• Title/Summary/Keyword: least-squares inversion

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A study of Kem County earthquake (Kern County 지진에 대한 연구)

  • 김준경
    • The Journal of Engineering Geology
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    • v.2 no.2
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    • pp.155-165
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    • 1992
  • The purpose of this study is to evaluate compatability of seismic source characteristics of the Kern County earthquake to those of Korean Peninsula seismotectonics. The compatability could be used to make Korean type response spectrum from the strong ground motions observed from the assingned earthquake. The July 21, 1952, Kern County, California, earthquake is the largest earthquake to occur in the western U.S. since 1906, and the repeat of this event poses a significant seismic hazard. The Kern County event was a complex thrusting event, with a surface rupture pattern that varied from pure leftlateral strike-slip to pure dip-slip. A time dependent moment tensor inversion was applied to ten observed teleseismic long-period body waves to investigate the source complexity. Since a conventional moment tensor inversion(constant geometry through time) returns a non-double-couple source when the seismic source changes(fault orientation and direction of slip) with time, we are required to use the time dependent moment tensor which allows a first-order mapping of the geometric and temporal complexity. From the moment tensor inversion, a two-point seismic source model with significant overlap for the White Wolf fault, which propagates upward(20 km to 5 km) from SW to NE, fits most of the observed seismic waveforms in the least squares sense. Comparison of P, T and B axes of focal mechanisms and focal depths suggests that seismic source characteristics of the Kern County earthquake is consistant with those of Korean Peninsula Seismotectonics.

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Fracture characterization with high frequency single-hole EM survey

  • Seo, Soon-Jee;Song, Yoon-Ho;Kim, Hee-Joon;Lee, Ki-Ha;Suh, Jung-Hee
    • Proceedings of the KSEEG Conference
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    • 1999.04a
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    • pp.90-93
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    • 1999
  • We present a high frequency electromagnetic (EM) inversion scheme for detecting and characterizing a fracture using single-hole data. At high frequencies, say above tens of mega-hertz, since displacement currents cannot be ignored, electrical permittivity as well as electrical conductivity is to be considered together for analyzing the EM scattering data. In this paper, we have developed a three-step inversion scheme to map the fracture and to evaluate its electrical conductivity and permittivity. We performed EM profiling along the z-axis using three-component receivers for each source. The model was excited by a vertical magnetic dipole and the resistant magnetic fields were inverted using the non-linear least-squares method. Background resistivity and permittivity were easily obtained using vertical magnetic fields below 1 MHz and above 10 MHz, respectively. Both the vertical and dipping sheets were successfully mapped using the phase difference between 40 and 41 MHz. The electrical property of the sheet was well resolved using the information obtained in the previous two steps and secondary magnetic fields. Our study shows the potential of imaging the fracture in single-hole survey environment using the high frequency EM method.

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Determination of Shallow Velocity-Interface Model by Pseudo Full Waveform Inversion (유사파형역산에 의한 천부의 속도-경계면 모델 결정)

  • Jeong, Sang Yong;Shin, Chang Soo;Yang, Seung Jin
    • Economic and Environmental Geology
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    • v.28 no.5
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    • pp.481-485
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    • 1995
  • This paper presents a new approaching method to determine the velocity and geometry of shallow subsurface from seismic refraction events. After picking the first breaks from seismic refraction data, we assume that field refraction seismogram can be replaced by the unit delta function having time shift of first break. Time curves are generated by shooting ray tracing. The partial derivatives seismogram for a damped least squares method is computed analytically at each step of the forward ray tracing. The technique is successfully tested on synthetic and real data. It has the advantage of real full waveform inversion, which is robust at low frequency band even if the initial guess is far from the true model.

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The ML scale in southern Korea (한반도 남부 지진의 지역 규모식)

  • 홍태경
    • Proceedings of the Earthquake Engineering Society of Korea Conference
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    • 2000.10a
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    • pp.73-80
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    • 2000
  • The distance correction term -logA0 of the local magnitude scale was estimated for earthquakes in southern Korea using linear least-squares inversion and interpolation scheme. Total 1054 short-period velocity seismograms from 107 local events recorded at hypocentral distances ranging from 10 to 480 km were used in this study. Simulated Wood-Anderson amplitudes were obtained from velocity seismograms with use of revised Wood-Anderson instrument response with static magnification 2080, damping factor 0.7, and natural period 0.8 sec. The estimated distance correction term for southern Korea is found to be -logA0=1.137 log(r/17) + 0.001159(r-17) + 20, where r is hypocentral distance in kilometers. The attenuation rate of this distance correction term falls between those of southern California and eastern North America.

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Improvement of Alignment Accuracy in Electron Tomography

  • Jou, Hyeong-Tae;Lee, Sujeong;Kim, Han-Joon
    • Applied Microscopy
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    • v.43 no.1
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    • pp.1-8
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    • 2013
  • We developed an improved method for tilt series alignment with fiducial markers in electron tomography. Based on previous works regarding alignment, we adapted the Levenberg-Marquardt method to solve the nonlinear least squares problem by incorporating a new formula for the alignment model. We also suggested a new method to estimate the initial value for inversion with higher accuracy. The proposed approach was applied to geopolymers. A better alignment of the tilt series was achieved than that by IMOD S/W. The initial value estimation provided both stability and a good rate of convergence since the new method uses all marker positions, including those partly covering the tilt images.

