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(searched for: doi:10.3997/1365-2397.26.1118.27952)
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Published: 1 May 2014
Journal: Geophysics
Abstract:
Offshore seismic and electromagnetic (EM) imaging for hydrocarbons can require up to tens of millions of parameters to describe the 3D distribution of complex seabed geology and relevant geophysical attributes. The imaging and data volumes for such problems are enormous. Descent-based methods are the only viable imaging approach, where it is often challenging to manage the convergence of stand-alone seismic and EM inversion experiments. When a joint seismic-EM inversion is implemented, convergence problems with descent-based methods are further aggravated. Moreover, resolution mismatches between seismic and EM pose another challenge for joint inversion. To overcome these problems, we evaluated a coupled seismic-EM inversion workflow and applied it to a set of full-wave-seismic, magnetotelluric (MT) and controlled-source electromagnetic (CSEM) data for subsalt imaging. In our workflow, we address disparate resolution properties between seismic and EM data by implementing the seismic inversion in the Laplace domain, where the wave equation is transformed into a diffusion equation. The resolution of seismic data thus becomes comparable to that of EM data. To mitigate the convergence problems, the full joint seismic-EM inverse problem is split into manageable components: separate seismic and EM inversions and an intermediate step that enforces structural coupling through a cross-gradient-only inversion and resistivity-velocity crossplots. In this workflow, stand-alone seismic and MT inversion are performed first. The cross-gradient-only inversion and the crossplots are used to precondition the resistivity and velocity models for subsequent stand-alone inversions. By repeating the sequence of the stand-alone seismic, MT, and cross-gradient-only inversions along with the crossplots, we introduce the seismic structural information into the resistivity model, and vice versa, significantly improving the salt geometry in both resistivity and velocity images. We conclude that the improved salt geometry can then be used to precondition a starting model for CSEM inversions, yielding significant improvement in the resistivity images of hydrocarbon reservoirs adjacent to the salt.
, Michael Commer, Gregory A. Newman
Geophysical Journal International, Volume 193, pp 1460-1473; https://doi.org/10.1093/gji/ggt071

Abstract:
We formulate a 3-D finite-element frequency-domain (FEFD) solution for electromagnetic (EM) diffusion and present efficient solution strategies. A system of FEFD equations is pre-conditioned by incomplete LU (ILU) and subsequently solved by the quasi-minimal residual (QMR) method. A rule of thumb for choosing an effective drop tolerance of ILU is proposed. When multiple sources are simulated in a given model, ILU is computed only once and is reused as a pre-conditioner for multiple QMR computations with different source vectors. Resulting solution vectors are also bootstrapped to reduce the number of QMR iterations required for the convergence. We demonstrate that when conductivity structures of an earth model and source frequencies are updated/perturbed, ILU that is computed from the previous model is still an effective and useful pre-conditioner for new forward modelling problems. Using the reusability of ILU, we also propose a new efficient way to overcome the slow convergence rate of the iterative FEFD solution in the static limit. We show that the reuse of ILU and solution bootstrapping serve as effective strategies for improving the computational efficiency of the iterative FEFD solution. Finally, we apply the proposed efficient solution strategies to marine EM survey scenarios in complex offshore models and further demonstrate their effectiveness.
Evan Schankee Um, Michael Commer, Gregory A. Newman
Published: 1 March 2012
Journal: Geophysics
Abstract:
We have investigated numerical characteristics of iterative solutions to the acoustic wave equation in the Laplace-Fourier (LF) domain. We transformed the time-domain acoustic wave equation into the LF domain; the transformed equation was discretized with finite differences and was solved with iterative methods. Finite-difference modeling experiments demonstrate that iterative methods require an infinitesimal stopping tolerance to accurately compute the pressure field especially at long offsets. To understand the requirement for such infinitesimal tolerance values, we analyzed the evolution of intermediate solution vectors, residual vectors, and search direction vectors during the iteration. The analysis showed that the requirement arises from the fact that in the solution space, the amplitude of the pressure field varies more than sixty orders of magnitude on the common log scale. Accordingly, we propose a rule of thumb for choosing a proper stopping tolerance value. We also examined numerical dispersion errors in terms of the grid sampling resolutions per skin depth and wavelength. We found that despite the similarity of the form of the acoustic wave and electromagnetic diffusion equations, the former is different from the latter due to the fact that in the LF domain, the skin depth of the acoustic wave equation is decoupled from its wavelength. This aspect requires that in the LF domain, its grid size be determined by considering the minimum grid sampling resolutions based not only the wavelength but also the skin depth.
Michael Commer, Gregory A. Newman, , Susan S. Hubbard
Published: 1 May 2011
Journal: Geophysics
Geophysics, Volume 76; https://doi.org/10.1190/1.3560156

Abstract:
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.
Michael Commer, Gregory A. Newman, , Susan S. Hubbard
Published: 1 January 2010
Abstract:
The spectral induced polarization (SIP) response of rocks and soils is a complex function of biological, chemical, and mineral subsurface processes. Its measured geophysical attribute, the complex resistivity (CR), represents a macroscopic parameter to relate SIP data to structural, mineral and hydraulic information of porous media and fluids contained therein. The complexity of subsurface CR distributions necessitates accounting for the three‐ dimensionality of the Earth and the development of adequate data interpretation algorithms (cf. Oldenburg and Li, 1994; Weller et al., 2000; Yang et al., 2000). In this work we describe the development and testing of a three‐ dimensional SIP inversion algorithm for CR based on the non‐linear conjugate gradient method and finite‐difference (FD) forward modeling. A hierarchical parallel architecture of the algorithm and an optimal FD mesh design allow for an economic use of today's parallel computing capabilities to process large field data sets. Two different types of forward modeling operators provide a tradeoff between computational speed and maximal SIP data simulation accuracy, the latter achieved by properly accounting for electromagnetic coupling effects. We demonstrate the benefits of directly inverting data containing EM coupling effects on synthetic data that represent a mineral exploration survey.
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