MATLAB code for data-driven initial model of 1D Schlumberger sounding curve

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. F21-F28 ◽  
Author(s):  
Jide Nosakare Ogunbo

A MATLAB code automatically performs partial curve matching of 1D apparent resistivity data recorded with the Schlumberger electrode array configuration. The two-layer master and auxiliary curves are used to systematically match through the branches of data extracting the corresponding model properties. Partial curve matching is a classical interpretation procedure of the sounding curve, which has been done manually. Results from the manual and automatic procedures are compared. The matched geoelectric models from the automatic process are retrieved more quickly, and these results are consistent because the process is digitalized and are not dependent on human numerical accuracy judgment. Magnitudes of random noise affect the final matched model parameters, yet these values are sufficient to be initial models for subsequent nonlinear inversion. It is hoped that for an inversion workflow, the code can be included to automatically find an initial resistivity model.

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. O1-O19 ◽  
Author(s):  
Mohammad S. Shahraeeni ◽  
Andrew Curtis ◽  
Gabriel Chao

A fast probabilistic inversion method for 3D petrophysical property prediction from inverted prestack seismic data has been developed and tested on a real data set. The inversion objective is to estimate the joint probability density function (PDF) of model vectors consisting of porosity, clay content, and water saturation components at each point in the reservoir, from data vectors with compressional- and shear-wave-impedance components that are obtained from the inversion of seismic data. The proposed inversion method is based on mixture density network (MDN), which is trained by a given set of training samples, and provides an estimate of the joint posterior PDF’s of the model parameters for any given data point. This method is much more time and memory efficient than conventional nonlinear inversion methods. The training data set is constructed using nonlinear petrophysical forward relations and includes different sources of uncertainty in the inverse problem such as variations in effective pressure, bulk modulus and density of hydrocarbon, and random noise in recorded data. Results showed that the standard deviations of all model parameters were reduced after inversion, which shows that the inversion process provides information about all parameters. The reduction of uncertainty in water saturation was smaller than that for porosity or clay content; nevertheless the maximum of the a posteriori (MAP) of model PDF clearly showed the boundary between brine saturated and oil saturated rocks at wellbores. The MAP estimates of different model parameters show the lateral and vertical continuity of these boundaries. Errors in the MAP estimate of different model parameters can be reduced using more accurate petrophysical forward relations. This fast, probabilistic, nonlinear inversion method can be applied to invert large seismic cubes for petrophysical parameters on a standard desktop computer.


2021 ◽  
Author(s):  
Sabyasachi Dash ◽  
◽  
Zoya Heidari ◽  

Conventional resistivity models often overestimate water saturation in organic-rich mudrocks and require extensive calibration efforts. Conventional resistivity-porosity-saturation models assume brine in the formation as the only conductive component contributing to resistivity measurements. Enhanced resistivity models for shaly-sand analysis include clay concentration and clay-bound water as contributors to electrical conductivity. These shaly-sand models, however, consider the existing clay in the rock as dispersed, laminated, or structural, which does not reliably describe the distribution of clay network in organic-rich mudrocks. They also do not incorporate other conductive minerals and organic matter, which can significantly impact the resistivity measurements and lead to uncertainty in water saturation assessment. We recently introduced a method that quantitatively assimilates the type and spatial distribution of all conductive components to improve reserves evaluation in organic-rich mudrocks using electrical resistivity measurements. This paper aims to verify the reliability of the introduced method for the assessment of water/hydrocarbon saturation in the Wolfcamp formation of the Permian Basin. Our recently introduced resistivity model uses pore combination modeling to incorporate conductive (clay, pyrite, kerogen, brine) and non-conductive (grains, hydrocarbon) components in estimating effective resistivity. The inputs to the model are volumetric concentrations of minerals, the conductivity of rock components, and porosity obtained from laboratory measurements or interpretation of well logs. Geometric model parameters are also critical inputs to the model. To simultaneously estimate the geometric model parameters and water saturation, we develop two inversion algorithms (a) to estimate the geometric model parameters as inputs to the new resistivity model and (b) to estimate the water saturation. Rock type, pore structure, and spatial distribution of rock components affect geometric model parameters. Therefore, dividing the formation into reliable petrophysical zones is an essential step in this method. The geometric model parameters are determined for each rock type by minimizing the difference between the measured resistivity and the resistivity, estimated from Pore Combination Modeling. We applied the new rock physics model to two wells drilled in the Permian Basin. The depth interval of interest was located in the Wolfcamp formation. The rock-class-based inversion showed variation in geometric model parameters, which improved the assessment of water saturation. Results demonstrated that the new method improved water saturation estimates by 32.1% and 36.2% compared to Waxman-Smits and Archie's models, respectively, in the Wolfcamp formation. The most considerable improvement was observed in the Middle and Lower Wolfcamp formation, where the average clay concentration was relatively higher than the other zones. Results demonstrated that the proposed method was shown to improve the estimates of hydrocarbon reserves in the Permian Basin by 33%. The hydrocarbon reserves were underestimated by an average of 70000 bbl/acre when water saturation was quantified using Archie's model in the Permian Basin. It should be highlighted that the new method did not require any calibration effort to obtain model parameters for estimating water saturation. This method minimizes the need for extensive calibration efforts for the assessment of hydrocarbon/water saturation in organic-rich mudrocks. By minimizing the need for extensive calibration work, we can reduce the number of core samples acquired. This is the unique contribution of this rock-physics-based workflow.


