A new nonlinear finite fault inversion with three-dimensional Green's functions: Application to the 1989 Loma Prieta, California, earthquake

2004 ◽  
Vol 109 (B2) ◽  
Author(s):  
Pengcheng Liu ◽  
Ralph J. Archuleta
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Finite Fault Inversion ◽  
Finite Fault ◽  
Loma Prieta

scholarly journals Source study of the 1906 San Francisco earthquake

1993 ◽  
Vol 83 (4) ◽  
pp. 981-1019 ◽  
Author(s):  
David J. Wald ◽  
Hiroo Kanamori ◽  
Donald V. Helmberger ◽  
Thomas H. Heaton
Keyword(s):  
San Francisco ◽  
Green's Functions ◽  
Green’S Functions ◽  
Body Waves ◽  
Source Analysis ◽  
Amplitude Ratios ◽  
Data Set ◽  
Loma Prieta Earthquake ◽  
Finite Fault ◽  
Loma Prieta

Abstract All quality teleseismic recordings of the great 1906 San Francisco earthquake archived in the 1908 Carnegie Report by the State Earthquake Investigation Commission were scanned and digitized. First order results were obtained by comparing complexity and amplitudes of teleseismic waveforms from the 1906 earthquake with well calibrated, similarly located, more recent earthquakes (1979 Coyote Lake, 1984 Morgan Hill, and 1989 Loma Prieta earthquakes) at nearly co-located modern stations. Peak amplitude ratios for calibration events indicated that a localized moment release of about 1 to 1.5 × 1027 dyne-cm was responsible for producing the peak the teleseismic body wave arrivals. At longer periods (50 to 80 sec), we found spectral amplitude ratios of the surface waves require a total moment release between 4 and 6 × 1027 dyne-cm for the 1906 earthquake, comparable to previous geodetic and surface wave estimates (Thatcher, 1975). We then made a more detailed source analysis using Morgan Hill S body waves as empirical Green's Functions in a finite fault subevent summation. The Morgan Hill earthquake was deemed most appropriate for this purpose as its mechanism is that of the 1906 earthquake in the central portion of the rupture. From forward and inverse empirical summations of Morgan Hill Green's functions, we obtained a good fit to the best quality teleseismic waveforms with a relatively simple source model having two regions of localized strong radiation separated spatially by about 110 km. Assuming the 1906 epicenter determined by Bolt (1968), this corresponds with a large asperity (on the order of the Loma Prieta earthquake) in the Golden Gate/San Francisco region and one about three times larger located northwest along strike between Point Reyes and Fort Ross. This model implies that much of the 1906 rupture zone may have occurred with relatively little 10 to 20 sec radiation. Consideration of the amplitude and frequency content of the 1906 teleseismic data allowed us to estimate the scale length of the largest asperity to be less than about 40 km. With rough constraints on the largest asperity (size and magnitude) we produced a suite of estimated synthetic ground velocities assuming a slip distribution similar to that of the Loma Prieta earthquake but with three times as much slip. For purposes of comparison with the recent, abundant Loma Prieta strong motion data set, we “moved” the largest 1906 asperity into Loma Prieta region. Peak ground velocity amplitudes are substantially greater than those recorded during the Loma Prieta earthquake, and are comparable to those predicted by the attenuation relationship of Joyner and Boore (1988) for a magnitude MW = 7.7 earthquake.

Three-Dimensional Green’s Functions in Anisotropic Elastic Bimaterials With Imperfect Interfaces

2003 ◽  
Vol 70 (2) ◽  
pp. 180-190 ◽  
Author(s):  
E. Pan
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Imperfect Interface ◽  
Boundary Integral ◽  
Stress Fields ◽  
Superposition Method ◽  
Interface Conditions ◽  
Complementary Part ◽  
Anisotropic Elastic

