Estimation of Slip Distribution of the 2007 Bengkulu Earthquake from GPS Observations Using the Least-Squares Inversion Method

AbstractA network of pointwise available height anomalies, derived from levelling and GPS observations, can be densified by adjusting a gravimetric quasigeoid using least-squares collocation. The resulting type of Corrector Surface Model (CSM) is applied by Norwegian surveyors to convert ellipsoidal heights to normal heights expressed in the official height system NN2000. In this work, the uncertainty related to the use of a CSM to predict differences in height anomaly was sought. As previously, the application of variograms to determine the local statistical properties of the adopted collocation model led to predictions that were consistent with their computed uncertainties. For the purpose of predicting height anomaly differences, the effect of collocation was seen to be moderate in general for the small spatial separations considered (< 10 km). However, the relative impact of collocation could be appreciable, and increasing with distance, near the network. At last, it was argued that conservative uncertainties of height anomaly differences may be obtained by rescaling output of a grid interpolation by \sqrt \Delta, where Δ is the spatial separation of the two locations for which the difference is sought.

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A NONLINEAR LEAST‐SQUARES METHOD FOR SEISMIC REFRACTION MAPPING—PART I: ALGORITHM AND PROCEDURE

Geophysics ◽

10.1190/1.1440257 ◽

1972 ◽

Vol 37 (2) ◽

pp. 260-272 ◽

Cited By ~ 6

Author(s):

Leonidas C. Ocola

Keyword(s):

Least Squares ◽

Least Squares Method ◽

Seismic Refraction ◽

Vertical Plane ◽

Nonlinear Least Squares ◽

Inversion Method ◽

Almost Everywhere ◽

Isotropic Media ◽

Time Term ◽

Nonlinear Least Squares Method

An iterative inversion method (Reframap) based on the kinematic properties of critically refracted waves is developed. The method is based on ray tracing and assumes homogeneous and isotropic media and ray paths confined to a vertical plane through each source‐detector pair. Unlike the earlier Profile or Time‐Term Methods, no restrictions are imposed on interface topography except that it be continuous almost everywhere (in the mathematical sense). As in the preexisting methods, more observations than unknowns are assumed. The algorithm and procedure, on which the Reframap Method is based, generate apparent dips for each source detector pair at the noncritical interfaces from the slope of a least‐squares line approximation to the interface functional in the neighborhood of each refraction point. In turn, the dip and path along the critical refractor is, at every iteration, pairwise approximated by a line through the critical refracting points. The incidence angles are computed recursively by Snell’s law. The solution of the overdetermined, nonlinear multiple refractor time‐distance system of simultaneous equations is sought by Marquardt’s algorithm for least‐squares estimation of critical refractor velocity and vertical thickness under each element.

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Slip distribution and source parameters of the 20 July 2017 Bodrum-Kos earthquake (Mw6.6) from GPS observations

Geodinamica Acta ◽

10.1080/09853111.2017.1408264 ◽

2017 ◽

Vol 30 (1) ◽

pp. 1-14 ◽

Cited By ~ 16

Author(s):

İ Tiryakioğlu ◽

B. Aktuğ ◽

C. Ö. Yiğit ◽

H. H. Yavaşoğlu ◽

H. Sözbilir ◽

...

Keyword(s):

Source Parameters ◽

Slip Distribution ◽

Gps Observations

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Nonlinear waveform inversion of plane‐wave seismograms in stratified elastic media

Geophysics ◽

10.1190/1.1443083 ◽

1991 ◽

Vol 56 (5) ◽

pp. 664-674 ◽

Cited By ~ 56

Author(s):

F. Kormendi ◽

M. Dietrich

Keyword(s):