2015 ◽  
Vol 58 (5) ◽  
Author(s):  
Sankar N. Bhattacharya

<p>Sensitivity kernels or partial derivatives of phase velocity (<em>c</em>) and group velocity (<em>U</em>) with respect to medium parameters are useful to interpret a given set of observed surface wave velocity data. In addition to phase velocities, group velocities are also being observed to find the radial anisotropy of the crust and mantle. However, sensitivities of group velocity for a radially anisotropic Earth have rarely been studied. Here we show sensitivities of group velocity along with those of phase velocity to the medium parameters <em>V<sub>SV</sub>, V<sub>SH </sub>, V<sub>PV</sub>, V<sub>PH , </sub></em><em>h</em><em> </em>and density in a radially anisotropic spherical Earth. The peak sensitivities for <em>U</em> are generally twice of those for <em>c</em>; thus <em>U</em> is more efficient than <em>c</em> to explore anisotropic nature of the medium. Love waves mainly depends on <em>V<sub>SH</sub></em> while Rayleigh waves is nearly independent of <em>V<sub>SH</sub></em> . The sensitivities show that there are trade-offs among these parameters during inversion and there is a need to reduce the number of parameters to be evaluated independently. It is suggested to use a nonlinear inversion jointly for Rayleigh and Love waves; in such a nonlinear inversion best solutions are obtained among the model parameters within prescribed limits for each parameter. We first choose <em>V<sub>SH</sub></em>, <em>V<sub>SV </sub></em>and <em>V<sub>PH</sub></em> within their corresponding limits; <em>V<sub>PV</sub></em> and <em>h</em> can be evaluated from empirical relations among the parameters. The density has small effect on surface wave velocities and it can be considered from other studies or from empirical relation of density to average P-wave velocity.</p>


2021 ◽  
Author(s):  
Andrea Manzoni ◽  
Aronne Dell'Oca ◽  
Martina Siena ◽  
Alberto Guadagnini

