Frequency‐domain acoustic‐wave modeling and inversion of crosshole data: Part II—Inversion method, synthetic experiments and real‐data results

In full‐wave inversion of seismic data in complex media it is desirable to use finite differences or finite elements for the forward modeling, but such methods are still prohibitively expensive when implemented in 3-D. Full‐wave 2-D inversion schemes are of limited utility even in 2-D media because they do not model 3-D dynamics correctly. Many seismic experiments effectively assume that the geology varies in two dimensions only but generate 3-D (point source) wavefields; that is, they are “two‐and‐one‐half‐dimensional” (2.5-D), and this configuration can be exploited to model 3-D propagation efficiently in such media. We propose a frequency domain full‐wave inversion algorithm which uses a 2.5-D finite difference forward modeling method. The calculated seismogram can be compared directly with real data, which allows the inversion to be iterated. We use a descents‐related method to minimize a least‐squares measure of the wavefield mismatch at the receivers. The acute nonlinearity caused by phase‐wrapping, which corresponds to time‐domain cycle‐skipping, is avoided by the strategy of either starting the inversion using a low frequency component of the data or constructing a starting model using traveltime tomography. The inversion proceeds by stages at successively higher frequencies across the observed bandwidth. The frequency domain is particularly efficient for crosshole configurations and also allows easy incorporation of attenuation, via complex velocities, in both forward modeling and inversion. This also requires the introduction of complex source amplitudes into the inversion as additional unknowns. Synthetic studies show that the iterative scheme enables us to achieve the theoretical maximum resolution for the velocity reconstruction and that strongly attenuative zones can be recovered with reasonable accuracy. Preliminary results from the application of the method to a real data set are also encouraging.

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3D induced-polarization data inversion for complex resistivity

Geophysics ◽

10.1190/1.3560156 ◽

2011 ◽

Vol 76 (3) ◽

pp. F157-F171 ◽

Cited By ~ 32

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.

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Time-lapse tomographic inversion using a Gaussian parameterization of the velocity changes

Geophysics ◽

10.1190/1.3442573 ◽

2010 ◽

Vol 75 (4) ◽

pp. U29-U38 ◽

Cited By ~ 8

Author(s):

Andreas Kjelsrud Evensen ◽

Martin Landrø

Keyword(s):

Large Scale ◽

Weighted Least Squares ◽

Real Data ◽

Time Lapse ◽

Two Dimensions ◽

Inversion Method ◽

Data Set ◽

Tomographic Inversion ◽

Gaussian Functions ◽

Velocity Changes

Most seismic studies of changes in traveltimes are of a qualitative nature and a major challenge in four dimensions is to use the information contained in time shifts to quantify the nature of velocity changes in the subsurface layers. We propose a 4D tomographic inversion method that uses time shifts from prestack seismic data to estimate parameters describing the 2D velocity field after changes have occurred. Prestack data allow for the usage of many offsets, thus increasing the information input for the inversion. The velocity changes are parameterized by a chosen number of Gaussian functions in two dimensions and weighted least-squares inversion is used to estimate the parameters describing these functions. We have found that the parameters describing the position and shape of the Gaussian velocity anomalies can be estimated with this method for simple synthetic cases. For more complex cases with overlapping Gaussian functions, resolution of the parameters can be difficult and in these cases our recommendation is to find the best fit for a simple smooth anomaly to a more complex real world. The method is tested on a real data set from a [Formula: see text] injection project above the Sleipner field in the North Sea, where quantification of changes is important for monitoring purposes. We have found that the noise levels in prestack traveltime data are on the high side for large-scale analysis; however, we estimate reasonable [Formula: see text] layer thickness and velocity compared to previous work in a nearby area.

