An efficient data‐subspace inversion method for 2-D magnetotelluric data

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 791-803 ◽  
Author(s):  
Weerachai Siripunvaraporn ◽  
Gary Egbert
Keyword(s):  
Significant Loss ◽  
Inversion Method ◽  
Data Sets ◽  
Reduced Basis ◽  
Sensitivity Matrix ◽  
Approximate Methods ◽  
Magnetotelluric Data ◽  
Data Set ◽  
Data Space ◽  
Occam’S Inversion

There are currently three types of algorithms in use for regularized 2-D inversion of magnetotelluric (MT) data. All seek to minimize some functional which penalizes data misfit and model structure. With the most straight‐forward approach (exemplified by OCCAM), the minimization is accomplished using some variant on a linearized Gauss‐Newton approach. A second approach is to use a descent method [e.g., nonlinear conjugate gradients (NLCG)] to avoid the expense of constructing large matrices (e.g., the sensitivity matrix). Finally, approximate methods [e.g., rapid relaxation inversion (RRI)] have been developed which use cheaply computed approximations to the sensitivity matrix to search for a minimum of the penalty functional. Approximate approaches can be very fast, but in practice often fail to converge without significant expert user intervention. On the other hand, the more straightforward methods can be prohibitively expensive to use for even moderate‐size data sets. Here, we present a new and much more efficient variant on the OCCAM scheme. By expressing the solution as a linear combination of rows of the sensitivity matrix smoothed by the model covariance (the “representers”), we transform the linearized inverse problem from the M-dimensional model space to the N-dimensional data space. This method is referred to as DASOCC, the data space OCCAM’s inversion. Since generally N ≪ M, this transformation by itself can result in significant computational saving. More importantly the data space formulation suggests a simple approximate method for constructing the inverse solution. Since MT data are smooth and “redundant,” a subset of the representers is typically sufficient to form the model without significant loss of detail. Computations required for constructing sensitivities and the size of matrices to be inverted can be significantly reduced by this approximation. We refer to this inversion as REBOCC, the reduced basis OCCAM’s inversion. Numerical experiments on synthetic and real data sets with REBOCC, DASOCC, NLCG, RRI, and OCCAM show that REBOCC is faster than both DASOCC and NLCG, which are comparable in speed. All of these methods are significantly faster than OCCAM, but are not competitive with RRI. However, even with a simple synthetic data set, we could not always get RRI to converge to a reasonable solution. The basic idea behind REBOCC should be more broadly applicable, in particular to 3-D MT inversion.

scholarly journals A super-Earth and a mini-Neptune around Kepler-59

2019 ◽  
Vol 491 (4) ◽  
pp. 5238-5247 ◽  
Author(s):  
X Saad-Olivera ◽  
C F Martinez ◽  
A Costa de Souza ◽  
F Roig ◽  
D Nesvorný
Keyword(s):  
Stability Analysis ◽  
Bayesian Inference ◽  
Spectroscopic Analysis ◽  
The Other ◽  
Inversion Method ◽  
Outer Planet ◽  
Data Sets ◽  
Dynamical Study ◽  
Data Set ◽  
Orbital Parameters

ABSTRACT We characterize the radii and masses of the star and planets in the Kepler-59 system, as well as their orbital parameters. The star parameters are determined through a standard spectroscopic analysis, resulting in a mass of $1.359\pm 0.155\, \mathrm{M}_\odot$ and a radius of $1.367\pm 0.078\, \mathrm{R}_\odot$. The obtained planetary radii are $1.5\pm 0.1\, R_\oplus$ for the inner and $2.2\pm 0.1\, R_\oplus$ for the outer planet. The orbital parameters and the planetary masses are determined by the inversion of Transit Timing Variations (TTV) signals. We consider two different data sets: one provided by Holczer et al. (2016), with TTVs only for Kepler-59c, and the other provided by Rowe et al. (2015), with TTVs for both planets. The inversion method applies an algorithm of Bayesian inference (MultiNest) combined with an efficient N-body integrator (Swift). For each of the data set, we found two possible solutions, both having the same probability according to their corresponding Bayesian evidences. All four solutions appear to be indistinguishable within their 2-σ uncertainties. However, statistical analyses show that the solutions from Rowe et al. (2015) data set provide a better characterization. The first solution infers masses of $5.3_{-2.1}^{+4.0}~M_{\mathrm{\oplus }}$ and $4.6_{-2.0}^{+3.6}~M_{\mathrm{\oplus }}$ for the inner and outer planet, respectively, while the second solution gives masses of $3.0^{+0.8}_{-0.8}~M_{\mathrm{\oplus }}$ and $2.6^{+0.9}_{-0.8}~M_{\mathrm{\oplus }}$. These values point to a system with an inner super-Earth and an outer mini-Neptune. A dynamical study shows that the planets have almost co-planar orbits with small eccentricities (e < 0.1), close to the 3:2 mean motion resonance. A stability analysis indicates that this configuration is stable over million years of evolution.

