Joint inversion of seismic traveltime and frequency-domain airborne electromagnetic data for hydrocarbon exploration

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. U9-U22 ◽  
Author(s):  
Jide Nosakare Ogunbo ◽  
Guy Marquis ◽  
Jie Zhang ◽  
Weizhong Wang
Keyword(s):  
Frequency Domain ◽  
Joint Inversion ◽  
Sedimentary Environment ◽  
Computational Cost ◽  
Velocity Model ◽  
Two Dimensions ◽  
Hydrocarbon Exploration ◽  
Three Dimensions ◽  
Data Sets ◽  
The One

Geophysical joint inversion requires the setting of a few parameters for optimum performance of the process. However, there are yet no known detailed procedures for selecting the various parameters for performing the joint inversion. Previous works on the joint inversion of electromagnetic (EM) and seismic data have reported parameter applications for data sets acquired from the same dimensional geometry (either in two dimensions or three dimensions) and few on variant geometry. But none has discussed the parameter selections for the joint inversion of methods from variant geometry (for example, a 2D seismic travel and pseudo-2D frequency-domain EM data). With the advantage of affordable computational cost and the sufficient approximation of a 1D EM model in a horizontally layered sedimentary environment, we are able to set optimum joint inversion parameters to perform structurally constrained joint 2D seismic traveltime and pseudo-2D EM data for hydrocarbon exploration. From the synthetic experiments, even in the presence of noise, we are able to prescribe the rules for optimum parameter setting for the joint inversion, including the choice of initial model and the cross-gradient weighting. We apply these rules on field data to reconstruct a more reliable subsurface velocity model than the one obtained by the traveltime inversions alone. We expect that this approach will be useful for performing joint inversion of the seismic traveltime and frequency-domain EM data for the production of hydrocarbon.

Inversion of airborne geophysics over the DO-27/DO-18 kimberlites — Part 2: Electromagnetics

2017 ◽  
Vol 5 (3) ◽  
pp. T313-T325 ◽  
Author(s):  
Dominique Fournier ◽  
Seogi Kang ◽  
Michael S. McMillan ◽  
Douglas W. Oldenburg
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Three Dimensions ◽  
Data Sets ◽  
Conductivity Model ◽  
Time Domain Data ◽  
Conductivity Structure ◽  
Lake Bottom ◽  
Geologic Interpretation ◽  
Lateral Extent

We focus on the task of finding a 3D conductivity structure for the DO-18 and DO-27 kimberlites, historically known as the Tli Kwi Cho (TKC) kimberlite complex in the Northwest Territories, Canada. Two airborne electromagnetic (EM) surveys are analyzed: a frequency-domain DIGHEM and a time-domain VTEM survey. Airborne time-domain data at TKC are particularly challenging because of the negative values that exist even at the earliest time channels. Heretofore, such data have not been inverted in three dimensions. In our analysis, we start by inverting frequency-domain data and positive VTEM data with a laterally constrained 1D inversion. This is important for assessing the noise levels associated with the data and for estimating the general conductivity structure. The analysis is then extended to a 3D inversion with our most recent optimized and parallelized inversion codes. We first address the issue about whether the conductivity anomaly is due to a shallow flat-lying conductor (associated with the lake bottom) or a vertical conductive pipe; we conclude that it is the latter. Both data sets are then cooperatively inverted to obtain a consistent 3D conductivity model for TKC that can be used for geologic interpretation. The conductivity model is then jointly interpreted with the density and magnetic susceptibility models from a previous paper. The addition of conductivity enriches the interpretation made with the potential fields in characterizing several distinct petrophysical kimberlite units. The final conductivity model also helps better define the lateral extent and upper boundary of the kimberlite pipes. This conductivity model is a crucial component of the follow-up paper in which our colleagues invert the airborne EM data to recover the time-dependent chargeability that further advances our geologic interpretation.

Seismic waveform inversion in the frequency domain, Part 2: Fault delineation in sediments using crosshole data

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 902-914 ◽  
Author(s):  
R. Gerhard Pratt ◽  
Richard M. Shipp
Keyword(s):  
Frequency Domain ◽  
Field Data ◽  
Sedimentary Environment ◽  
Waveform Inversion ◽  
Normal Fault ◽  
Velocity Model ◽  
Viscous Effects ◽  
Seismic Waveform ◽  
Wavefield Inversion ◽  
High Degree