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2D modeling and inversion of gravity data using density contrast varying with depth and source–basement geometry described by the Fourier series

Geophysics ◽

10.1190/1.1635044 ◽

2003 ◽

Vol 68 (6) ◽

pp. 1909-1916 ◽

Cited By ~ 11

Author(s):

Juan García‐Abdeslem

Keyword(s):

Fourier Series ◽

Gravity Data ◽

Forward Modeling ◽

Density Contrast ◽

Nonlinear Inversion ◽

Bouguer Gravity ◽

Data Set ◽

Cubic Polynomial ◽

Broad Variety ◽

And Inversion

A method is developed for 2D forward modeling and nonlinear inversion of gravity data. The forward modeling calculates the gravity anomaly caused by a 2D source body with an assumed depth‐dependent density contrast given by a cubic polynomial. The source body is bounded at depth by a smooth, curvilinear surface given by the Fourier series, which represents the basement. The weighted and damped discrete nonlinear inverse method presented here can invert gravity data to infer the geometry of the source body. The use of the Fourier series to define the basement geometry allows the interpreter to reconstruct a broad variety of geometries for the geologic structures using a small number of free parameters. Both modeling and inversion methods are illustrated with examples using field gravity data across the San Jacinto graben in southern California and across the Sayula basin in Jalisco, Mexico. The inversion of the San Jacinto graben residual Bouguer gravity data yields results compatible with those from previous interpretations of the same data set, suggesting that this geologic structure accommodates about 2.5 km of sediments. The inversion of the residual Bouguer gravity data across the Sayula basin suggests a maximum of 1‐km‐thick sedimentary infill.

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Multidimensional scaling for the evaluation of a geostatistical seismic elastic inversion methodology

Geophysics ◽

10.1190/geo2013-0037.1 ◽

2014 ◽

Vol 79 (1) ◽

pp. M1-M10 ◽

Cited By ~ 22

Author(s):

Leonardo Azevedo ◽

Ruben Nunes ◽

Pedro Correia ◽

Amílcar Soares ◽

Luis Guerreiro ◽

...

Keyword(s):

Multidimensional Scaling ◽

Metric Space ◽

Synthetic Data ◽

Real Data ◽

Seismic Inversion ◽

Inversion Algorithm ◽

Data Set ◽

The Real ◽

Geostatistical Inversion ◽

Impedance Models

Due to the nature of seismic inversion problems, there are multiple possible solutions that can equally fit the observed seismic data while diverging from the real subsurface model. Consequently, it is important to assess how inverse-impedance models are converging toward the real subsurface model. For this purpose, we evaluated a new methodology to combine the multidimensional scaling (MDS) technique with an iterative geostatistical elastic seismic inversion algorithm. The geostatistical inversion algorithm inverted partial angle stacks directly for acoustic and elastic impedance (AI and EI) models. It was based on a genetic algorithm in which the model perturbation at each iteration was performed recurring to stochastic sequential simulation. To assess the reliability and convergence of the inverted models at each step, the simulated models can be projected in a metric space computed by MDS. This projection allowed distinguishing similar from variable models and assessing the convergence of inverted models toward the real impedance ones. The geostatistical inversion results of a synthetic data set, in which the real AI and EI models are known, were plotted in this metric space along with the known impedance models. We applied the same principle to a real data set using a cross-validation technique. These examples revealed that the MDS is a valuable tool to evaluate the convergence of the inverse methodology and the impedance model variability among each iteration of the inversion process. Particularly for the geostatistical inversion algorithm we evaluated, it retrieves reliable impedance models while still producing a set of simulated models with considerable variability.

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

Geophysics ◽

10.1190/1.1527076 ◽

2002 ◽

Vol 67 (6) ◽

pp. 1753-1768 ◽

Cited By ~ 37

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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Comparison of source-independent methods of elastic waveform inversion

Geophysics ◽

10.1190/1.2356256 ◽

2006 ◽

Vol 71 (6) ◽

pp. R91-R100 ◽

Cited By ~ 26

Author(s):

Kun Xu ◽

Stewart A. Greenhalgh ◽

MiaoYue Wang

Keyword(s):