scholarly journals Revising the retrieval technique of a long-term stratospheric HNO<sub>3</sub> data set: from a constrained matrix inversion to the optimal estimation algorithm

2011 ◽  
Vol 29 (7) ◽  
pp. 1317-1330 ◽  
Author(s):  
I. Fiorucci ◽  
G. Muscari ◽  
R. L. de Zafra
Keyword(s):  
Optimal Estimation ◽  
Matrix Inversion ◽  
The Arctic ◽  
Inversion Method ◽  
Data Sets ◽  
Vertical Profiles ◽  
Mixing Ratio ◽  
Data Set ◽  
The Antarctic

Abstract. The Ground-Based Millimeter-wave Spectrometer (GBMS) was designed and built at the State University of New York at Stony Brook in the early 1990s and since then has carried out many measurement campaigns of stratospheric O3, HNO3, CO and N2O at polar and mid-latitudes. Its HNO3 data set shed light on HNO3 annual cycles over the Antarctic continent and contributed to the validation of both generations of the satellite-based JPL Microwave Limb Sounder (MLS). Following the increasing need for long-term data sets of stratospheric constituents, we resolved to establish a long-term GMBS observation site at the Arctic station of Thule (76.5° N, 68.8° W), Greenland, beginning in January 2009, in order to track the long- and short-term interactions between the changing climate and the seasonal processes tied to the ozone depletion phenomenon. Furthermore, we updated the retrieval algorithm adapting the Optimal Estimation (OE) method to GBMS spectral data in order to conform to the standard of the Network for the Detection of Atmospheric Composition Change (NDACC) microwave group, and to provide our retrievals with a set of averaging kernels that allow more straightforward comparisons with other data sets. The new OE algorithm was applied to GBMS HNO3 data sets from 1993 South Pole observations to date, in order to produce HNO3 version 2 (v2) profiles. A sample of results obtained at Antarctic latitudes in fall and winter and at mid-latitudes is shown here. In most conditions, v2 inversions show a sensitivity (i.e., sum of column elements of the averaging kernel matrix) of 100 ± 20 % from 20 to 45 km altitude, with somewhat worse (better) sensitivity in the Antarctic winter lower (upper) stratosphere. The 1σ uncertainty on HNO3 v2 mixing ratio vertical profiles depends on altitude and is estimated at ~15 % or 0.3 ppbv, whichever is larger. Comparisons of v2 with former (v1) GBMS HNO3 vertical profiles, obtained employing the constrained matrix inversion method, show that v1 and v2 profiles are overall consistent. The main difference is at the HNO3 mixing ratio maximum in the 20–25 km altitude range, which is smaller in v2 than v1 profiles by up to 2 ppbv at mid-latitudes and during the Antarctic fall. This difference suggests a better agreement of GBMS HNO3 v2 profiles with both UARS/ and EOS Aura/MLS HNO3 data than previous v1 profiles.

Time-lapse acoustic impedance variations during CO2 injection in Weyburn oilfield, Canada

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. M1-M13 ◽  
Author(s):  
Yichuan Wang ◽  
Igor B. Morozov
Keyword(s):  
Oil Recovery ◽  
Seismic Data ◽  
Acoustic Impedance ◽  
Time Lapse ◽  
Time Shift ◽  
Co2 Injection ◽  
Inversion Method ◽  
Data Sets ◽  
Storage Site ◽  
Data Set

For seismic monitoring injected fluids during enhanced oil recovery or geologic [Formula: see text] sequestration, it is useful to measure time-lapse (TL) variations of acoustic impedance (AI). AI gives direct connections to the mechanical and fluid-related properties of the reservoir or [Formula: see text] storage site; however, evaluation of its subtle TL variations is complicated by the low-frequency and scaling uncertainties of this attribute. We have developed three enhancements of TL AI analysis to resolve these issues. First, following waveform calibration (cross-equalization) of the monitor seismic data sets to the baseline one, the reflectivity difference was evaluated from the attributes measured during the calibration. Second, a robust approach to AI inversion was applied to the baseline data set, based on calibration of the records by using the well-log data and spatially variant stacking and interval velocities derived during seismic data processing. This inversion method is straightforward and does not require subjective selections of parameterization and regularization schemes. Unlike joint or statistical inverse approaches, this method does not require prior models and produces accurate fitting of the observed reflectivity. Third, the TL AI difference is obtained directly from the baseline AI and reflectivity difference but without the uncertainty-prone subtraction of AI volumes from different seismic vintages. The above approaches are applied to TL data sets from the Weyburn [Formula: see text] sequestration project in southern Saskatchewan, Canada. High-quality baseline and TL AI-difference volumes are obtained. TL variations within the reservoir zone are observed in the calibration time-shift, reflectivity-difference, and AI-difference images, which are interpreted as being related to the [Formula: see text] injection.