In this paper, three-dimensional Green’s functions in anisotropic elastic bimaterials with imperfect interface conditions are derived based on the extended Stroh formalism and the Mindlin’s superposition method. Four different interface models are considered: perfect-bond, smooth-bond, dislocation-like, and force-like. While the first one is for a perfect interface, other three models are for imperfect ones. By introducing certain modified eigenmatrices, it is shown that the bimaterial Green’s functions for the three imperfect interface conditions have mathematically similar concise expressions as those for the perfect-bond interface. That is, the physical-domain bimaterial Green’s functions can be obtained as a sum of a homogeneous full-space Green’s function in an explicit form and a complementary part in terms of simple line-integrals over [0,π] suitable for standard numerical integration. Furthermore, the corresponding two-dimensional bimaterial Green’s functions have been also derived analytically for the three imperfect interface conditions. Based on the bimaterial Green’s functions, the effects of different interface conditions on the displacement and stress fields are discussed. It is shown that only the complementary part of the solution contributes to the difference of the displacement and stress fields due to different interface conditions. Numerical examples are given for the Green’s functions in the bimaterials made of two anisotropic half-spaces. It is observed that different interface conditions can produce substantially different results for some Green’s stress components in the vicinity of the interface, which should be of great interest to the design of interface. Finally, we remark that these bimaterial Green’s functions can be implemented into the boundary integral formulation for the analysis of layered structures where imperfect bond may exist.

THREE‐DIMENSIONAL INDUCED POLARIZATION AND ELECTROMAGNETIC MODELING

Geophysics ◽  
1975 ◽  
Vol 40 (2) ◽  
pp. 309-324 ◽  
Author(s):  
Gerald W. Hohmann
Keyword(s):  
Integral Equation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Induced Polarization ◽  
The Body ◽  
Scale Model ◽  
Two Dimensional ◽  
Electromagnetic Modeling ◽  
The Earth

The induced polarization (IP) and electromagnetic (EM) responses of a three‐dimensional body in the earth can be calculated using an integral equation solution. The problem is formulated by replacing the body by a volume of polarization or scattering current. The integral equation is reduced to a matrix equation, which is solved numerically for the electric field in the body. Then the electric and magnetic fields outside the inhomogeneity can be found by integrating the appropriate dyadic Green’s functions over the scattering current. Because half‐space Green’s functions are used, it is only necessary to solve for scattering currents in the body—not throughout the earth. Numerical results for a number of practical cases show, for example, that for moderate conductivity contrasts the dipole‐dipole IP response of a body five units in strike length approximates that of a two‐dimensional body. Moving an IP line off the center of a body produces an effect similar to that of increasing the depth. IP response varies significantly with conductivity contrast; the peak response occurs at higher contrasts for two‐dimensional bodies than for bodies of limited length. Very conductive bodies can produce negative IP response due to EM induction. An electrically polarizable body produces a small magnetic field, so that it is possible to measure IP with a sensitive magnetometer. Calculations show that horizontal loop EM response is enhanced when the background resistivity in the earth is reduced, thus confirming scale model results.

Dynamic Observer Method Based on Modified Green’s Functions for Robust and More Stable Inverse Algorithms

2008 ◽  
Author(s):  
Priscila F. B. Sousa ◽  
Ana P. Fernandes ◽  
Vale´rio Luiz Borges ◽  
George S. Dulikravich ◽  
Gilmar Guimara˜es
Keyword(s):  
Heat Transfer ◽  
Transfer Function ◽  
Green's Functions ◽  
Transfer Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Original Method ◽  
Identification Algorithm ◽  
Transfer Function Model ◽  
Function Model

This work presents a modified procedure to use the concept of dynamic observers based on Green’s functions to solve inverse problems. The original method can be divided in two distinct steps: i) obtaining a transfer function model GH and; ii) obtaining heat transfer functions GQ and GN and building an identification algorithm. The transfer function model, GH, is obtained from the equivalent dynamic systems theory using Green’s functions. The modification presented here proposes two different improvements in the original technique: i) A different method of obtaining the transfer function model, GH, using analytical functions instead of numerical procedures, and ii) Definition of a new concept of GH to allow the use of more than one response temperature. Obtaining the heat transfer functions represents an important role in the observer method and is crucial to allow the technique to be directly applied to two or three-dimensional heat conduction problems. The idea of defining the new GH function is to improve the robustness and stability of the algorithm. A new dynamic equivalent system for the thermal model is then defined in order to allow the use of two or more temperature measurements. Heat transfer function, GH can be obtained numerically or analytically using Green’s function method. The great advantage of deriving GH analytically is to simplify the procedure and minimize the estimative errors.

Sign in / Sign up

Export Citation Format

Share Document