Incorporating geological dip information into geophysical inversions

Geophysics ◽  
2000 ◽  
Vol 65 (1) ◽  
pp. 148-157 ◽  
Author(s):  
Yaoguo Li ◽  
Douglas W. Oldenburg
Keyword(s):  
Objective Function ◽  
Induced Polarization ◽  
Dc Resistivity ◽  
Arbitrary Direction ◽  
Linear Structures ◽  
New Model ◽  
Strike Direction ◽  
Dip Angle ◽  
Derivatives Of ◽  
True Structure

Geological bodies are often linear structures that have well‐defined strike direction and dip angle. We develop a new model objective function that allows this important information to be incorporated into geophysical inversions. A rotation matrix is applied to the horizontal and vertical derivatives of the model so that the derivative in an arbitrary direction is obtained. A model objective function that measures the flatness with respect to the rotated derivatives favors models that have elongated features with the specified strike and dip angle. Formulations for both 2-D and 3-D cases are presented, and they are illustrated using examples from dc resistivity and induced polarization (IP) problems. Synthetic and field examples show that an inversion carried out using known dip information produces a model that has higher resolution and provides a better representation of the true structure.

Inversion of induced polarization data

Geophysics ◽  
1994 ◽  
Vol 59 (9) ◽  
pp. 1327-1341 ◽  
Author(s):  
Douglas W. Oldenburg ◽  
Yaoguo Li
Keyword(s):  
Inverse Problem ◽  
Objective Function ◽  
Effective Conductivity ◽  
Optimization Theory ◽  
Induced Polarization ◽  
Dc Resistivity ◽  
Earth Structure ◽  
Nonlinear Inverse Problem ◽  
Polarization Data ◽  
The Earth

We develop three methods to invert induced polarization (IP) data. The foundation for our algorithms is an assumption that the ultimate effect of chargeability is to alter the effective conductivity when current is applied. This assumption, which was first put forth by Siegel and has been routinely adopted in the literature, permits the IP responses to be numerically modeled by carrying out two forward modelings using a DC resistivity algorithm. The intimate connection between DC and IP data means that inversion of IP data is a two‐step process. First, the DC potentials are inverted to recover a background conductivity. The distribution of chargeability can then be found by using any one of the three following techniques: (1) linearizing the IP data equation and solving a linear inverse problem, (2) manipulating the conductivities obtained after performing two DC resistivity inversions, and (3) solving a nonlinear inverse problem. Our procedure for performing the inversion is to divide the earth into rectangular prisms and to assume that the conductivity σ and chargeability η are constant in each cell. To emulate complicated earth structure we allow many cells, usually far more than there are data. The inverse problem, which has many solutions, is then solved as a problem in optimization theory. A model objective function is designed, and a “model” (either the distribution of σ or η)is sought that minimizes the objective function subject to adequately fitting the data. Generalized subspace methodologies are used to solve both inverse problems, and positivity constraints are included. The IP inversion procedures we design are generic and can be applied to 1-D, 2-D, or 3-D earth models and with any configuration of current and potential electrodes. We illustrate our methods by inverting synthetic DC/IP data taken over a 2-D earth structure and by inverting dipole‐dipole data taken in Quebec.

scholarly journals Balancing and Simulation of a Double Crank-Rocker Engine Model for Optimum Reduction of Shaking Forces and Shaking Moments

2021 ◽  
Vol 8 (2) ◽  
pp. 237-245
Author(s):  
Anwr M. Albaghdadi ◽  
Masri B. Baharom ◽  
Shaharin A. Sualiman
Keyword(s):  
Dynamic Analysis ◽  
Objective Function ◽  
Conventional Method ◽  
Optimization Process ◽  
New Model ◽  
Engine Model ◽  
Design Variables ◽  
Driving Torque ◽  
Related Design ◽  
Shaking Moment

In this paper, a new configuration of Crank-Rocker (CR) model has been proposed by duplicating its mechanism. The method has been implemented to overcome vibration problem on a single-piston Crank-Rocker engine caused by system unbalance. The new method suggests combining conventional method of adding counterweights to reduce shaking forces and eliminating the inertial moments on system by implementing the new layout. A dynamic study of the new model is presented, then the objective function is derived and implemented to perform the optimization process. Related design variables and system constraints are introduced to determine attached counterweights optimized characteristics. For results validation, the simulation, dynamic analysis, and optimization process were conducted using ADAMS VIEW® software. The output results were presented and discussed to verify the validity of the suggested method. It was noticed that the method was very effective and has managed to reduce the total shaking forces by about 91%, shaking moment by about 66%; and the driving torque by 27%.