SH-SH wave inversion for S-wave velocity and density

Geophysics ◽  
2022 ◽  
pp. 1-59
Author(s):  
Fucai Dai ◽  
Feng Zhang ◽  
Xiangyang Li
Keyword(s):  
Wave Velocity ◽  
Inversion Method ◽  
Data Sets ◽  
Sh Wave ◽  
S Wave ◽  
Data Set ◽  
Sh Waves ◽  
Model Parameter ◽  
Wave Inversion ◽  
Impedance Contrast

SS-waves (SV-SV waves and SH-SH waves) are capable of inverting S-wave velocity ( VS) and density ( ρ) because they are sensitive to both parameters. SH-SH waves can be separated from multicomponent data sets more effectively than the SV-SV wave because the former is decoupled from the PP-wave in isotropic media. In addition, the SH-SH wave can be better modeled than the SV-SV wave in the case of strong velocity/impedance contrast because the SV-SV wave has multicritical angles, some of which can be quite small when velocity/ impedance contrast is strong. We derived an approximate equation of the SH-SH wave reflection coefficient as a function of VS and ρ in natural logarithm variables. The approximation has high accuracy, and it enables the inversion of VS and ρ in a direct manner. Both coefficients corresponding to VS and ρ are “model-parameter independent” and thus there is no need for prior estimate of any model parameter in inversion. Then, we developed an SH-SH wave inversion method, and demonstrated it by using synthetic data sets and a real SH-SH wave prestack data set from the west of China. We found that VS and ρ can be reliably estimated from the SH-SH wave of small angles.

Geostatistical Joint Interpretation of Gravity and Magnetotelluric Data of the US Cordillera

2021 ◽  
Author(s):  
Mohammad Shehata ◽  
Hideki Mizunaga
Keyword(s):  
Gravity Data ◽  
Three Dimensional ◽  
Data Sets ◽  
Spatial Expansion ◽  
Magnetotelluric Data ◽  
Data Set ◽  
Entire Area ◽  
Mean Values ◽  
Local Means ◽  
The Us

&lt;p&gt;Long-period magnetotelluric and gravity data were acquired to investigate the US cordillera's crustal structure. The magnetotelluric data are being acquired across the continental USA on a quasi-regular grid of &amp;#8764;70 km spacing as an electromagnetic component of the National Science Foundation EarthScope/USArray Program. International Gravimetreique Bureau compiled gravity Data at high spatial resolution. Due to the difference in data coverage density, the geostatistical joint integration was utilized to map the subsurface structures with adequate resolution. First, a three-dimensional inversion of each data set was applied separately.&lt;/p&gt;&lt;p&gt;The inversion results of both data sets show a similarity of structure for data structuralizing. The individual result of both data sets is resampled at the same locations using the kriging method by considering each inversion model to estimate the coefficient. Then, the Layer Density Correction (LDC) process's enhanced density distribution was applied to MT data's spatial expansion process. Simple Kriging with varying Local Means (SKLM) was applied to the residual analysis and integration. For this purpose, the varying local means of the resistivity were estimated using the corrected gravity data by the Non-Linear Indicator Transform (NLIT), taking into account the spatial correlation. After that, the spatial expansion analysis of MT data obtained sparsely was attempted using the estimated local mean values and SKLM method at the sections where the MT survey was carried out and for the entire area where density distributions exist. This research presents the integration results and the stand-alone inversion results of three-dimensional gravity and magnetotelluric data.&lt;/p&gt;

Robust Well-Test Interpretation by Using Nonlinear Regression With Parameter and Data Transformations

SPE Journal ◽  
2011 ◽  
Vol 16 (03) ◽  
pp. 698-712 ◽  
Author(s):  
Aysegul Dastan ◽  
Roland N. Horne
Keyword(s):  
Parameter Space ◽  
Nonlinear Regression ◽  
Wavelet Transformation ◽  
Data Sets ◽  
Wavelet Basis ◽  
Test Interpretation ◽  
Well Test ◽  
Reduced Basis ◽  
Data Set ◽  
Improved Performance

