Multiscale resistivity inversion based on convolutional wavelet transform

2020 ◽  
Vol 223 (1) ◽  
pp. 132-143 ◽  
Author(s):  
Yonghao Pang ◽  
Lichao Nie ◽  
Bin Liu ◽  
Zhengyu Liu ◽  
Ning Wang
Keyword(s):  
Wavelet Transform ◽  
A Priori ◽  
Geophysical Methods ◽  
Spatial Domain ◽  
Inversion Method ◽  
Model Parameters ◽  
Imaging Method ◽  
Feature Parameters ◽  
Resistivity Model ◽  
Resistivity Inversion

SUMMARY The resistivity imaging method, an effective geophysical technique, has been widely used in environmental, engineering and hydrological fields. The inversion method based on smooth constraint is one of the most commonly used methods. However, this method causes the resistivity to change smoothly and makes it difficult to describe geological boundaries accurately. An accurate description of the target's boundaries often requires a priori information gained with other methods (such as other geophysical methods or geological drilling). To address this issue, a multiscale inversion method is proposed for extracting boundary features and inverting feature parameters from different scales. In this method, a convolution kernel is used to extract the boundary information from the resistivity model. The model parameters are transformed from the spatial domain to the feature domain via a convolutional wavelet transform. The feature parameters of different scales can then be obtained by solving the inversion equation in the feature domain. After that, the resistivity model of the spatial domain is reconverted from the feature domain by deconvolution transform of the inversion result. Numerical simulations and experiments show that the new multiscale resistivity inversion method has the ability to locate and depict boundaries of geological targets with high accuracy.

Transient electromagnetic search engine for real-time imaging

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. E277-E285 ◽  
Author(s):  
Jide Nosakare Ogunbo ◽  
Jie Zhang ◽  
Xiong Zhang
Keyword(s):  
Real Time ◽  
Search Engine ◽  
Solution Space ◽  
Inversion Method ◽  
Model Parameters ◽  
Transient Electromagnetic ◽  
Model Solutions ◽  
Resistivity Model ◽  
2D Resistivity ◽  
Engine Method

To image the resistivity distribution of the subsurface, transient electromagnetic (TEM) surveying has been established as an effective geophysical method. Conventionally, an inversion method is applied to resolve the model parameters from the available measurements. However, significant time and effort are involved in preparing and executing an inversion and this prohibits its use as a real-time decision-making tool to optimize surveying in the field. We have developed a search engine method to find approximate 1D resistivity model solutions for circular central-loop configuration TEM data in real time. The search engine method is a concept used for query searches from large databases on the Internet. By extension, approximate solutions to any input TEM data can be found rapidly by searching a preestablished database. This database includes a large number of forward simulation results that represent the possible model solutions. The database size is optimized by the survey depth of investigation and the sensitivity analysis of the model layers. The fast-search speed is achieved by using the multiple randomized [Formula: see text]-dimensional tree method. In addition to its high speed in finding solutions, the search engine method provides a solution space that quantifies the resolutions and uncertainties of the results. We apply the search engine method to find 1D model solutions at different data points and then interpolate them to a pseudo-2D resistivity model. We tested the method with synthetic and real data.

Self-potential Data Interpretation for Two Co-axial Structures Utilizing the RMS Parameter

2020 ◽  
Vol 25 (1) ◽  
pp. 15-23
Author(s):  
Khalid S. Essa ◽  
Zein E. Diab ◽  
Mahmoud Elhussein
Keyword(s):  
A Priori ◽  
Source Parameters ◽  
Data Interpretation ◽  
The Body ◽  
Inversion Method ◽  
Model Parameters ◽  
Polarization Angle ◽  
Potential Field Data ◽  
Rms Error ◽  
Self Potential

We have developed an algorithm to obtain the model parameters for two co-axial structures from self-potential data. The method uses the first numerical horizontal derivatives calculated from the observed self-potential anomaly employing filters of sequential window lengths (s-values) so as to gauge the model constraints for the shallow and deep structures. In addition, this algorithm uses a standard inversion method for solving a non-linear equation based on the lowest root-mean-square (RMS) error of the estimated model parameters. The body constraints are the depth, polarization angle and electric dipole moment of each structure. Our approach models the self-potential dataset as an aggregation of spheres, horizontal cylinders, and vertical cylinders. These simple bodies are used to approximate, without a priori expectations, the furthermost plausible position and/or area of intersection. In other words, the bodies are used to estimate the true values of the source parameters for the two-co-axial bodies at different s-values. Minimizing the RMS error has the advantage of optimizing all model factors. The proposed technique is tested using a numerical model with and without noise and on self-potential field data acquired at a site in Germany. In all cases, the assessed body parameters are reasonable approximations of the known values.

