A holistic approach to inversion of frequency-domain airborne EM data

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. G301-G312 ◽  
Author(s):  
Ross Brodie ◽  
Malcolm Sambridge
Keyword(s):  
Frequency Domain ◽  
Synthetic Data ◽  
Holistic Approach ◽  
Data Sets ◽  
Data Set ◽  
Zero Level ◽  
Airborne Electromagnetic ◽  
Available Information ◽  
Airborne Electromagnetic Data ◽  
Parameter Values

We have developed a holistic method for simultaneously calibrating, processing, and inverting frequency-domain airborne electromagnetic data. A spline-based, 3D, layered conductivity model covering the complete survey area was recovered through inversion of the entire raw airborne data set and available independent conductivity and interface-depth data. The holistic inversion formulation includes a mathematical model to account for systematic calibration errors such as incorrect gain and zero-level drift. By taking these elements into account in the inversion, the need to preprocess the airborne data prior to inversion is eliminated. Conventional processing schemes involve the sequential application of a number of calibration corrections, with data from each frequency treated separately. This is followed by inversion of each multifrequency sample in isolation from other samples.By simultaneously considering all of the available information in a holistic inversion, we are able to exploit interfrequency and spatial-coherency characteristics of the data. The formulation ensures that the conductivity and calibration models are optimal with respect to the airborne data and prior information. Introduction of interfrequency inconsistency and multistage error propagation stemming from the sequential nature of conventional processing schemes is also avoided. We confirm that accurate conductivity and calibration parameter values are recovered from holistic inversion of synthetic data sets. We demonstrate that the results from holistic inversion of raw survey data are superior to the output of conventional 1D inversion of final processed data. In addition to the technical benefits, we expect that holistic inversion will reduce costs by avoiding the expensive calibration-processing-recalibration paradigm. Furthermore, savings may also be made because specific high-altitude zero-level observations, needed for conventional processing, may not be required.

A Bayesian approach to modeling 2D gravity data using polygons

Geophysics ◽  
2017 ◽  
Vol 82 (1) ◽  
pp. G1-G21 ◽  
Author(s):  
William J. Titus ◽  
Sarah J. Titus ◽  
Joshua R. Davis
Keyword(s):  
Gravity Data ◽  
Synthetic Data ◽  
Gravity Inversion ◽  
Limiting Factor ◽  
Data Sets ◽  
Data Set ◽  
Local Optima ◽  
Occupancy Probability ◽  
Compute Model ◽  
Parameter Values

We apply a Bayesian Markov chain Monte Carlo formalism to the gravity inversion of a single localized 2D subsurface object. The object is modeled as a polygon described by five parameters: the number of vertices, a density contrast, a shape-limiting factor, and the width and depth of an encompassing container. We first constrain these parameters with an interactive forward model and explicit geologic information. Then, we generate an approximate probability distribution of polygons for a given set of parameter values. From these, we determine statistical distributions such as the variance between the observed and model fields, the area, the center of area, and the occupancy probability (the probability that a spatial point lies within the subsurface object). We introduce replica exchange to mitigate trapping in local optima and to compute model probabilities and their uncertainties. We apply our techniques to synthetic data sets and a natural data set collected across the Rio Grande Gorge Bridge in New Mexico. On the basis of our examples, we find that the occupancy probability is useful in visualizing the results, giving a “hazy” cross section of the object. We also find that the role of the container is important in making predictions about the subsurface object.

scholarly journals Methods for estimating uncertainty in factor analytic solutions

2014 ◽  
Vol 7 (3) ◽  
pp. 781-797 ◽  
Author(s):  
P. Paatero ◽  
S. Eberly ◽  
S. G. Brown ◽  
G. A. Norris
Keyword(s):  
Environmental Protection Agency ◽  
Synthetic Data ◽  
Analytic Solutions ◽  
Data Sets ◽  
Random Errors ◽  
Data Set ◽  
Factor Analytic ◽  
Uncertainty Estimates ◽  
Multilinear Engine ◽  
Analytic Models

Abstract. The EPA PMF (Environmental Protection Agency positive matrix factorization) version 5.0 and the underlying multilinear engine-executable ME-2 contain three methods for estimating uncertainty in factor analytic models: classical bootstrap (BS), displacement of factor elements (DISP), and bootstrap enhanced by displacement of factor elements (BS-DISP). The goal of these methods is to capture the uncertainty of PMF analyses due to random errors and rotational ambiguity. It is shown that the three methods complement each other: depending on characteristics of the data set, one method may provide better results than the other two. Results are presented using synthetic data sets, including interpretation of diagnostics, and recommendations are given for parameters to report when documenting uncertainty estimates from EPA PMF or ME-2 applications.

