Subsurface imaging using magnetotelluric data

Geophysics ◽  
1988 ◽  
Vol 53 (1) ◽  
pp. 104-117 ◽  
Author(s):  
S. Levv ◽  
D. Oldenburg ◽  
J. Wang

A linear programming approach is developed to construct a pseudo‐impulse response for magnetotelluric (MT) data. The constructed time function is made up of discrete pulses whose amplitudes depend upon the electromagnetic reflection and transmission coefficients at various layer interfaces. The arrival time of an individual pulse corresponds to the time for a reference signal to travel a particular raypath from the surface to a reflector and back. The display of the impulse responses recovered from many stations produces an MT reflectivity section which is analogous to the image ray section regularly interpreted in reflection seismology. Application of linear programming inversion to one‐dimensional conductivity models shows the viability of the method and validates the physical interpretation of the pseudo‐impulse response function. Using a number of simple two‐dimensional geologic models, we show that a line of MT stations acquired perpendicular to strike produces a reflectivity section which is an image of the explored target. The interpretation of the MT image section follows the conventional guidelines used in reflection seismology; features such as traveltime pullup, primary and multiple reflections, and diffraction events are evident on the final section.

Geophysics ◽  
1986 ◽  
Vol 51 (2) ◽  
pp. 383-395 ◽  
Author(s):  
Kenneth P. Whittall ◽  
D. W. Oldenburg

We present a flexible, one‐dimensional magnetotelluric (MT) inversion algorithm based on inverse scattering theory. The algorithm easily generates different classes of conductivity‐depth profiles so the interpreter may choose models that satisfy any external geologic or geophysical constraints. The two‐stage process is based on the work of Weidelt. The first stage uses the MT frequency‐domain data to construct an impulse response analogous to a deconvolved seismogram with or without a free‐surface assumption. Since this is a linear problem (a Laplace transform), numerous impulse responses may be generated by linear inverse techniques which handle data errors robustly. We minimize four norms of the impulse response in order to construct varied classes of limited‐structure earth models. We choose such models to prevent overinterpreting the limited number of inaccurate MT observations. The second stage of the algorithm maps the impulse response to the conductivity model using any of four Fredholm integral equations of the second kind. We evaluate the performance of each of the four mappings and recommend the Burridge and Gopinath‐Sondhi formulations. We also evaluate three approximations to the second‐stage equations. These approximations are fast and easy to implement on small computers. We find the one which includes first‐order multiple reflections to be the most accurate.


2020 ◽  
Vol 14 (2) ◽  
pp. 108-113
Author(s):  
Ewa Pawłuszewicz

AbstractThe problem of realisation of linear control systems with the h–difference of Caputo-, Riemann–Liouville- and Grünwald–Letnikov-type fractional vector-order operators is studied. The problem of existing minimal realisation is discussed.


2012 ◽  
Author(s):  
Krishnamoorthy Kalyanam ◽  
Swaroop Darbha ◽  
Myoungkuk Park ◽  
Meir Pachter ◽  
Phil Chandler ◽  
...  

Author(s):  
Mingjie Zhang ◽  
Ole Øiseth

AbstractA convolution-based numerical algorithm is presented for the time-domain analysis of fluidelastic instability in tube arrays, emphasizing in detail some key numerical issues involved in the time-domain simulation. The unit-step and unit-impulse response functions, as two elementary building blocks for the time-domain analysis, are interpreted systematically. An amplitude-dependent unit-step or unit-impulse response function is introduced to capture the main features of the nonlinear fluidelastic (FE) forces. Connections of these elementary functions with conventional frequency-domain unsteady FE force coefficients are discussed to facilitate the identification of model parameters. Due to the lack of a reliable method to directly identify the unit-step or unit-impulse response function, the response function is indirectly identified based on the unsteady FE force coefficients. However, the transient feature captured by the indirectly identified response function may not be consistent with the physical fluid-memory effects. A recursive function is derived for FE force simulation to reduce the computational cost of the convolution operation. Numerical examples of two tube arrays, containing both a single flexible tube and multiple flexible tubes, are provided to validate the fidelity of the time-domain simulation. It is proven that the present time-domain simulation can achieve the same level of accuracy as the frequency-domain simulation based on the unsteady FE force coefficients. The convolution-based time-domain simulation can be used to more accurately evaluate the integrity of tube arrays by considering various nonlinear effects and non-uniform flow conditions. However, the indirectly identified unit-step or unit-impulse response function may fail to capture the underlying discontinuity in the stability curve due to the prespecified expression for fluid-memory effects.


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