&lt;p&gt;We consider transient three-dimensional (3D) two-phase (oil and water) flows, taking place at the core-scale. In this context, we aim at exploiting the full information content associated with available information of (i) the 3D distribution of oil saturation and (ii) the overall pressure difference across the rock sample, to estimate the set of model parameters. We consider a continuum-scale description of the system behavior upon relying on the widely employed Brooks-Corey model for the characterization of relative permeabilities and on the capillary pressure correlation introduced by Skjaeveland et al. (2000). To provide a transparent way of assessing the results of the inversion, we rely on a synthetic reference scenario. The latter is intended to mimic having at our disposal 3D and section-averaged distributions of (time-dependent) oil saturations of the kind that can be acquired during typical laboratory experiments. These are in turn corrupted by way of a random noise, to address the influence of experimental uncertainties. We focus on diverse scenarios encompassing imbibition and drainage conditions. We employ two population-based optimization algorithms, i.e., (i) the particle swarm optimization (PSO); and (ii) the differential evolution (DE), which enable one to effectively tackle the high-dimensionality parameters space (i.e., 12 dimensions in our setting) we consider. Model calibration results are of satisfactory quality for the majority of the tested scenarios, whereas the DE algorithm is associated with highest effectiveness.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;References&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;S.M. Skjaeveland; L.M. Siqveland; A. Kjosavik; W.L. Hammervold Thomas; G.A. Virnovsky (2000). Capillary Pressure Correlation for Mixed-Wet Reservoirs SPE Res Eval &amp; Eng 3 (01): 60&amp;#8211;67. https://doi.org/10.2118/60900-PA&lt;/p&gt;


Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. E277-E285 ◽  
Author(s):  
Jide Nosakare Ogunbo ◽  
Jie Zhang ◽  
Xiong Zhang

To image the resistivity distribution of the subsurface, transient electromagnetic (TEM) surveying has been established as an effective geophysical method. Conventionally, an inversion method is applied to resolve the model parameters from the available measurements. However, significant time and effort are involved in preparing and executing an inversion and this prohibits its use as a real-time decision-making tool to optimize surveying in the field. We have developed a search engine method to find approximate 1D resistivity model solutions for circular central-loop configuration TEM data in real time. The search engine method is a concept used for query searches from large databases on the Internet. By extension, approximate solutions to any input TEM data can be found rapidly by searching a preestablished database. This database includes a large number of forward simulation results that represent the possible model solutions. The database size is optimized by the survey depth of investigation and the sensitivity analysis of the model layers. The fast-search speed is achieved by using the multiple randomized [Formula: see text]-dimensional tree method. In addition to its high speed in finding solutions, the search engine method provides a solution space that quantifies the resolutions and uncertainties of the results. We apply the search engine method to find 1D model solutions at different data points and then interpolate them to a pseudo-2D resistivity model. We tested the method with synthetic and real data.


Geophysics ◽  
1973 ◽  
Vol 38 (6) ◽  
pp. 1109-1129 ◽  
Author(s):  
W. E. Glenn ◽  
Jisoo Ryu ◽  
S. H. Ward ◽  
W. J. Peeples ◽  
R. J. Phillips

It is demonstrated that the generalized linear inverse theory may be applied to vertical magnetic dipole sounding problems. An analysis of inversion of theoretical data for a two‐layer model illustrates the method and indicates certain features not inherent in the commonly practiced curve‐matching method of interpretation. In particular, the standard deviations of the layered model parameters may be estimated. Also the data may contain varying degrees of information about individual model parameters. Indeed, the information density matrix may be used to optimize the data information distribution by choosing only data that contributes information above some minimal level. The relative importance of the information distribution to the determination of individual model parameters may be assessed using both the structure of the information density matrix and the size of the estimated parameter standard deviations. Data may be removed until the estimated standard deviations of the parameters exceed some critical values. This process may be viewed as a method of experimental design such that information/cost ratios may be maximized. Also, if the economy of the interpretation is a serious consideration, then the same process could be used to eliminate those data that have minimal information and whose exclusion does not significantly effect the parameter resolution. This process would tend to maximize interpretation/cost ratios. Inversion analyses of four sets of data previously interpreted by the curve‐matching method illustrate the inherent features of the inverse method. Results of the inverse method of interpretation may be used to make a statistical evaluation of both the fit between observed and predicted data and the resolution of the model parameters.