Bayesian Classifier for Sparsity-Promoting Feature Selection

2015 ◽  
Vol 29 (06) ◽  
pp. 1550022 ◽  
Author(s):  
Danlei Xu ◽  
Lan Du ◽  
Hongwei Liu ◽  
Penghui Wang
Keyword(s):  
Feature Selection ◽  
Synthetic Data ◽  
Original Data ◽  
Radar Data ◽  
Bayesian Classifier ◽  
Classification Model ◽  
Data Sets ◽  
Data Set ◽  
Classification Boundary ◽  
Nonlinear Mappings

A Bayesian classifier for sparsity-promoting feature selection is developed in this paper, where a set of nonlinear mappings for the original data is performed as a pre-processing step. The linear classification model with such mappings from the original input space to a nonlinear transformation space can not only construct the nonlinear classification boundary, but also realize the feature selection for the original data. A zero-mean Gaussian prior with Gamma precision and a finite approximation of Beta process prior are used to promote sparsity in the utilization of features and nonlinear mappings in our model, respectively. We derive the Variational Bayesian (VB) inference algorithm for the proposed linear classifier. Experimental results based on the synthetic data set, measured radar data set, high-dimensional gene expression data set, and several benchmark data sets demonstrate the aggressive and robust feature selection capability and comparable classification accuracy of our method comparing with some other existing classifiers.

Sparse reflectivity inversion for nonstationary seismic data with surface-related multiples: Numerical and field-data experiments

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. R199-R217 ◽  
Author(s):  
Xintao Chai ◽  
Shangxu Wang ◽  
Genyang Tang
Keyword(s):  
Seismic Data ◽  
Resolution Enhancement ◽  
Synthetic Data ◽  
Data Sets ◽  
Data Set ◽  
Anelastic Attenuation ◽  
Seismic Resolution ◽  
Text Filtering ◽  
The Stability ◽  
Reflectivity Inversion

Seismic data are nonstationary due to subsurface anelastic attenuation and dispersion effects. These effects, also referred to as the earth’s [Formula: see text]-filtering effects, can diminish seismic resolution. We previously developed a method of nonstationary sparse reflectivity inversion (NSRI) for resolution enhancement, which avoids the intrinsic instability associated with inverse [Formula: see text] filtering and generates superior [Formula: see text] compensation results. Applying NSRI to data sets that contain multiples (addressing surface-related multiples only) requires a demultiple preprocessing step because NSRI cannot distinguish primaries from multiples and will treat them as interference convolved with incorrect [Formula: see text] values. However, multiples contain information about subsurface properties. To use information carried by multiples, with the feedback model and NSRI theory, we adapt NSRI to the context of nonstationary seismic data with surface-related multiples. Consequently, not only are the benefits of NSRI (e.g., circumventing the intrinsic instability associated with inverse [Formula: see text] filtering) extended, but also multiples are considered. Our method is limited to be a 1D implementation. Theoretical and numerical analyses verify that given a wavelet, the input [Formula: see text] values primarily affect the inverted reflectivities and exert little effect on the estimated multiples; i.e., multiple estimation need not consider [Formula: see text] filtering effects explicitly. However, there are benefits for NSRI considering multiples. The periodicity and amplitude of the multiples imply the position of the reflectivities and amplitude of the wavelet. Multiples assist in overcoming scaling and shifting ambiguities of conventional problems in which multiples are not considered. Experiments using a 1D algorithm on a synthetic data set, the publicly available Pluto 1.5 data set, and a marine data set support the aforementioned findings and reveal the stability, capabilities, and limitations of the proposed method.