Summary Nonlinear regression is a well-established technique in well-test interpretation. However, this widely used technique is vulnerable to issues commonly observed in real data sets—specifically, sensitivity to noise, parameter uncertainty, and dependence on starting guess. In this paper, we show significant improvements in nonlinear regression by using transformations on the parameter space and the data space. Our techniques improve the accuracy of parameter estimation substantially. The techniques also provide faster convergence, reduced sensitivity to starting guesses, automatic noise reduction, and data compression. In the first part of the paper, we show, for the first time, that Cartesian parameter transformations are necessary for correct statistical representation of physical systems (e.g., the reservoir). Using true Cartesian parameters enables nonlinear regression to search for the optimal solution homogeneously on the entire parameter space, which results in faster convergence and increases the probability of convergence for a random starting guess. Nonlinear regression using Cartesian parameters also reveals inherent ambiguities in a data set, which may be left concealed when using existing techniques, leading to incorrect conclusions. We proposed suitable Cartesian transform pairs for common reservoir parameters and used a Monte Carlo technique to verify that the transform pairs generate Cartesian parameters. The second part of the paper discusses nonlinear regression using the wavelet transformation of the data set. The wavelet transformation is a process that can compress and denoise data automatically. We showed that only a few wavelet coefficients are sufficient for an improved performance and direct control of nonlinear regression. By using regression on a reduced wavelet basis rather than the original pressure data points, we achieved improved performance in terms of likelihood of convergence and narrower confidence intervals. The wavelet components in the reduced basis isolate the key contributors to the response and, hence, use only the relevant elements in the pressure-transient signal. We investigated four different wavelet strategies, which differ in the method of choosing a reduced wavelet basis. Combinations of the techniques discussed in this paper were used to analyze 20 data sets to find the technique or combination of techniques that works best with a particular data set. Using the appropriate combination of our techniques provides very robust and novel interpretation techniques, which will allow for reliable estimation of reservoir parameters using nonlinear regression.

A rapid four-dimensional resistivity data inversion method using temporal segmentation

2020 ◽  
Vol 221 (1) ◽  
pp. 586-602 ◽  
Author(s):  
Bin Liu ◽  
Yonghao Pang ◽  
Deqiang Mao ◽  
Jing Wang ◽  
Zhengyu Liu ◽  
...  
Keyword(s):  
Current Data ◽  
Inversion Method ◽  
Data Sets ◽  
Temporal Segmentation ◽  
Data Set ◽  
Subsurface Structures ◽  
Data Inversion ◽  
Rapid Changes ◽  
High Level ◽  
Acquisition Cycle

SUMMARY 4-D electrical resistivity tomography (ERT), an important geophysical method, is widely used to observe dynamic processes within static subsurface structures. However, because data acquisition and inversion consume large amounts of time, rapid changes that occur in the medium during a single acquisition cycle are difficult to detect in a timely manner via 4-D inversion. To address this issue, a scheme is proposed in this paper for restructuring continuously measured data sets and performing GPU-parallelized inversion. In this scheme, multiple reference time points are selected in an acquisition cycle, which allows all of the acquired data to be sequentially utilized in a 4-D inversion. In addition, the response of the 4-D inversion to changes in the medium has been enhanced by increasing the weight of new data being added dynamically to the inversion process. To improve the reliability of the inversion, our scheme uses actively varied time-regularization coefficients, which are adjusted according to the range of the changes in model resistivity; this range is predicted by taking the ratio between the independent inversion of the current data set and historical 4-D inversion model. Numerical simulations and experiments show that this new 4-D inversion method is able to locate and depict rapid changes in medium resistivity with a high level of accuracy.

scholarly journals 3D induced-polarization data inversion for complex resistivity

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. F157-F171 ◽  
Author(s):  
Michael Commer ◽  
Gregory A. Newman ◽  
Kenneth H. Williams ◽  
Susan S. Hubbard
Keyword(s):  
Environmental Remediation ◽  
Large Scale ◽  
Forward Modeling ◽  
Induced Polarization ◽  
Inversion Method ◽  
Data Sets ◽  
Inversion Algorithm ◽  
Data Set ◽  
Complex Resistivity ◽  
Data Inversion