Elastic Wave ◽

Frequency Domain ◽

Numerical Experiments ◽

Random Noise ◽

Waveform Inversion ◽

Seismic Inversion ◽

Inversion Method ◽

Practical Procedure ◽

Wave Inversion ◽

Full Waveform

In this paper, we investigate several source-independent methods of nonlinear full-waveform inversion of multicomponent elastic-wave data. This includes iterative estimation of source signature (IES), standard trace normalization (STN), and average trace normalization (ATN) inversion methods. All are based on the finite-element method in the frequency domain. One synthetic elastic crosshole model is used to compare the recovered images with all these methods as well as the known source signature (KSS) inversion method. The numerical experiments show that the IES method is superior to both STN and ATN methods in two-component, elastic-wave inversion in the frequency domain when the source signature is unknown. The STN and ATN methods have limitations associated with near-zero amplitudes (or polarity reversals) in traces from one of the components, which destroy the energy balance in the normalized traces and cause a loss of frequency information. But the ATN method is somewhat superior to the STN method in suppressing random noise and improving stability, as the developed formulas and the numerical experiments show. We suggest the IES method as a practical procedure for multicomponent seismic inversion.

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Fast 2-D ray+Born migration/inversion in complex media

Geophysics ◽

10.1190/1.1444513 ◽

1999 ◽

Vol 64 (1) ◽

pp. 162-181 ◽

Cited By ~ 82

Author(s):

Philippe Thierry ◽

Stéphane Operto ◽

Gilles Lambaré

Keyword(s):

Numerical Approximation ◽

Reference Model ◽

Real Data ◽

Model Parameters ◽

Complex Media ◽

Inversion Algorithm ◽

Numerical Approximations ◽

Data Set ◽

Cpu Time ◽

Computational Evaluation

In this paper, we evaluate the capacity of a fast 2-D ray+Born migration/inversion algorithm to recover the true amplitude of the model parameters in 2-D complex media. The method is based on a quasi‐Newtonian linearized inversion of the scattered wavefield. Asymptotic Green’s functions are computed in a smooth reference model with a dynamic ray tracing based on the wavefront construction method. The model is described by velocity perturbations associated with diffractor points. Both the first traveltime and the strongest arrivals can be inverted. The algorithm is implemented with several numerical approximations such as interpolations and aperture limitation around common midpoints to speed the algorithm. Both theoritical and numerical aspects of the algorithm are assessed with three synthetic and real data examples including the 2-D Marmousi example. Comparison between logs extracted from the exact Marmousi perturbation model and the computed images shows that the amplitude of the velocity perturbations are recovered accurately in the regions of the model where the ray field is single valued. In the presence of caustics, neither the first traveltime nor the most energetic arrival inversion allow for a full recovery of the amplitudes although the latter improves the results. We conclude that all the arrivals associated with multipathing through transmission caustics must be taken into account if the true amplitude of the perturbations is to be found. Only 22 minutes of CPU time is required to migrate the full 2-D Marmousi data set on a Sun SPARC 20 workstation. The amplitude loss induced by the numerical approximations on the first traveltime and the most energetic migrated images are evaluated quantitatively and do not exceed 8% of the energy of the image computed without numerical approximation. Computational evaluation shows that extension to a 3-D ray+Born migration/inversion algorithm is realistic.

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Determination of relative angles and anisotropic resistivity using multicomponent induction logging data

Geophysics ◽

10.1190/1.1778233 ◽

2004 ◽

Vol 69 (4) ◽

pp. 898-908 ◽

Cited By ~ 13

Author(s):

Zhiyi Zhang ◽

Liming Yu ◽

Berthold Kriegshäuser ◽

Lev Tabarovsky

Keyword(s):

Sensitivity Analysis ◽

Azimuth Angle ◽

Inversion Method ◽

Inversion Algorithm ◽

Data Set ◽

Simultaneous Inversion ◽

Induction Logging ◽

Em Induction ◽

Whole Space ◽

Dip Angle

We have developed a new algorithm that retrieves information about relative dip angle, relative azimuth angle, vertical resistivity, and horizontal resistivity from multicomponent EM induction logging data. To investigate how relative dip and azimuth angles affect multicomponent induction logging data, we performed a sensitivity analysis using an anisotropic whole space model. Based upon the sensitivity analysis, we designed a two‐step procedure to recover relative dip, relative azimuth, horizontal resistivity, and vertical resistivity. In the first step, the observed data are transformed into a new data set independent of the azimuth angle; a simultaneous inversion method recovers relative dip angle, vertical resistivity, and horizontal resistivity. In the second step, a 1D line search is performed to decide relative azimuth angle. Synthetic and field data tests indicate that the new inversion algorithm can extract information about relative dip and azimuth angles as well as the anisotropic resistivity structure from multicomponent induction loggingdata.

