Computation of Cole‐Cole parameters from IP data

Geophysics ◽  
1997 ◽  
Vol 62 (2) ◽  
pp. 436-448 ◽  
Author(s):  
Yuval ◽  
Douglas W. Oldenburg
Keyword(s):  
Simulated Annealing ◽  
Time Domain ◽  
Field Data ◽  
Decay Curve ◽  
Inversion Algorithm ◽  
Data Set ◽  
The Earth ◽  
Very Fast Simulated Annealing ◽  
Structure Formula ◽  
Decay Parameters

We develop a process to estimate Cole‐Cole parameters from time‐domain induced polarization (IP) surveys carried out over a nonuniform earth. The recovery of parameters takes the following steps. We first divide the earth into rectangular cells and assume that the Cole‐Cole decay parameters [Formula: see text] and c constant in each cell. Apparent chargeability data measured at times [Formula: see text] after the cessation of the input current are inverted using a 2-D inversion algorithm to recover the intrinsic chargeability structure [Formula: see text] for k = 1, L, where L is the number of time channels measured. When carrying out this inversion, it is necessary to introduce a normalization criterion so that the inversion outputs from the different time channels can be meshingfully combined. The L chargeability structures provide L estimates of the chargeability decay curve for each cell. The desired intrinsic Cole‐Cole parameters are recovered from these decay curves using a very fast simulated annealing (VFSA) algorithm. Application of the process in all cells provides interpretation maps of [Formula: see text], τ(x,z), and c(x, z). Our analysis is demonstrated on a synthetic example and is implemented on a field data set. The application of the process to field data yields reasonable results.

scholarly journals Normalized nonzero-lag crosscorrelation elastic full-waveform inversion

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. R1-R10 ◽  
Author(s):  
Zhendong Zhang ◽  
Tariq Alkhalifah ◽  
Zedong Wu ◽  
Yike Liu ◽  
Bin He ◽  
...  
Keyword(s):  
Field Data ◽  
Extreme Values ◽  
Time Lag ◽  
Waveform Inversion ◽  
Optimal Time ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Velocity Models ◽  
Full Waveform ◽  
The Earth

Full-waveform inversion (FWI) is an attractive technique due to its ability to build high-resolution velocity models. Conventional amplitude-matching FWI approaches remain challenging because the simplified computational physics used does not fully represent all wave phenomena in the earth. Because the earth is attenuating, a sample-by-sample fitting of the amplitude may not be feasible in practice. We have developed a normalized nonzero-lag crosscorrelataion-based elastic FWI algorithm to maximize the similarity of the calculated and observed data. We use the first-order elastic-wave equation to simulate the propagation of seismic waves in the earth. Our proposed objective function emphasizes the matching of the phases of the events in the calculated and observed data, and thus, it is more immune to inaccuracies in the initial model and the difference between the true and modeled physics. The normalization term can compensate the energy loss in the far offsets because of geometric spreading and avoid a bias in estimation toward extreme values in the observed data. We develop a polynomial-type weighting function and evaluate an approach to determine the optimal time lag. We use a synthetic elastic Marmousi model and the BigSky field data set to verify the effectiveness of the proposed method. To suppress the short-wavelength artifacts in the estimated S-wave velocity and noise in the field data, we apply a Laplacian regularization and a total variation constraint on the synthetic and field data examples, respectively.

Structurally constrained impedance inversion

2016 ◽  
Vol 4 (4) ◽  
pp. T577-T589 ◽  
Author(s):  
Haitham Hamid ◽  
Adam Pidlisecky
Keyword(s):  
Objective Function ◽  
Seismic Data ◽  
Field Data ◽  
A Priori ◽  
Structural Constraints ◽  
Inversion Algorithm ◽  
Data Set ◽  
Impedance Inversion ◽  
Single Trace ◽  
Complex Geology