Plane Wave ◽

Least Squares ◽

Wave Velocity ◽

Generalized Least Squares ◽

P Wave ◽

Gradient Algorithm ◽

Stratified Medium ◽

Inversion Method ◽

Inversion Algorithm ◽

Frequency Wave

We present a method for determining the elastic parameters of a horizontally stratified medium from its plane‐wave reflectivity. The nonlinear inverse problem is iteratively solved by using a generalized least‐squares formalism. The proposed method uses the (relatively) fast convergence properties of the conjugate gradient algorithm and achieves computational efficiency through analytical solutions for calculating the reference and perturbational wavefields. The solution method is implemented in the frequency‐wave slowness domain and can be readily adapted to various source‐receiver configurations. The behavior of the algorithm conforms to the predictions of generalized least‐squares inverse theory: the inversion scheme yields satisfactory results as long as the correct velocity trends are introduced in the starting model. In practice, the inversion algorithm should be applied first in the precritical region because of the strong nonlinear behavior of postcritical data with respect to velocity perturbations. The suggested inversion strategy consists of first inverting for the density and P‐wave velocity (or P‐wave impedance) by considering plane waves in the low slowness region (near‐normal angles of incidence), then in optimizing for the S‐wave velocity by progressively including contributions from the high slowness region (steep angles of incidence). Numerical experiments performed with noise‐free synthetic data prove that the proposed inversion method satisfactorialy reconstructs the elastic properties of a stratified medium from a limited set of plane‐wave components, at a reasonable computing cost.

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Warping least-squares inversion for 4D velocity change: Gulf of Mexico case study

Interpretation ◽

10.1190/int-2018-0145.1 ◽

2019 ◽

Vol 7 (2) ◽

pp. SB23-SB31

Author(s):

Chang Li ◽

Mark Meadows ◽

Todd Dygert

Keyword(s):

Gulf Of Mexico ◽

Least Squares ◽

Synthetic Data ◽

Inversion Method ◽

Velocity Change ◽

Data Set ◽

Phase Constraints ◽

Free Case ◽

Velocity Changes

We have developed a new trace-based, warping least-squares inversion method to quantify 4D velocity changes. There are two steps to solve for these velocity changes: (1) dynamic warping with phase constraints to align the baseline and monitor traces and (2) least-squares inversion for 4D velocity changes incorporating the time shifts and 4D amplitude differences (computed after trace alignment by warping). We have demonstrated this new inversion workflow using simple synthetic layered models. For the noise-free case, phase-constrained warping is superior to standard, amplitude-based warping by improving trace alignment, resulting in more accurate inverted velocity changes (less than 1% error). For synthetic data with 6% rms noise, inverted velocity changes are reasonably accurate (less than 10% error). Additional inversion tests with migrated finite-difference data shot over a realistic anticline model result in less than 10% error. The inverted velocity changes on a 4D field data set from the Gulf of Mexico are more interpretable and consistent with the dynamic reservoir model than those estimated from the conventional time-strain method.

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Adaptive Least-Squares Collocation Algorithm Considering Distance Scale Factor for GPS Crustal Velocity Field Fitting and Estimation

Remote Sensing ◽

10.3390/rs11222692 ◽

2019 ◽

Vol 11 (22) ◽

pp. 2692 ◽

Cited By ~ 1

Author(s):

Wei Qu ◽

Hailu Chen ◽

Shichuan Liang ◽

Qin Zhang ◽

Lihua Zhao ◽

...

Keyword(s):

Least Squares ◽

Covariance Function ◽

High Reliability ◽

Scale Factor ◽

Distance Scale ◽

Crustal Movement ◽

Least Squares Collocation ◽

Crustal Velocity ◽

Regional Tectonic ◽

Gps Observations

High-precision, high-reliability, and high-density GPS crustal velocity are extremely important requirements for geodynamic analysis. The least-squares collocation algorithm (LSC) has unique advantages over crustal movement models to overcome observation errors in GPS data and the sparseness and poor geometric distribution in GPS observations. However, traditional LSC algorithms often encounter negative covariance statistics, and thus, calculating statistical Gaussian covariance function based on the selected distance interval leads to inaccurate estimation of the correlation between the random signals. An unreliable Gaussian statistical covariance function also leads to inconsistency in observation noise and signal variance. In this study, we present an improved LSC algorithm that takes into account the combination of distance scale factor and adaptive adjustment to overcome these problems. The rationality and practicability of the new algorithm was verified by using GPS observations. Results show that the new algorithm introduces the distance scale factor, which effectively weakens the influence of systematic errors by improving the function model. The new algorithm can better reflect the characteristics of GPS crustal movement, which can provide valuable basic data for use in the analysis of regional tectonic dynamics using GPS observations.