A crosshole experiment was carried out in a layered sedimentary environment in which a normal fault is known to cut through the section. Initial traveltime inversions produced stable but low‐resolution images from which the fault could be only vaguely inferred. To image the fault, wavefield inversion was used to produce a velocity model consistent with the detailed phase and amplitude of the data at a number of frequencies. Our wavefield inversion scheme uses a classical, descent‐type algorithm for decreasing the data misfit by iteratively computing the gradient of this misfit by repeated forward and backward propagations. Our propagator is a full‐wave equation, frequency‐domain, acoustic, finite‐difference method. The use of the frequency‐space domain yields computational advantages for multisource data and allows an easy incorporation of viscous effects. By running wavefield inversion on the field data, a quantitative velocity image was produced that yielded a significantly improved image of the fault (when compared with the original traveltime inversions). Because the original field data were noisy and contained a high degree of multiple scattering (from the layering of the sediments), the transmitted arrivals were selectively windowed to enhance the image. The sediments at the site were strongly attenuating; we therefore used a viscoacoustic model during the modeling and the inversion that correctly simulated the observed decrease in amplitude with increasing frequency and source‐receiver offset. Furthermore, since the traveltime inversion indicated a high degree of anisotropy at the site, a fixed, homogeneous level of anisotropy was used during the inversion. Tests at varying levels of anisotropy confirmed the improvement in image quality and in data fit when anisotropy was incorporated. The final image was verified by examining the distribution of the residuals in the frequency domain, by comparing time‐domain modeled wavefields with the observed data, and by direct comparison with borehole logs.

Organization of simple cell responses in the three-dimensional (3-D) frequency domain

1994 ◽  
Vol 11 (2) ◽  
pp. 295-306 ◽  
Author(s):  
J. McLean ◽  
L. A. Palmer
Keyword(s):  
Spatial Frequency ◽  
Frequency Domain ◽  
Spectral Response ◽  
Temporal Frequency ◽  
Three Dimensional ◽  
Direction Selectivity ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Simple Cells ◽  
Amplitude Spectra

AbstractThe amplitude spectra of simple cells in areas 17 and 18 were estimated in two and three dimensions (2–D and 3–D) using drifting sinusoidal gratings. In 2–D, responses were sampled with 16 x 16 resolution in spatial and temporal frequency at the optimal orientation. In 3–D, responses were sampled with 12 x 12 x 10 resolution in spatial frequency, orientation, and temporal frequency. For 45/50 cells studied, the spatial attributes of the receptive fields (RFs) were independent of temporal frequency except for a scale factor. The five exceptions to this general finding could be described as follows: For four area 17 cells, responses in the null direction increased with temporal frequency, reducing direction selectivity. For one area 18 cell, the optimal spatial frequency increased with temporal frequency and vice versa. The 2–D discrete Fourier transform was applied to all of the estimated amplitude spectra assuming zero spatial and temporal phase. These transforms were compared with the results of first-order reverse correlations as described in the previous paper (McLean et al., 1994). Direction selective cells exhibited excitatory subregions that were obliquely oriented in space-time in both the raw correlation data and inverse transforms of the spectral data. The slopes of the subregions found in these two measures were highly correlated. Direction indices obtained from space and frequency domain measures were comparable. We demonstrate that the spectral response profiles of most simple cells are aligned with the coordinate axes in frequency domain. That is, they may be considered one-quadrant separable, suggesting that these cells are not velocity tuned per se, but are tuned for spatiotemporal frequency. The spectral bandwidth establishes the range of velocities to which these cells will respond. These findings are consistent with the one-quadrant separability constraint of linear quadrature models. We conclude that most simple cells perform as roughly linear filters in two dimensions of space and time.

An implicit finite-difference operator for the Helmholtz equation

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. T97-T107 ◽  
Author(s):  
Chunlei Chu ◽  
Paul L. Stoffa
Keyword(s):  
Finite Difference ◽  
Helmholtz Equation ◽  
Frequency Domain ◽  
Difference Operator ◽  
Computational Cost ◽  
Finite Difference Discretization ◽  
Implicit Finite Difference ◽  
Explicit Finite Difference ◽  
The One ◽  
Difference Discretization

We have developed an implicit finite-difference operator for the Laplacian and applied it to solving the Helmholtz equation for computing the seismic responses in the frequency domain. This implicit operator can greatly improve the accuracy of the simulation results without adding significant extra computational cost, compared with the corresponding conventional explicit finite-difference scheme. We achieved this by taking advantage of the inherently implicit nature of the Helmholtz equation and merging together the two linear systems: one from the implicit finite-difference discretization of the Laplacian and the other from the discretization of the Helmholtz equation itself. The end result of this simple yet important merging manipulation is a single linear system, similar to the one resulting from the conventional explicit finite-difference discretizations, without involving any differentiation matrix inversions. We analyzed grid dispersions of the discrete Helmholtz equation to show the accuracy of this implicit finite-difference operator and used two numerical examples to demonstrate its efficiency. Our method can be extended to solve other frequency domain wave simulation problems straightforwardly.