In complex geology, the presence of highly dipping structures can complicate impedance inversion. We have developed a structurally constrained inversion in which a computationally well-behaved objective function is minimized subject to structural constraints. This approach allows the objective function to incorporate structural orientation in the form of dips into our inversion algorithm. Our method involves a multitrace impedance inversion and a rotation of an orthogonal system of derivative operators. Local dips used to constrain the derivative operators were estimated from migrated seismic data. In addition to imposing structural constraints on the inversion model, this algorithm allows for the inclusion of a priori knowledge from boreholes. We investigated this algorithm on a complex synthetic 2D model as well as a seismic field data set. We compared the result obtained with this approach with the results from single trace-based inversion and laterally constrained inversion. The inversion carried out using dip information produces a model that has higher resolution that is more geologically realistic compared with other methods.

Viscoacoustic waveform inversion of velocity structures in the time domain

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. R103-R119 ◽  
Author(s):  
Jianyong Bai ◽  
David Yingst ◽  
Robert Bloor ◽  
Jacques Leveille
Keyword(s):  
Finite Difference ◽  
Time Domain ◽  
Field Data ◽  
Wave Equations ◽  
Finite Difference Methods ◽  
Waveform Inversion ◽  
Data Set ◽  
Velocity Models ◽  
Difference Methods ◽  
The Time Domain

Because of the conversion of elastic energy into heat, seismic waves are attenuated and dispersed as they propagate. The attenuation effects can reduce the resolution of velocity models obtained from waveform inversion or even cause the inversion to produce incorrect results. Using a viscoacoustic model consisting of a single standard linear solid, we discovered a theoretical framework of viscoacoustic waveform inversion in the time domain for velocity estimation. We derived and found the viscoacoustic wave equations for forward modeling and their adjoint to compensate for the attenuation effects in viscoacoustic waveform inversion. The wave equations were numerically solved by high-order finite-difference methods on centered grids to extrapolate seismic wavefields. The finite-difference methods were implemented satisfying stability conditions, which are also presented. Numerical examples proved that the forward viscoacoustic wave equation can simulate attenuative behaviors very well in amplitude attenuation and phase dispersion. We tested acoustic and viscoacoustic waveform inversions with a modified Marmousi model and a 3D field data set from the deep-water Gulf of Mexico for comparison. The tests with the modified Marmousi model illustrated that the seismic attenuation can have large effects on waveform inversion and that choosing the most suitable inversion method was important to obtain the best inversion results for a specific seismic data volume. The tests with the field data set indicated that the inverted velocity models determined from the acoustic and viscoacoustic inversions were helpful to improve images and offset gathers obtained from migration. Compared to the acoustic inversion, viscoacoustic inversion is a realistic approach for real earth materials because the attenuation effects are compensated.

Application of very fast simulated annealing and differential evolution in the search for FO-CRS wavefield attributes

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. O81-O92
Author(s):  
German Garabito ◽  
João Carlos R. Cruz
Keyword(s):  
Global Optimization ◽  
Simulated Annealing ◽  
Differential Evolution ◽  
Seismic Data ◽  
Optimization Algorithms ◽  
Two Dimensions ◽  
Seismic Section ◽  
Data Set ◽  
Computational Costs ◽  
Very Fast Simulated Annealing

The finite-offset common-reflection-surface (FO-CRS) stack method can be used to simulate any common-offset (CO) seismic section by stacking prestack seismic data along the surfaces defined by the paraxial hyperbolic traveltime approximation. In two dimensions, the FO-CRS stacking operator depends on five kinematic wavefield attributes for every time sample of the target CO section. The main problem with this method is identifying a computationally efficient data-driven search strategy for accurately determining the best set of FO-CRS attributes that produce the optimal coherence measure of the seismic signal in the prestack data. Identifying a global optimization algorithm with the best performance is a challenge when solving this optimization problem. This is because the objective function is multimodal and involves a large volume of data, which leads to high computational costs. We introduced a comparative and competitive study through the application of two global optimization algorithms that simultaneously search the FO-CRS attributes from the prestack seismic data, very fast simulated annealing (VFSA) and the differential evolution (DE). By applying this FO-CRS stack to the Marmousi synthetic seismic data set, we have compared the performances of the two optimization algorithms with regard to their efficiency and effectiveness in estimating the five FO-CRS attributes. To analyze the robustness of the two algorithms, we apply them to real land seismic data and show their ability to find the near-optimal attributes and to improve reflection events in noisy data with a very low fold. We reveal that VFSA is efficient in reaching the optimal coherence value with the lowest computational costs, and that DE is effective and reliable in reaching the optimal coherence for determining the best five searched-for attributes. Regardless of the differences, the FO-CRS stack produces enhanced and regularized high-quality CO sections using both global optimization methods.