scholarly journals Advanced Methods of Joint Inversion of Multiphysics Data for Mineral Exploration

Geosciences ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 262
Author(s):  
Michael S. Zhdanov ◽  
Michael Jorgensen ◽  
Leif Cox
Keyword(s):  
Joint Inversion ◽  
Mineral Exploration ◽  
A Priori ◽  
Geophysical Methods ◽  
Physical Property ◽  
Model Parameters ◽  
Time Inversion ◽  
Structural Constraints ◽  
Considerable Uncertainty ◽  
Additional Information

Different geophysical methods provide information about various physical properties of rock formations and mineralization. In many cases, this information is mutually complementary. At the same time, inversion of the data for a particular survey is subject to considerable uncertainty and ambiguity as to causative body geometry and intrinsic physical property contrast. One productive approach to reducing uncertainty is to jointly invert several types of data. Non-uniqueness can also be reduced by incorporating additional information derived from available geological and/or geophysical data in the survey area to reduce the searching space for the solution. This additional information can be incorporated in the form of a joint inversion of multiphysics data. This paper presents an overview of the main ideas and principles of novel methods of joint inversion, developed over the last decade, which do not require a priori knowledge about specific empirical or statistical relationships between the different model parameters and/or their attributes. These approaches are designated as follows: (1) Gramian constraints; (2) Gramian-based structural constraints; (3) localized Gramian constraints; and (4) joint focusing constraints. We provide a short description of the mathematical foundations of each of these approaches and discuss the practical aspects of their applications in mineral exploration.

scholarly journals Direct inversion of the apparent complex‐resistivity spectrum

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1399-1404 ◽  
Author(s):  
J. Xiang ◽  
N. B. Jones ◽  
D. Cheng ◽  
F. S. Schlindwein
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Optimal Parameter ◽  
Geophysical Methods ◽  
Inversion Method ◽  
Model Parameters ◽  
Complex Resistivity ◽  
Direct Inversion ◽  
Optimal Parameter Estimation ◽  
Cole Model

Cole‐Cole model parameters are widely used to interpret electrical geophysical methods and are obtained by inverting the induced polarization (IP) spectrum. This paper presents a direct inversion method for parameter estimation based on multifold least‐squares estimation. Two algorithms are described that provide optimal parameter estimation in the least‐squares sense. Simulations demonstrate that both algorithms can provide direct apparent spectral parameter inversion for complex resistivity data. Moreover, the second algorithm is robust under reasonably high noise.

Joint inversion of Rayleigh-wave dispersion and P-wave refraction data for laterally varying layered models

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. EN49-EN59 ◽  
Author(s):  
Daniele Boiero ◽  
Laura Valentina Socco
Keyword(s):  
Rayleigh Wave ◽  
Joint Inversion ◽  
A Priori ◽  
P Wave ◽  
Inversion Method ◽  
Model Parameters ◽  
Data Set ◽  
Wave Refraction ◽  
Velocity Models ◽  
Refraction Data

We implemented a joint inversion method to build P- and S-wave velocity models from Rayleigh-wave and P-wave refraction data, specifically designed to deal with laterally varying layered environments. A priori information available over the site and any physical law to link model parameters can be also incorporated. We tested and applied the algorithm behind the method. The results from a field data set revealed advantages with respect to individual surface-wave analysis (SWA) and body wave tomography (BWT). The algorithm imposed internal consistency for all the model parameters relaxing the required a priori assumptions (i.e., Poisson’s ratio level of confidence in SWA) and the inherent limitations of the two methods (i.e., velocity decreases for BWT).