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Sensitivity Analysis of FWI Applied to OVSP Synthetic Data for Fault Detection and Characterization in Crystalline Rocks

Geosciences ◽

10.3390/geosciences11110442 ◽

2021 ◽

Vol 11 (11) ◽

pp. 442

Author(s):

Yassine Abdelfettah ◽

Christophe Barnes

Keyword(s):

Fault Detection ◽

Reference Model ◽

Synthetic Data ◽

Inversion Method ◽

Physical Parameters ◽

Wave Inversion ◽

Full Wave ◽

Imaging Results ◽

Antenna Length ◽

Sensitivity Studies

We have performed several sensitivity studies to assess the ability of the Full Wave Inversion method to detect, delineate and characterize faults in a crystalline geothermal reservoir from OVSP data. The distant goal is to apply the method to the Soultz-sous-Forêts site (France). Our approach consists of performing synthetic Full Wave 2D Inversion experiments using offset vertical seismic and comparing the estimated fields provided by the inversion, i.e., the estimated underground images, to the initial reference model including the fault target. We first tuned the inversion algorithmic parameters in order to adapt the FWI software, originally dedicated to a sedimentary context, to a crystalline context. In a second step, we studied the sensitivity of the FWI fault imaging results as a function of the acquisition geometry parameters, namely, the number of shots, the intershot distance, the maximum offset and also the antenna length and well deviation. From this study, we suggest rules to design the acquisition geometry in order to improve the fault detection, delineation and characterization. In a third step, we studied the sensitivity of the FWI fault imaging results as a function of the fault or the fault zone characteristics, namely, the fault dip, thickness and the contrast of physical parameters between the fault materials and the surrounding fresh rocks. We have shown that a fault with high dip, between 60 and 90° as thin as 10 m (i.e. lower than a tenth of the seismic wavelength of 120 m for Vp and 70 m for Vs) can be imaged by FWI, even in the presence of additive gaussian noise. In summary, for a crystalline geological context, and dealing with acceptable S/N ratio data, the FWI show a high potential for accurately detecting, delineating and characterizing the fault zones.

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Effects of full transmitting-current waveforms on transient electromagnetics: Insights from modeling the Albany graphite deposit

Geophysics ◽

10.1190/geo2018-0573.1 ◽

2019 ◽

Vol 84 (4) ◽

pp. E255-E268 ◽

Cited By ~ 4

Author(s):

Sihong Zeng ◽

Xiangyun Hu ◽

Jianhui Li ◽

Colin G. Farquharson ◽

Peter C. Wood ◽

...

Keyword(s):

Real Data ◽

Forward Modeling ◽

Northern Ontario ◽

Data Set ◽

Rock Types ◽

Full Waveform ◽

Transient Electromagnetic ◽

Steady Stage ◽

Geologic Model ◽

Off Time

In transient electromagnetic (TEM) methods, the full transmitting-current waveform, not just the abrupt turn-off, can have effects on the measured responses. A 3D finite-element time-domain forward-modeling solver was used to investigate these effects. This was motivated by an attempt to match, via forward-modeling, real data from the Albany graphite deposit in northern Ontario, Canada. Initial modeling results for homogeneous half-spaces illustrate the effects that a full waveform can have on TEM responses, especially the durations of the steady stage and turn-off time. For the Albany data set, a geophysical conductivity model was developed from a geologic model that itself had been constructed predominantly from drillhole information. The conductivities of the various geologic units in the model were first estimated based on typical conductivity values for the respective rock types, then adjusted to fit the measured TEM data as closely as possible. We found that the TEM responses differed significantly from the pure step-off response and that incorporating the effects of the full waveform (particularly the linear ramp turn-off) greatly improved the match between observed and computed responses, especially for the early measurement times. In addition, this Albany example illustrates the presence of sign changes in TEM data caused primarily by localized conductivity targets.

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