Combined DC resistivity and induced polarization (DC-IP) for mapping the internal composition of a mine waste rock pile in Nova Scotia, Canada

2018 ◽  
Vol 150 ◽  
pp. 40-51 ◽  
Author(s):  
Christopher Power ◽  
Panagiotis Tsourlos ◽  
Murugan Ramasamy ◽  
Aristeidis Nivorlis ◽  
Martin Mkandawire
Keyword(s):  
Nova Scotia ◽  
Mine Waste ◽  
Induced Polarization ◽  
Waste Rock ◽  
Dc Resistivity ◽  
Rock Pile ◽  
Waste Rock Pile ◽  
Mine Waste Rock

An examination of the relationship between time‐domain integral chargeability and the Cole‐Cole impedance model

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1249-1252 ◽  
Author(s):  
Kenneth Duckworth ◽  
H. Thomas Calvert
Keyword(s):  
Electrical Properties ◽  
Frequency Dependence ◽  
Time Constant ◽  
Time Domain ◽  
Induced Polarization ◽  
Dc Resistivity ◽  
Impedance Model ◽  
Domain Integral ◽  
The Relationship

The Cole‐Cole impedance model developed in Pelton et al. (1978) for describing the induced polarization (IP) phenomenon has proven to be useful for characterizing the electrical properties of rocks. The model characterizes the impedance Z(ω) of a rock using only four parameters as follows [Formula: see text] where [Formula: see text] is the DC resistivity, m is the dimensionless chargeability, τ is the time constant, c is the frequency dependence, and [Formula: see text] [Formula: see text]

scholarly journals Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion

Geophysics ◽  
2001 ◽  
Vol 66 (1) ◽  
pp. 174-187 ◽  
Author(s):  
William Rodi ◽  
Randall L. Mackie
Keyword(s):  
Inverse Problems ◽  
Objective Function ◽  
Complete Solution ◽  
Model Space ◽  
Conjugate Gradients ◽  
Nonlinear Inversion ◽  
Spatial Derivatives ◽  
Computationally Intensive ◽  
Derivatives Of ◽  
Special Case

We investigate a new algorithm for computing regularized solutions of the 2-D magnetotelluric inverse problem. The algorithm employs a nonlinear conjugate gradients (NLCG) scheme to minimize an objective function that penalizes data residuals and second spatial derivatives of resistivity. We compare this algorithm theoretically and numerically to two previous algorithms for constructing such “minimum‐structure” models: the Gauss‐Newton method, which solves a sequence of linearized inverse problems and has been the standard approach to nonlinear inversion in geophysics, and an algorithm due to Mackie and Madden, which solves a sequence of linearized inverse problems incompletely using a (linear) conjugate gradients technique. Numerical experiments involving synthetic and field data indicate that the two algorithms based on conjugate gradients (NLCG and Mackie‐Madden) are more efficient than the Gauss‐Newton algorithm in terms of both computer memory requirements and CPU time needed to find accurate solutions to problems of realistic size. This owes largely to the fact that the conjugate gradients‐based algorithms avoid two computationally intensive tasks that are performed at each step of a Gauss‐Newton iteration: calculation of the full Jacobian matrix of the forward modeling operator, and complete solution of a linear system on the model space. The numerical tests also show that the Mackie‐Madden algorithm reduces the objective function more quickly than our new NLCG algorithm in the early stages of minimization, but NLCG is more effective in the later computations. To help understand these results, we describe the Mackie‐Madden and new NLCG algorithms in detail and couch each as a special case of a more general conjugate gradients scheme for nonlinear inversion.

scholarly journals Direct current (DC) resistivity and induced polarization (IP) monitoring of active layer dynamics at high temporal resolution

2015 ◽  
Vol 119 ◽  
pp. 16-28 ◽  
Author(s):  
Joseph Doetsch ◽  
Thomas Ingeman-Nielsen ◽  
Anders V. Christiansen ◽  
Gianluca Fiandaca ◽  
Esben Auken ◽  
...  
Keyword(s):  
Active Layer ◽  
Temporal Resolution ◽  
Direct Current ◽  
Induced Polarization ◽  
High Temporal Resolution ◽  
Dc Resistivity