scholarly journals Noise reduction with reflection supervirtual interferometry

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. V249-V256
Author(s):  
Kai Lu ◽  
Zhaolun Liu ◽  
Sherif Hanafy ◽  
Gerard Schuster
Keyword(s):  
Noise Reduction ◽  
Field Data ◽  
Signal To Noise Ratio ◽  
Signal To Noise ◽  
Data Set ◽  
Reflection Data ◽  
The Poor ◽  
The Earth ◽  
The Common ◽  
Noise Ratio

To image deeper portions of the earth, geophysicists must record reflection data with much greater source-receiver offsets. The problem with these data is that the signal-to-noise ratio (S/N) significantly diminishes with greater offset. In many cases, the poor S/N makes the far-offset reflections imperceptible on the shot records. To mitigate this problem, we have developed supervirtual reflection interferometry (SVI), which can be applied to far-offset reflections to significantly increase their S/N. The key idea is to select the common pair gathers where the phases of the correlated reflection arrivals differ from one another by no more than a quarter of a period so that the traces can be coherently stacked. The traces are correlated and summed together to create traces with virtual reflections, which in turn are convolved with one another and stacked to give the reflection traces with much stronger S/Ns. This is similar to refraction SVI except far-offset reflections are used instead of refractions. The theory is validated with synthetic tests where SVI is applied to far-offset reflection arrivals to significantly improve their S/N. Reflection SVI is also applied to a field data set where the reflections are too noisy to be clearly visible in the traces. After the implementation of reflection SVI, the normal moveout velocity can be accurately picked from the SVI-improved data, leading to a successful poststack migration for this data set.

Separation of regional and residual magnetic field data

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 431-439 ◽  
Author(s):  
Yaoguo Li ◽  
Douglas W. Oldenburg
Keyword(s):  
Magnetic Field ◽  
Field Data ◽  
Power Spectra ◽  
Magnetic Data ◽  
Inversion Algorithm ◽  
Large Area ◽  
Data Set ◽  
Regional Sources ◽  
Magnetic Inversion ◽  
Susceptibility Model

We present a method for separating regional and residual magnetic fields using a 3-D magnetic inversion algorithm. The separation is achieved by inverting the observed magnetic data from a large area to construct a regional susceptibility distribution. The magnetic field produced by the regional susceptibility model is then used as the regional field, and the residual data are obtained by simple subtraction. The advantages of this method of separation are that it introduces little distortion to the shape of the extracted anomaly and that it is not affected significantly by factors such as topography and the overlap of power spectra of regional and residual fields. The proposed method is tested using a synthetic example having varying relative positions between the local and regional sources and then using a field data set from Australia. Results show that the residual field extracted using this method enables good recovery of target susceptibility distribution from inversions.

scholarly journals Waveform inversion using a logarithmic wavefield

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. R31-R42 ◽  
Author(s):  
Changsoo Shin ◽  
Dong-Joo Min
Keyword(s):  
Objective Function ◽  
Field Data ◽  
Velocity Structure ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Velocity Model ◽  
Matrix Formalism ◽  
Inversion Algorithm ◽  
Data Set ◽  
Short Period