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High-resolution prestack seismic inversion using a hybrid FISTA least-squares strategy

Geophysics ◽

10.1190/geo2013-0077.1 ◽

2013 ◽

Vol 78 (5) ◽

pp. R185-R195 ◽

Cited By ~ 32

Author(s):

Daniel O. Pérez ◽

Danilo R. Velis ◽

Mauricio D. Sacchi

Keyword(s):

High Resolution ◽

Least Squares ◽

Large Scale ◽

Cost Effective ◽

Seismic Inversion ◽

Iterative Solvers ◽

Gradient Algorithm ◽

Inversion Method ◽

Thresholding Algorithm ◽

Sparse Solutions

A new inversion method to estimate high-resolution amplitude-versus-angle attributes (AVA) attributes such as intercept and gradient from prestack data is presented. The proposed technique promotes sparse-spike reflectivities that, when convolved with the source wavelet, fit the observed data. The inversion is carried out using a hybrid two-step strategy that combines fast iterative shrinkage-thresholding algorithm (FISTA) and a standard least-squares (LS) inversion. FISTA, which can be viewed as an extension of the classical gradient algorithm, provides sparse solutions by minimizing the misfit between the modeled and the observed data, and the [Formula: see text]-norm of the solution. FISTA is used to estimate the location in time of the main reflectors. Then, LS is used to retrieve the appropriate reflectivity amplitudes that honor the data. FISTA, like other iterative solvers for [Formula: see text]-norm regularization, does not require matrices in explicit form, making it easy to apply, economic in computational terms, and adequate for solving large-scale problems. As a consequence, the FISTA+LS strategy represents a simple and cost-effective new procedure to solve the AVA inversion problem. Results on synthetic and field data show that the proposed hybrid method can obtain high-resolution AVA attributes from noisy observations, making it an interesting alternative to conventional methods.

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Correction to “Determination of rock friction constitutive parameters using an iterative least squares inversion method” by Linda A. Reinen and John D. Weeks

Journal of Geophysical Research Atmospheres ◽

10.1029/94jb00598 ◽

1994 ◽

Vol 99 (B4) ◽

pp. 7281

Author(s):

Linda A. Reinen ◽

John D. Weeks

Keyword(s):

Least Squares ◽

Inversion Method ◽

Rock Friction ◽

Constitutive Parameters

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Generalization of level-set inversion to an arbitrary number of geological units in a regularized least-squares framework

Geophysics ◽

10.1190/geo2020-0263.1 ◽

2021 ◽

pp. 1-76

Author(s):

Jérémie Giraud ◽

Mark Lindsay ◽

Mark Jessell

Keyword(s):

Least Squares ◽

Level Set ◽

Arbitrary Number ◽

Tectonic Setting ◽

Physical Property ◽

Inversion Method ◽

Regularized Least Squares ◽

Signed Distance ◽

Geological Unit ◽

Geological Units

We present an inversion method for the recovery of the geometry of an arbitrary number of geological units using a regularized least-squares framework. The method addresses cases where each geological unit can be modeled using a constant physical property. Each geological unit or group assigned with the same physical property value is modeled using the signed-distance to its interface with other units. We invert for this quantity and recover the location of interfaces between units using the level-set method. We formulate and solve the inverse problem in a least-squares sense by inverting for such signed-distances. The sensitivity matrix to perturbations of the interfaces is obtained using the chain rule and model mapping from the signed-distance is used to recover physical properties. Exploiting the flexibility of the framework we develop allows any number of rocks units to be considered. In addition, it allows the design and use of regularization incorporating prior information to encourage specific features in the inverted model. We apply this general inversion approach to gravity data favoring minimum adjustments of the interfaces between rock units to fit the data. The method is first tested using noisy synthetic data generated for a model comprised of six distinct units and several scenarios are investigated. It is then applied to field data from the Yerrida Basin (Australia) where we investigate the geometry of a prospective greenstone belt. The synthetic example demonstrates the proof-of-concept of the proposed methodology, while the field application provides insights into, and potential re-interpretation of, the tectonic setting of the area.

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