Training for Huge Data set with On Line Pruning Regression by LS-SVM

  • Kim, Dae-Hak;Shim, Joo-Yong;Oh, Kwang-Sik
    • Proceedings of the Korean Statistical Society Conference
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    • 2003.10a
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    • pp.137-141
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    • 2003
  • LS-SVM(least squares support vector machine) is a widely applicable and useful machine learning technique for classification and regression analysis. LS-SVM can be a good substitute for statistical method but computational difficulties are still remained to operate the inversion of matrix of huge data set. In modern information society, we can easily get huge data sets by on line or batch mode. For these kind of huge data sets, we suggest an on line pruning regression method by LS-SVM. With relatively small number of pruned support vectors, we can have almost same performance as regression with full data set.

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Incremental Multi-classification by Least Squares Support Vector Machine

  • Oh, Kwang-Sik;Shim, Joo-Yong;Kim, Dae-Hak
    • Journal of the Korean Data and Information Science Society
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    • v.14 no.4
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    • pp.965-974
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    • 2003
  • In this paper we propose an incremental classification of multi-class data set by LS-SVM. By encoding the output variable in the training data set appropriately, we obtain a new specific output vectors for the training data sets. Then, online LS-SVM is applied on each newly encoded output vectors. Proposed method will enable the computation cost to be reduced and the training to be performed incrementally. With the incremental formulation of an inverse matrix, the current information and new input data are used for building another new inverse matrix for the estimation of the optimal bias and lagrange multipliers. Computational difficulties of large scale matrix inversion can be avoided. Performance of proposed method are shown via numerical studies and compared with artificial neural network.

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2D Inversion of Magnetic Data using Resolution Model Constraint (분해능 모델 제한자를 사용하는 자력탐사자료의 2차원 역산)

  • Cho, In-Ky;Kang, Hye-Jin;Lee, Keun-Soo;Ko, Kwang-Beom;Kim, Jong-Nam;You, Young-June;Han, Kyeong-Soo;Shin, Hong-Jun
    • Geophysics and Geophysical Exploration
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    • v.16 no.3
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    • pp.131-138
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    • 2013
  • We developed a method for inverting magnetic data to image 2D susceptibility models. The major difficulty in the inversion of the potential data is the nonuniqueness. Furthermore, generally the number of inversion blocks are greater than the number of the magnetic data available, and thus the magnetic inversion leads to under-determined problem, which aggravates the nonuniqueness. When the magnetic data were inverted by the general least-squares method, the anomalous susceptibility would be concentrated near the surface in the inverted section. To overcome this nonuniqueness problem, we propose a new resolution model constraint that is calculated from the parameter resolution. The model constraint imposes large penalty on the model parameter with good resolution, on the other hand small penalty on the model parameter with poor resolution. Thus, the deep-seated model parameter, generally having poor resolution, can be effectively resolved. The developed inversion algorithm is applied to the inversion of the synthetic data for typical models of magnetic anomalies and is tested on real airborne data obtained at the Okcheon belt of Korea.

An Application of loop-loop EM Method for Geotechnical Survey (지반조사를 위한 loop-loop 전자탐사 기법의 적용)

  • You Jin-Sang;Song Yoonho;Seo1 Soon-Jee;Song Young-Soo
    • Geophysics and Geophysical Exploration
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    • v.4 no.2
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    • pp.25-33
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    • 2001
  • Loop-loop electromagnetic (EM) survey in frequency domain has been carried out in order to provide basic solution to geotechnical applications. Source and receiver configuration may be horizontal co-planar (HCP) and/or vertical co-planar (VCP). Three quadrature components of mutual impedance ratio for each configuration are used to construct the subsurface image. For the purpose of obtaining the model response and validating the reasonable performance of the inversion, we obtained each responses of two-layered and three-layered earth models and two-dimensional (2-D) isolated anomalous body. The response of 2-D isolated anomalous body has been calculated using extended Born approximation for the solution of 2.5-D integral equation describing EM scattering problem. As a result of the least-squares inversion with variable Lagrangian multiplier, we could construct more resolvable image from HCP data than VCP data. Furthermore, joint inversion of HCP and VCP data made better stability and resolution of the inversion. Resistivity values, however, did not exactly match the true ones. Loop-loop EM field data was obtained with EM34-3XL system manufactured by Geonics Ltd. (Canada). Electrical resistivity survey was conducted on the same line for the comparison in advance. Since the constructed image from loop-loop EM data by 2-D inversion algorithm showed almost similar resistivity distribution to that from electrical resistivity one, we expect the developed 2.5-D loop-loop EM inversion program can be applied for the reconnaissance site survey.

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Development of Inversion Analysis Framework to Determine Nonlinear Shear Moduli of Soils In Situ (현장시험을 통해 지반의 비선형 전단탄성계수를 산정하기 위한 역해석방법의 개발)

  • Ahn, Jae-Hun
    • Journal of the Korean Society of Hazard Mitigation
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    • v.8 no.3
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    • pp.87-93
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    • 2008
  • The large scale shaker can be employed to measure linear and nonlinear shear moduli of soils in situ as a function of shear strain. The method involves applying dynamic loads on a surface foundation measuring the dynamic response of the soil mass beneath the foundation with embedded instrumentation. This paper focuses on the development of a framework of the inverse analysis for the interpretation of test data to estimate linear and nonlinear shear moduli of soils along with the necessity of the inverse analysis. The suggested framework is based on the nonlinear least squares but it uses two iterative loops to account for the nonlinear behavior of soil that sensors are not located. The validity of the suggested inversion framework is tested through a series of numerical parametric studies. An example use of the suggested inversion framework is also shown. Because the field condition may affect the accuracy of suggested method, it is important to conduct a preliminary inverse analysis to quantify the discrepancy between the estimated modulus and the baseline.