Although waveform inversion has been studied extensively since its beginning [Formula: see text] ago, applications to seismic field data have been limited, and most of those applications have been for global-seismology- or engineering-seismology-scale problems, not for exploration-scale data. As an alternative to classical waveform inversion, we propose the use of a new, objective function constructed by taking the logarithm of wavefields, allowing consideration of three types of objective function, namely, amplitude only, phase only, or both. In our wave form inversion, we estimate the source signature as well as the velocity structure by including functions of amplitudes and phases of the source signature in the objective function. We compute the steepest-descent directions by using a matrix formalism derived from a frequency-domain, finite-element/finite-difference modeling technique. Our numerical algorithms are similar to those of reverse-time migration and waveform inversion based on the adjoint state of the wave equation. In order to demonstrate the practical applicability of our algorithm, we use a synthetic data set from the Marmousi model and seismic data collected from the Korean continental shelf. For noise-free synthetic data, the velocity structure produced by our inversion algorithm is closer to the true velocity structure than that obtained with conventional waveform inversion. When random noise is added, the inverted velocity model is also close to the true Marmousi model, but when frequencies below [Formula: see text] are removed from the data, the velocity structure is not as good as those for the noise-free and noisy data. For field data, we compare the time-domain synthetic seismograms generated for the velocity model inverted by our algorithm with real seismograms and find that the results show that our inversion algorithm reveals short-period features of the subsurface. Although we use wrapped phases in our examples, we still obtain reasonable results. We expect that if we were to use correctly unwrapped phases in the inversion algorithm, we would obtain better results.

Mitigating remanent magnetization effects in magnetic data using the normalized source strength

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. J25-J32 ◽  
Author(s):  
Mark Pilkington ◽  
Majid Beiki
Keyword(s):  
Magnetic Field ◽  
Remanent Magnetization ◽  
Field Data ◽  
Magnetic Data ◽  
Magnetization Distribution ◽  
Source Strength ◽  
Inversion Algorithm ◽  
Data Set ◽  
Magnetic Field Data ◽  
The Magnetic Field

We have developed an approach for the interpretation of magnetic field data that can be used when measured anomalies are affected by significant remanent magnetization components. The method deals with remanent effects by using the normalized source strength (NSS), a quantity calculated from the eigenvectors of the magnetic gradient tensor. The NSS is minimally affected by the direction of remanent magnetization present and compares well with other transformations of the magnetic field that are used for the same purpose. It therefore offers a way of inverting magnetic data containing the effects of remanent magnetizations, particularly when these are unknown and are possibly varying within a given data set. We use a standard 3D inversion algorithm to invert NSS data from an area where varying remanence directions are apparent, resulting in a more reliable image of the subsurface magnetization distribution than possible using the observed magnetic field data directly.

Simultaneous reconstruction of 1-D susceptibility and conductivity from electromagnetic data

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 33-47 ◽  
Author(s):  
Zhiyi Zhang ◽  
Douglas W. Oldenburg
Keyword(s):  
Cost Function ◽  
Objective Functions ◽  
Inversion Algorithm ◽  
Data Set ◽  
Circular Loop ◽  
Simultaneous Inversion ◽  
The Earth ◽  
Simultaneous Reconstruction ◽  
Single Data ◽  
The Cost

In this paper, we develop an inversion algorithm to simultaneously recover 1-D distributions of electric conductivity and magnetic susceptibility from a single data set. The earth is modeled as a series of homogeneous layers of known thickness with constant but unknown conductivities and susceptibilities. The medium of interest is illuminated by a horizontal circular loop source located above the surface of the earth. The secondary signals from the earth are received by a circular loop receiver located some distance from the source. The model objective function in the inversion, which we refer to as the cost function, is a weighted sum of model objective functions of conductivity and susceptibility. We minimize this cost function subject to the data constraints and show how the choice of weights for the model objective functions of conductivity and susceptibility affects the results of the inversion through 1-D synthetic examples. We also invert 3-D synthetic and field data. From these examples we conclude that simultaneous inversion of electromagnetic (EM) data can provide useful information about the conductivity and susceptibility distributions.

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