The conductive and capacitive material properties of the subsurface can be quantified through the frequency-dependent complex resistivity. However, the routine three-dimensional (3D) interpretation of voluminous induced polarization (IP) data sets still poses a challenge due to large computational demands and solution nonuniqueness. We have developed a flexible methodology for 3D (spectral) IP data inversion. Our inversion algorithm is adapted from a frequency-domain electromagnetic (EM) inversion method primarily developed for large-scale hydrocarbon and geothermal energy exploration purposes. The method has proven to be efficient by implementing the nonlinear conjugate gradient method with hierarchical parallelism and by using an optimal finite-difference forward modeling mesh design scheme. The method allows for a large range of survey scales, providing a tool for both exploration and environmental applications. We experimented with an image focusing technique to improve the poor depth resolution of surface data sets with small survey spreads. The algorithm’s underlying forward modeling operator properly accounts for EM coupling effects; thus, traditionally used EM coupling correction procedures are not needed. The methodology was applied to both synthetic and field data. We tested the benefit of directly inverting EM coupling contaminated data using a synthetic large-scale exploration data set. Afterward, we further tested the monitoring capability of our method by inverting time-lapse data from an environmental remediation experiment near Rifle, Colorado. Similar trends observed in both our solution and another 2D inversion were in accordance with previous findings about the IP effects due to subsurface microbial activity.

Occam’s inversion to generate smooth, two‐dimensional models from magnetotelluric data

Geophysics ◽  
1990 ◽  
Vol 55 (12) ◽  
pp. 1613-1624 ◽  
Author(s):  
C. deGroot‐Hedlin ◽  
S. Constable
Keyword(s):  
Joint Inversion ◽  
Synthetic Data ◽  
Real Data ◽  
Theoretical Models ◽  
Resolving Power ◽  
Magnetotelluric Data ◽  
Data Set ◽  
Occam’S Inversion ◽  
Non Gaussian ◽  
True Structure

Magnetotelluric (MT) data are inverted for smooth 2-D models using an extension of the existing 1-D algorithm, Occam’s inversion. Since an MT data set consists of a finite number of imprecise data, an infinity of solutions to the inverse problem exists. Fitting field or synthetic electromagnetic data as closely as possible results in theoretical models with a maximum amount of roughness, or structure. However, by relaxing the misfit criterion only a small amount, models which are maximally smooth may be generated. Smooth models are less likely to result in overinterpretation of the data and reflect the true resolving power of the MT method. The models are composed of a large number of rectangular prisms, each having a constant conductivity. [Formula: see text] information, in the form of boundary locations only or both boundary locations and conductivity, may be included, providing a powerful tool for improving the resolving power of the data. Joint inversion of TE and TM synthetic data generated from known models allows comparison of smooth models with the true structure. In most cases, smoothed versions of the true structure may be recovered in 12–16 iterations. However, resistive features with a size comparable to depth of burial are poorly resolved. Real MT data present problems of non‐Gaussian data errors, the breakdown of the two‐dimensionality assumption and the large number of data in broadband soundings; nevertheless, real data can be inverted using the algorithm.

Fast 2D inversion of large borehole EM induction data sets with an efficient Fréchet-derivative approximation

Geophysics ◽  
2009 ◽  
Vol 74 (1) ◽  
pp. E75-E91 ◽  
Author(s):  
Gong Li Wang ◽  
Carlos Torres-Verdín ◽  
Jesús M. Salazar ◽  
Benjamin Voss
Keyword(s):  
Electrical Resistivity ◽  
Synthetic Data ◽  
Large Data ◽  
Inversion Method ◽  
Central Component ◽  
Data Sets ◽  
Spatial Distributions ◽  
Desktop Computer ◽  
Data Set ◽  
Uncertainty Estimator

In addition to reliability and stability, the efficiency and expediency of inversion methods have long been a strong concern for their routine applications by well-log interpreters. We have developed and successfully validated a new inversion method to estimate 2D parametric spatial distributions of electrical resistivity from array-induction measurements acquired in a vertical well. The central component of the method is an efficient approximation to Fréchet derivatives where both the incident and adjoint fields are precomputed and kept unchanged during inversion. To further enhance the overall efficiency of the inversion, we combined the new approximation with both the improved numerical mode-matching method and domain decomposition. Examples of application with synthetic data sets show that the new methodis computer efficient and capable of retrieving original model re-sistivities even in the presence of noise, performing equally well in both high and low contrasts of formation resistivity. In thin resistive beds, the new inversion method estimates more accurate resistivities than standard commercial deconvolution software. We also considered examples of application with field data sets that confirm the new method can successfully process a large data set that includes 200 beds in approximately [Formula: see text] of CPU time on a desktop computer. In addition to 2D parametric spatial distributions of electrical resistivity, the new inversion method provides a qualitative indicator of the uncertainty of estimated parameters based on the estimator’s covariance matrix. The uncertainty estimator provides a qualitative measure of the nonuniqueness of estimated resistivity parameters when the data misfit lies within the measurement error (noise).

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