scholarly journals Frequency-Domain Common Image Gathers for Quickly Checking the Accuracy of Migration Velocity

2021 ◽  
Vol 9 ◽  
Author(s):  
Haemin Kim ◽  
Yongchae Cho ◽  
Yunseok Choi ◽  
Seungwon Ko ◽  
Changsoo Shin
Keyword(s):  
Frequency Domain ◽  
Deviant Behavior ◽  
Computational Cost ◽  
Real Data ◽  
Velocity Model ◽  
Complex Velocity ◽  
Hybrid Domain ◽  
The Common ◽  
Low Computational Cost ◽  
Complex Velocity Model

The common image gather (CIG) method enables qualitative and quantitative evaluation of the velocity model through the image. The most common such methods are offset-domain common image gather (ODCIG) and angle-domain common image gather (ADCIG). The challenge is that it requires a great deal of additional computation besides migration. We, therefore, introduce a new CIG method that has low computational cost: frequency-domain common image gather (FDCIG). FDCIG simply rearranges data using a gradient (partial image) calculated in the process of obtaining a migration image to represent it in the frequency-depth domain. We apply the FDCIG method to the layered model to show how FDCIGs behave when the velocity model is inaccurate. We also introduced the 3-D SEG/EAGE salt model to show how to apply the FDCIG method in the hybrid domain. Last, we applied 2-D real data. These sample field data also indicate that even in a complex velocity model, deviant behavior by FDCIG appears intuitively if the background velocity is inaccurate.

THE BOSONIC SIGMA MODEL ON A COMPACT SURFACE

1990 ◽  
Vol 05 (25) ◽  
pp. 2031-2037 ◽  
Author(s):  
M. LEBLANC ◽  
P. MADSEN ◽  
R. B. MANN ◽  
D. G. C. McKEON
Keyword(s):  
Sigma Model ◽  
Stereographic Projection ◽  
Two Dimensions ◽  
Compact Surface ◽  
Three Dimensions ◽  
Dimensional Euclidean Space ◽  
Nonlinear Sigma Model ◽  
Β Function ◽  
The One ◽  
Infrared Divergences

A stereographic projection is used to map the bosonic nonlinear sigma model with torsion from two-dimensional Euclidean space onto a sphere-S2 embedded in three dimensions. The one-loop β-function of the torsionless σ-model is determined using operator regularization to handle ultraviolet divergences. Only by excluding the lowest eigenstate of the rotation operator on the sphere can the usual β-function be recovered; inclusion of this eigenstate leads to severe infrared divergences. Both the ultraviolet and infrared divergences can be regulated by working in n, rather than two, dimensions, in which case the contribution of the lowest mode cancels exactly against the contribution of all other modes, resulting in a vanishing β-function.

Kirchhoff migration using eikonal equation traveltimes

Geophysics ◽  
1994 ◽  
Vol 59 (5) ◽  
pp. 810-817 ◽  
Author(s):  
Samuel H. Gray ◽  
William P. May
Keyword(s):  
Ray Tracing ◽  
Data Storage ◽  
Eikonal Equation ◽  
Synthetic Data ◽  
Velocity Model ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Regular Grid ◽  
Data Set ◽  
Kirchhoff Migration

The use of ray shooting followed by interpolation of traveltimes onto a regular grid is a popular and robust method for computing diffraction curves for Kirchhoff migration. An alternative to this method is to compute the traveltimes by directly solving the eikonal equation on a regular grid, without computing raypaths. Solving the eikonal equation on such a grid simplifies the problem of interpolating times onto the migration grid, but this method is not well defined at points where two different branches of the traveltime field meet. Also, computational and data storage issues that are relatively unimportant for performance in two dimensions limit the applicability of both schemes in three dimensions. A new implementation of a gridded eikonal equation solver has been designed to address these problems. A 2-D version of this algorithm is tested by using it to generate traveltimes to migrate the Marmousi synthetic data set using the exact velocity model. The results are compared with three other images: an F-X migration (a standard for comparison), a Kirchhoff migration using ray tracing, and a Kirchhoff migration using traveltimes generated by a commonly used eikonal equation solver. The F-X‐migrated image shows the imaging objective more clearly than any of the Kirchhoff migrations, and we advance a heuristic reason to explain this fact. Of the Kirchhoff migrations, the one using ray tracing produces the best image, and the other two are of comparable quality.

