sandstones vary with stress due to the presence of stress‐sensitive regions within the rock, such as grain boundaries, microcracks, fractures, etc. Since the response of any microcracks and grain boundaries to a change in stress depends on their orientation relative to the principal stress axes, elastic‐wave velocities are sensitive to reservoir stress path. The vertical P‐ and S‐wave velocities, the small‐offset P‐ and SV‐wave normal‐moveout (NMO) velocities, and the P‐wave amplitude‐versus‐offset (AVO) are sensitive to different combinations of vertical and horizontal stress. The relationships between these quantities and the change in stress can be calibrated using a repeat seismic, sonic log, checkshot or vertical seismic profile (VSP) at the location of a well at which the change in reservoir pressure has been measured. Alternatively, the variation of velocity with azimuth and distance from the borehole, obtained by dipole radial profiling, can be used. Having calibrated these relationships, the theory allows the reservoir stress path to be monitored using time‐lapse seismic by combining changes in the vertical P‐wave impedance, changes in the P‐wave NMO and AVO behaviour, and changes in the S‐wave impedance.
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Volumes & issues
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Volume 72 (2023 - 2024)
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Volume 71 (2022 - 2023)
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Volume 70 (2021 - 2022)
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Volume 69 (2021)
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Volume 68 (2020)
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Volume 67 (2019)
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Volume 66 (2018)
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Volume 65 (2017)
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Volume 64 (2015 - 2016)
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Volume 63 (2015)
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Volume 62 (2014)
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Volume 61 (2013)
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Volume 60 (2012)
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Volume 59 (2011)
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Volume 58 (2010)
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Volume 57 (2009)
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Volume 56 (2008)
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Volume 55 (2007)
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Volume 54 (2006)
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Volume 53 (2005)
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Volume 52 (2004)
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Volume 51 (2003)
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Volume 50 (2002)
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Volume 49 (2001)
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Volume 48 (2000)
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Volume 47 (1999)
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Volume 46 (1998)
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Volume 45 (1997)
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Volume 44 (1996)
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Volume 43 (1995)
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Volume 42 (1994)
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Volume 41 (1993)
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Volume 40 (1992)
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Volume 39 (1991)
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Volume 38 (1990)
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Volume 37 (1989)
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Volume 36 (1988)
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Volume 35 (1987)
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Volume 33 (1985)
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Volume 32 (1984)
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Volume 31 (1983)
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Volume 30 (1982)
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Volume 29 (1981)
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Volume 28 (1980)
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Volume 27 (1979)
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Volume 26 (1978)
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Volume 25 (1977)
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Volume 24 (1976)
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Volume 23 (1975)
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Volume 22 (1974)
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Volume 21 (1973)
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Volume 20 (1972)
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Volume 19 (1971)
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Volume 18 (1970)
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Volume 17 (1969)
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Volume 16 (1968)
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Volume 15 (1967)
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Volume 14 (1966)
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Volume 13 (1965)
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Volume 12 (1964)
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Volume 11 (1963)
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Volume 10 (1962)
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Volume 9 (1961)
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Volume 8 (1960)
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Volume 7 (1959)
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Volume 6 (1958)
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Volume 5 (1957)
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Volume 4 (1956)
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Volume 3 (1955)
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Volume 2 (1954)
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Volume 1 (1953)