Author(s):  
Nazmul Islam

This paper presents an analysis and experiment results that were conducted to assess the effect of combining an AC signal with a DC bias when generating the electric field on electrode arrays needed to impart electroosmosis within a microchannel. The analysis was done using COMSOL 3.5a in which currently available theoretical models for EO flows were embedded in the software and solved numerically. The simulation evaluate the effects of channel geometry, frequency of excitation, electrode array geometry, and AC signal with a DC bias on the flow imparted on an electrically conducting fluid. For the AC driven flow, the simulation results indicate the existence of an optimized frequency of excitation and an optimum geometry that lead to the maximum net forward flow of the pump. No relevant net flows were generated with the symmetric electrode arrays with a constant magnitude of AC voltage applied to both electrodes. However, superimposing a DC signal over the AC signal on the same symmetric electrode array lead to a noticeable net forward flow of 18.70 μL/min. On the other hand asymmetric electrode pattern can generate flow in both cases and can improve the microflow inside the micro-channel. Experimental flow measurements were performed on several electrode array configurations manufactured using typical MEMS fabrication techniques. The experimental results are in good agreement with the simulation data. They confirm that using an asymmetric electrode array excited by an AC signal with a DC bias leads to a significant improvement in flow rates in comparison to the flow rates obtained in an asymmetric electrode array configuration excited just with an AC signal.


Geophysics ◽  
1986 ◽  
Vol 51 (3) ◽  
pp. 788-799 ◽  
Author(s):  
Jorge O. Parra ◽  
Thomas E. Owen

A numerical procedure for predicting cavity signatures for a dipole‐dipole array configuration in hole‐to‐ hole resistivity measurements has been developed. This electrode geometry is implemented from the general solution for a point source of current near an air‐filled cylindrical cavity or an air‐filled cylinder surrounded by a concentric conductive or resistive halo region embedded in a homogeneous conducting host medium to simulate hole‐to‐hole resistivity measurements. Cavity signatures obtained for several vertical offset distances between the source and detector dipoles as well as multiply spaced dipole‐dipole responses suggest that a processing technique may be devised to identify directly the position of the cavity inhomogeneity with respect to the boreholes. The results also show that the presence of a concentric halo region more conductive than the host medium influences the overall signature by either reducing or enhancing the effect of the air‐filled cavity depending upon the halo size and conductivity contrast. In comparison, a halo region more resistive than the host medium always influences the composite signature by enhancing the effect of the air‐filled cavity.


Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 783-790 ◽  
Author(s):  
Shashi P. Sharma ◽  
Pertti Kaikkonen

A platelike conducting body in free space is used as a model to invert transient electromagnetic data using the very fast simulated annealing procedure as a global optimization tool. When the host rock conductivity is non‐zero, acceptable fits between the observed and computed responses are difficult to obtain. In general, the conducting body is assigned a lower conductance, larger dimensions (strike length and depth extent) and a smaller depth than the true values. We approximate the response of a conducting host to yield reliable estimates of model parameters as well as a good fit between the observed and computed responses. Our procedure is based on the assumption that the observed electromagnetic response is the sum of the response due to the conductive target and the response due to conducting surroundings (host and overburden). It is also assumed that the host response is laterally invariant, implying a layered earth and fixed source‐receiver geometry. The validity of the superposition assumption is tested against the full solution for a conductive plate in a finite conducting host. The efficacy of our approach is demonstrated using noise‐free and noisy synthetic data and two field examples measured in different geological conditions.


1994 ◽  
Vol 84 (6) ◽  
pp. 1971-1977 ◽  
Author(s):  
Eric Sandvol ◽  
Thomas Hearn

Abstract We have developed a bootstrap method to estimate errors associated with inverting SKS waveforms for shear-wave splitting parameters. Although presented for shear-wave splitting inversions, this method is suitable for any waveform inversion procedure. The bootstrap error estimation method consists of multiple inversions of simulated data that imitate the original data with differing noise sequences. The results of the bootstrap inversions are used to directly calculate variances and covariances for all model parameters. We employ a bootstrap error estimation technique to nonlinear inversion for shear-wave splitting parameters. Since seismic data have correlated errors, the bootstrap method was modified for stationary bandlimited time series. This modified bootstrap method was applied to shear-wave splitting measurements from over 60 pairs of horizontal seismograms. The method is stable under a large range of noise conditions. By using this bootstrap method, we can distinguish among data with no apparent splitting, data with splitting, and noisy data.


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