Residual migration: Applications and limitations

Geophysics ◽  
1985 ◽  
Vol 50 (1) ◽  
pp. 110-126 ◽  
Author(s):  
Daniel H. Rothman ◽  
Stewart A. Levin ◽  
Fabio Rocca
Keyword(s):  
Seismic Data ◽  
Computational Cost ◽  
Velocity Model ◽  
Original Data ◽  
Migration Velocity ◽  
Data Sets ◽  
Dispersion Method ◽  
Effective Velocity ◽  
Low Dispersion ◽  
Residual Processing

The correct migration of seismic data depends on the accuracy of the chosen velocity model. Rocca and Salvador (1982) showed that small errors in the velocity model may be efficiently corrected by applying a residual migration to previously migrated data, rather than remigrating the original data with a corrected velocity field. The effective velocity used in this residual processing is usually small compared to the original migration velocity. This decreases computational cost relative to a full migration, and allows the initial migration to be done with a less accurate but faster algorithm than would otherwise be required. The possible advantages are many. The overall cost of migration may be reduced, a consideration especially important when migrating 3-D data sets. Migration quality may be improved, because the location of mispositioned reflectors can be corrected and because of the freedom to choose initial migration with a high dip, low dispersion method such as Stolt migration. Interactive residual sharpening of the migrated image also becomes feasible. We discuss the theoretical and practical limitations of residual migration and quantify the related reductions of effective dip, velocity, and frequency after initial migration. We determine how accurate the initial migration velocity must be to justify use of this approach and analyze aliasing and numerical artifacts. Field data examples using Kirchhoff summation and finite‐difference migration illustrate the features and drawbacks of the method.

Enhancement of diffractions in prestack domain by means of a finite-offset double-square-root traveltime

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. V81-V96 ◽  
Author(s):  
Tiago A. Coimbra ◽  
Jorge H. Faccipieri ◽  
João H. Speglich ◽  
Leiv-J. Gelius ◽  
Martin Tygel
Keyword(s):  
Extraction Process ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Data Sets ◽  
Square Root ◽  
Data Set ◽  
Main Challenge ◽  
Two Parameters ◽  
General Source

Exploration of redundancy contained in the seismic data set assures enhancement of images that are based on stacking results. This enhancement is the goal of developing multiparametric traveltime equations that are able to approximate reflection and diffraction events in general source-receiver configurations. The main challenge of using these equations is to estimate a large number of parameters in a computationally feasible, reliable, and fast way. To obtain a better fit for diffraction traveltime events than the ones in the literature, we have derived a finite-offset (FO) double-square-root (DSR) diffraction traveltime equation (which depends on 10 parameters in three dimensions and four parameters in two dimensions). Moreover, to reduce the number of parameters, we have developed another version called simplified FO-DSR diffraction traveltime equation (which depends on five parameters in three dimensions and two parameters in two dimensions), which delivers a similar performance. We have developed operators that make use of the simplified FO-DSR traveltime equation to construct the so-called diffraction-only data set volumes (or, more simply, D-volumes) assuring enhancement in the diffraction extraction process. The D-volume construction has two steps: first, a stacking procedure to separate the diffraction events from the input data set and second, a spreading procedure to enhance the quality of these diffractions. As proof of concept, our approach has been tested on 2D/3D synthetic and 2D field data sets with successful results.

scholarly journals Multidimensional research on university engagement using a mixed method approach

2021 ◽  
Vol 24 (2) ◽  
Author(s):  
Helena Benito Mundet ◽  
Esther Llop Escorihuela ◽  
Marta Verdaguer Planas ◽  
Joaquim Comas Matas ◽  
Ariadna Lleonart Sitjar ◽  
...  
Keyword(s):  
Two Dimensions ◽  
Point Of View ◽  
Three Dimensions ◽  
Theoretical Point ◽  
Social Commitment ◽  
Cognition And Emotion ◽  
Nominal Groups ◽  
Valid Instrument ◽  
The One ◽  
Definition Of

The commitment or academic implication (engagement) of universitystudents has become a fundamental element for their welfare and academicperformance and, furthermore, it is also related to their professional futureand social commitment. For this reason, the definition of the concept and theprovision of assessment strategies and tools are essential to know the learningexperiences that lead to enhancing the academic involvement of the students.To develop our research, we have used a mixed quantitative and qualitativemethodology: exploratory and confirmatory factor analysis on the one hand,and discussion groups using the nominal groups technique on the other hand.We have set three different objectives: first, to delve into the multidimensionalmodel of the construct; second, to validate a questionnaire that allows forevaluation of the students’ perception of the learning methodologies used inthe classroom; and third, to check the manageability of the nominal groupsas a qualitative method of analysis. The results demonstrate that our newproposal provides a statistically valid instrument aimed at determining theperceptions of own engagement and an effective, efficient and motivatingqualitative method for students. However, regarding the multidimensionalityof the construct, contrary to the more accepted theoretical point of view thatconsiders three dimensions of engagement (behaviour, cognition and emotion),our results only reveal two dimensions (cognitive-emotional and behavioural).In the discussion and comments section we give possible explanations for thiscontradiction.

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