A constrained global inversion method using an overparameterized scheme: Application to poststack seismic data

Geophysics ◽  
2001 ◽  
Vol 66 (2) ◽  
pp. 613-626 ◽  
Author(s):  
Xin‐Quan Ma
Keyword(s):  
Simulated Annealing ◽  
Seismic Data ◽  
A Priori ◽  
Constant Thickness ◽  
Inversion Method ◽  
Model Parameters ◽  
A Priori Information ◽  
Initial Model ◽  
Seismic Waveform ◽  
Priori Information

A global optimization algorithm using simulated annealing has advantages over local optimization approaches in that it can escape from being trapped in local minima and it does not require a good initial model and function derivatives to find a global minimum. It is therefore more attractive and suitable for seismic waveform inversion. I adopt an improved version of a simulated annealing algorithm to invert simultaneously for acoustic impedance and layer interfaces from poststack seismic data. The earth’s subsurface is overparameterized by a series of microlayers with constant thickness in two‐way traveltime. The algorithm is constrained using the low‐frequency impedance trend and has been made computationally more efficient using this a priori information as an initial model. A search bound of each parameter, derived directly from the a priori information, reduces the nonuniqueness problem. Application of this technique to synthetic and field data examples helps one recover the true model parameters and reveals good continuity of estimated impedance across a seismic section. This approach has the capability of revealing the high‐resolution detail needed for reservoir characterization when a reliable migrated image is available with good well ties.

scholarly journals Computational Method for Wavefront Sensing Based on Transport-Of-Intensity Equation

Photonics ◽  
2021 ◽  
Vol 8 (6) ◽  
pp. 177
Author(s):  
Iliya Gritsenko ◽  
Michael Kovalev ◽  
George Krasin ◽  
Matvey Konoplyov ◽  
Nikita Stsepuro
Keyword(s):  
A Priori ◽  
Spherical Wave ◽  
Computational Method ◽  
Optical Systems ◽  
Radius Of Curvature ◽  
Imaging Method ◽  
Wavefront Sensing ◽  
Phase Imaging ◽  
Transport Of Intensity Equation ◽  
Priori Information

Recently the transport-of-intensity equation as a phase imaging method turned out as an effective microscopy method that does not require the use of high-resolution optical systems and a priori information about the object. In this paper we propose a mathematical model that adapts the transport-of-intensity equation for the purpose of wavefront sensing of the given light wave. The analysis of the influence of the longitudinal displacement z and the step between intensity distributions measurements on the error in determining the wavefront radius of curvature of a spherical wave is carried out. The proposed method is compared with the traditional Shack–Hartmann method and the method based on computer-generated Fourier holograms. Numerical simulation showed that the proposed method allows measurement of the wavefront radius of curvature with radius of 40 mm and with accuracy of ~200 μm.

Generalised DOPs with Consideration of the Influence Function of Signal-in-Space Errors

2011 ◽  
Vol 64 (S1) ◽  
pp. S3-S18 ◽  
Author(s):  
Yuanxi Yang ◽  
Jinlong Li ◽  
Junyi Xu ◽  
Jing Tang
Keyword(s):  
Least Squares ◽  
Stochastic Models ◽  
Influence Function ◽  
A Priori ◽  
Functional Model ◽  
Global Navigation Satellite Systems ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Integrated Navigation ◽  
Satellite Systems

Integrated navigation using multiple Global Navigation Satellite Systems (GNSS) is beneficial to increase the number of observable satellites, alleviate the effects of systematic errors and improve the accuracy of positioning, navigation and timing (PNT). When multiple constellations and multiple frequency measurements are employed, the functional and stochastic models as well as the estimation principle for PNT may be different. Therefore, the commonly used definition of “dilution of precision (DOP)” based on the least squares (LS) estimation and unified functional and stochastic models will be not applicable anymore. In this paper, three types of generalised DOPs are defined. The first type of generalised DOP is based on the error influence function (IF) of pseudo-ranges that reflects the geometry strength of the measurements, error magnitude and the estimation risk criteria. When the least squares estimation is used, the first type of generalised DOP is identical to the one commonly used. In order to define the first type of generalised DOP, an IF of signal–in-space (SIS) errors on the parameter estimates of PNT is derived. The second type of generalised DOP is defined based on the functional model with additional systematic parameters induced by the compatibility and interoperability problems among different GNSS systems. The third type of generalised DOP is defined based on Bayesian estimation in which the a priori information of the model parameters is taken into account. This is suitable for evaluating the precision of kinematic positioning or navigation. Different types of generalised DOPs are suitable for different PNT scenarios and an example for the calculation of these DOPs for multi-GNSS systems including GPS, GLONASS, Compass and Galileo is given. New observation equations of Compass and GLONASS that may contain additional parameters for interoperability are specifically investigated. It shows that if the interoperability of multi-GNSS is not fulfilled, the increased number of satellites will not significantly reduce the generalised DOP value. Furthermore, the outlying measurements will not change the original DOP, but will change the first type of generalised DOP which includes a robust error IF. A priori information of the model parameters will also reduce the DOP.

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