Marlim R3D: A realistic model for controlled-source electromagnetic simulations — Phase 2: The controlled-source electromagnetic data set

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. E293-E299
Author(s):  
Jorlivan L. Correa ◽  
Paulo T. L. Menezes
Keyword(s):  
A Priori ◽  
Synthetic Data ◽  
Realistic Model ◽  
Earth Model ◽  
Data Sets ◽  
Data Set ◽  
Geoelectric Model ◽  
Controlled Source ◽  
The North ◽  
Electromagnetic Simulations

Synthetic data provided by geoelectric earth models are a powerful tool to evaluate a priori a controlled-source electromagnetic (CSEM) workflow effectiveness. Marlim R3D (MR3D) is an open-source complex and realistic geoelectric model for CSEM simulations of the postsalt turbiditic reservoirs at the Brazilian offshore margin. We have developed a 3D CSEM finite-difference time-domain forward study to generate the full-azimuth CSEM data set for the MR3D earth model. To that end, we fabricated a full-azimuth survey with 45 towlines striking the north–south and east–west directions over a total of 500 receivers evenly spaced at 1 km intervals along the rugged seafloor of the MR3D model. To correctly represent the thin, disconnected, and complex geometries of the studied reservoirs, we have built a finely discretized mesh of [Formula: see text] cells leading to a large mesh with a total of approximately 90 million cells. We computed the six electromagnetic field components (Ex, Ey, Ez, Hx, Hy, and Hz) at six frequencies in the range of 0.125–1.25 Hz. In our efforts to mimic noise in real CSEM data, we summed to the data a multiplicative noise with a 1% standard deviation. Both CSEM data sets (noise free and noise added), with inline and broadside geometries, are distributed for research or commercial use, under the Creative Common License, at the Zenodo platform.

Detection of sharp lateral discontinuities through the analysis of surface-wave propagation

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. EN77-EN90 ◽  
Author(s):  
Paolo Bergamo ◽  
Laura Valentina Socco
Keyword(s):  
Surface Wave ◽  
Fault Location ◽  
Synthetic Data ◽  
Finite Element Method Simulation ◽  
Fault System ◽  
Energy Concentration ◽  
Data Sets ◽  
Data Set ◽  
Shallow Subsurface ◽  
Velocity Models

Surface-wave (SW) techniques are mainly used to retrieve 1D velocity models and are therefore characterized by a 1D approach, which might prove unsatisfactory when relevant 2D effects are present in the investigated subsurface. In the case of sharp and sudden lateral heterogeneities in the subsurface, a strategy to tackle this limitation is to estimate the location of the discontinuities and to separately process seismic traces belonging to quasi-1D subsurface portions. We have addressed our attention to methods aimed at locating discontinuities by identifying anomalies in SW propagation and attenuation. The considered methods are the autospectrum computation and the attenuation analysis of Rayleigh waves (AARW). These methods were developed for purposes and/or scales of analysis that are different from those of this work, which aims at detecting and characterizing sharp subvertical discontinuities in the shallow subsurface. We applied both methods to two data sets, synthetic data from a finite-element method simulation and a field data set acquired over a fault system, both presenting an abrupt lateral variation perpendicularly crossing the acquisition line. We also extended the AARW method to the detection of sharp discontinuities from large and multifold data sets and we tested these novel procedures on the field case. The two methods are proven to be effective for the detection of the discontinuity, by portraying propagation phenomena linked to the presence of the heterogeneity, such as the interference between incident and reflected wavetrains, and energy concentration as well as subsequent decay at the fault location. The procedures we developed for the processing of multifold seismic data set showed to be reliable tools in locating and characterizing subvertical sharp heterogeneities.

Inversion of ground constant offset loop-loop electromagnetic data for a large range of induction numbers

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. E11-E21 ◽  
Author(s):  
Julien Guillemoteau ◽  
Pascal Sailhac ◽  
Charles Boulanger ◽  
Jérémie Trules
Keyword(s):  
Synthetic Data ◽  
Test Site ◽  
Maxwell Theory ◽  
Data Set ◽  
Electromagnetic Data ◽  
Apparent Conductivity ◽  
Airborne Electromagnetic ◽  
Phase Data ◽  
Ground Conductivity ◽  
Good Agreement