Wavefield decomposition in arbitrary direction and an imaging condition based on stratigraphic dip

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. S299-S312
Author(s):  
Xuebao Guo ◽  
Ying Shi ◽  
Weihong Wang ◽  
Hongliang Jing ◽  
Zhen Zhang
Keyword(s):  
Hilbert Transform ◽  
New Method ◽  
Frequency Noise ◽  
Arbitrary Direction ◽  
Vector Method ◽  
Imaging Condition ◽  
Dip Angle ◽  
The Hilbert Transform ◽  
Angle Gather ◽  
Wavefield Decomposition

In reverse time migration (RTM), wavefield decomposition can play an important role in addressing the issue of migration noise, especially low-frequency noise. The complete wavefield decomposition based on the Hilbert transform is a commonly used method in RTM, but it is accompanied by extra wavefield simulation and wavefield storage. We have developed three distinct methods. The first is a convenient method for wavefield decomposition, which is based on Poynting vectors. Only the unit vector in one direction is needed to realize the wavefield decomposition in an arbitrary direction by this method. It breaks through the limitation that the Hilbert transform-based method is applicable only to the up- and downgoing wave or left- and right-going wave decomposition, and the calculation cost is negligible compared with RTM. The second is a method based on the instantaneous wavenumber, which we developed for calculating the wave propagation direction. On the basis of wavefield decomposition, the imaging angle gather from the new method performs better than that of the Poynting vector method. Meanwhile, it also is used for generating the incident angle gather and dip angle gather. The latter expresses the dip angle of underground strata. More importantly, the above methods allow us to control the wavefield decomposition direction and three angles at any position underground. The third adopts a stratigraphic imaging condition method, and we briefly analyze the relationship between the new method and the inverse-scattering imaging condition. The stratigraphic imaging condition maps the results to the dip angle of the stratum through a spatial gradient wavefield, which can enhance the effective imaging information. The above three kinds of angle gathers also can be constructed by the stratigraphic imaging condition. Numerical experiments demonstrate that the imaging results and the angle gathers obtained by our proposed method have higher accuracy and resolution.

scholarly journals The 2018 Mw 7.5 Palu Earthquake: A Supershear Rupture Event Constrained by InSAR and Broadband Regional Seismograms

2019 ◽  
Vol 11 (11) ◽  
pp. 1330 ◽  
Author(s):  
Jin Fang ◽  
Caijun Xu ◽  
Yangmao Wen ◽  
Shuai Wang ◽  
Guangyu Xu ◽  
...  
Keyword(s):  
Pulse Propagation ◽  
The South ◽  
The North ◽  
Strike Direction ◽  
Slip Pulse ◽  
Rupture Model ◽  
Dip Angle ◽  
Total Seismic Moment ◽  
The City ◽  
North And South

The 28 September 2018 Mw 7.5 Palu earthquake occurred at a triple junction zone where the Philippine Sea, Australian, and Sunda plates are convergent. Here, we utilized Advanced Land Observing Satellite-2 (ALOS-2) interferometry synthetic aperture radar (InSAR) data together with broadband regional seismograms to investigate the source geometry and rupture kinematics of this earthquake. Results showed that the 2018 Palu earthquake ruptured a fault plane with a relatively steep dip angle of ~85°. The preferred rupture model demonstrated that the earthquake was a supershear event from early on, with an average rupture speed of 4.1 km/s, which is different from the common supershear events that typically show an initial subshear rupture. The rupture expanded rapidly (~4.1 km/s) from the hypocenter and propagated bilaterally towards the north and south along the strike direction during the first 8 s, and then to the south. Four visible asperities were ruptured during the slip pulse propagation, which resulted in four significant deformation lobes in the coseismic interferogram. The maximum slip of 6.5 m was observed to the south of the city of Palu, and the total seismic moment released within 40 s was 2.64 × 1020 N·m, which was equivalent to Mw 7.55. Our results shed some light on the transtensional tectonism in Sulawesi, given that the 2018 Palu earthquake was dominated by left-lateral strike slip (slip maxima is 6.2 m) and that some significant normal faulting components (slip maxima is ~3 m) were resolved as well.

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