Ground loop-loop electromagnetic surveys are often conducted to fulfill the low-induction-number condition. To image the distribution of electric conductivity inside the ground, it is then necessary to collect a multioffset data set. We considered that less time-consuming constant offset measurements can also reach this objective. This can be achieved by performing multifrequency soundings, which are commonly performed for the airborne electromagnetic method. Ground multifrequency soundings have to be interpreted carefully because they contain high-induction-number data. These data are interpreted in two steps. First, the in-phase and out-of-phase data are converted into robust apparent conductivities valid for all the induction numbers. Second, the apparent conductivity data are inverted in 1D and 2D to obtain the true distribution of the ground conductivity. For the inversion, we used a general half-space Jacobian for the apparent conductivity valid for all the induction numbers. This method was applied and validated on synthetic data computed with the full Maxwell theory. The method was then applied on field data acquired in the test site of Provins, in the Parisian basin, France. The result revealed good agreement with borehole and geologic information, demonstrating the applicability of our method.

A periodically varying code for improving deblending of simultaneous sources in marine acquisition

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. V213-V225 ◽  
Author(s):  
Shaohuan Zu ◽  
Hui Zhou ◽  
Yangkang Chen ◽  
Shan Qu ◽  
Xiaofeng Zou ◽  
...  
Keyword(s):  
Field Data ◽  
Synthetic Data ◽  
Data Sets ◽  
Ocean Bottom ◽  
Data Set ◽  
Acceptable Model ◽  
Model Subspace ◽  
New Form ◽  
Simultaneous Source ◽  
Practical Field

We have designed a periodically varying code that can avoid the problem of the local coherency and make the interference distribute uniformly in a given range; hence, it was better at suppressing incoherent interference (blending noise) and preserving coherent useful signals compared with a random dithering code. We have also devised a new form of the iterative method to remove interference generated from the simultaneous source acquisition. In each iteration, we have estimated the interference using the blending operator following the proposed formula and then subtracted the interference from the pseudodeblended data. To further eliminate the incoherent interference and constrain the inversion, the data were then transformed to an auxiliary sparse domain for applying a thresholding operator. During the iterations, the threshold was decreased from the largest value to zero following an exponential function. The exponentially decreasing threshold aimed to gradually pass the deblended data to a more acceptable model subspace. Two numerically blended synthetic data sets and one numerically blended practical field data set from an ocean bottom cable were used to demonstrate the usefulness of our proposed method and the better performance of the periodically varying code over the traditional random dithering code.

2.5‐D inversion of frequency‐domain electromagnetic data generated by a grounded‐wire source

Geophysics ◽  
2002 ◽  
Vol 67 (6) ◽  
pp. 1753-1768 ◽  
Author(s):  
Yuji Mitsuhata ◽  
Toshihiro Uchida ◽  
Hiroshi Amano
Keyword(s):  
Frequency Domain ◽  
Regularization Parameter ◽  
Synthetic Data ◽  
Magnetic Data ◽  
Statistical Criterion ◽  
Model Parameters ◽  
Inversion Algorithm ◽  
Gas Field ◽  
Data Set ◽  
Transient Electromagnetic

Interpretation of controlled‐source electromagnetic (CSEM) data is usually based on 1‐D inversions, whereas data of direct current (dc) resistivity and magnetotelluric (MT) measurements are commonly interpreted by 2‐D inversions. We have developed an algorithm to invert frequency‐Domain vertical magnetic data generated by a grounded‐wire source for a 2‐D model of the earth—a so‐called 2.5‐D inversion. To stabilize the inversion, we adopt a smoothness constraint for the model parameters and adjust the regularization parameter objectively using a statistical criterion. A test using synthetic data from a realistic model reveals the insufficiency of only one source to recover an acceptable result. In contrast, the joint use of data generated by a left‐side source and a right‐side source dramatically improves the inversion result. We applied our inversion algorithm to a field data set, which was transformed from long‐offset transient electromagnetic (LOTEM) data acquired in a Japanese oil and gas field. As demonstrated by the synthetic data set, the inversion of the joint data set automatically converged and provided a better resultant model than that of the data generated by each source. In addition, our 2.5‐D inversion accounted for the reversals in the LOTEM measurements, which is impossible using 1‐D inversions. The shallow parts (above about 1 km depth) of the final model obtained by our 2.5‐D inversion agree well with those of a 2‐D inversion of MT data.

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