scholarly journals The Effects of Atmospheric Models on the Estimation of Infrasonic Source Functions at the Source Physics Experiment

2020 ◽  
Vol 110 (3) ◽  
pp. 998-1010 ◽  
Author(s):  
Christian Poppeliers ◽  
Lauren Bronwyn Wheeler ◽  
Leiph Preston
Keyword(s):  
Green's Functions ◽  
Time Window ◽  
Green’S Functions ◽  
Atmospheric Model ◽  
Weather Data ◽  
Atmospheric Models ◽  
Data Set ◽  
Model Type ◽  
Physics Experiment ◽  
Source Physics

ABSTRACT We invert infrasound signals for an equivalent seismoacoustic source function using different atmospheric models to produce the necessary Green’s functions. The infrasound signals were produced by a series of underground chemical explosions as part of the Source Physics Experiment (SPE). In a previous study, we inverted the infrasound data using so-called predictive atmospheric models, which were based on historic, regional-scaled, publicly available weather observations interpolated onto a 3D grid. For the work presented here, we invert the same infrasound data, but using atmospheric models based on weather data collected in a time window that includes the approximate time of the explosion experiments, which we term postdictive models. We build two versions of the postdictive models for each SPE event: one that is based solely on the regional scaled observations, and one that is based on both regional scaled observations combined with on-site observations obtained by a weather sonde released at the time of the SPE. We then invert the observed data set three times, once for each atmospheric model type. We find that the estimated seismoacoustic source functions are relatively similar in waveform shape regardless of which atmospheric model that we used to construct the Green’s functions. However, we find that the amplitude of the estimated source functions is systematically dependent on the atmospheric model type: using the predictive atmospheric models to invert the data generally yields estimated source functions that are larger in amplitude than those estimated using the postdictive models.

Implementation of the Marchenko method

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. WB29-WB45 ◽  
Author(s):  
Jan Thorbecke ◽  
Evert Slob ◽  
Joeri Brackenhoff ◽  
Joost van der Neut ◽  
Kees Wapenaar
Keyword(s):  
Green's Functions ◽  
Time Window ◽  
Iterative Scheme ◽  
Green’S Functions ◽  
Neumann Series ◽  
Colorado School ◽  
Direct Inversion ◽  
Marchenko Equation ◽  
Conventional Scheme ◽  
Convergence Of The Scheme

The Marchenko method makes it possible to compute subsurface-to-surface Green’s functions from reflection measurements at the surface. Applications of the Marchenko method have already been discussed in many papers, but its implementation aspects have not yet been discussed in detail. Solving the Marchenko equation is an inverse problem. The Marchenko method computes a solution of the Marchenko equation by an (adaptive) iterative scheme or by a direct inversion. We have evaluated the iterative implementation based on a Neumann series, which is considered to be the conventional scheme. At each iteration of this scheme, a convolution in time and an integration in space are performed between a so-called focusing (update) function and the reflection response. In addition, by applying a time window, one obtains an update, which becomes the input for the next iteration. In each iteration, upgoing and downgoing focusing functions are updated with these terms. After convergence of the scheme, the resulting upgoing and downgoing focusing functions are used to compute the upgoing and downgoing Green’s functions with a virtual-source position in the subsurface and receivers at the surface. We have evaluated this algorithm in detail and developed an implementation that reproduces our examples. The software fits into the Seismic Unix software suite of the Colorado School of Mines.

scholarly journals An adapted eigenvalue-based filter for ocean ambient noise processing

Geophysics ◽  
2020 ◽  
Vol 85 (1) ◽  
pp. KS29-KS38 ◽  
Author(s):  
Guoli Wu ◽  
Hefeng Dong ◽  
Ganpan Ke ◽  
Junqiang Song
Keyword(s):  
Covariance Matrix ◽  
Ambient Noise ◽  
Green's Functions ◽  
Green’S Functions ◽  
Homogeneous Distribution ◽  
Noise Sources ◽  
Data Set ◽  
Recording Time ◽  
Receiver Array ◽  
Sample Covariance

Accurate approximations of Green’s functions retrieved from the correlations of ambient noise require a homogeneous distribution of random and uncorrelated noise sources. In the real world, the existence of highly coherent, strong directional noise generated by ships, earthquakes, and other human activities can result in biases in the ambient-noise crosscorrelations (NCCs). We have developed an adapted eigenvalue-based filter to attenuate the interference of strong directional sources. The filter is based on the statistical model of the sample covariance matrix and can separate different components of the data covariance matrix in the eigenvalue spectrum. To improve the effectiveness and make it adaptable for different data sets, a weight is introduced to the filter. Then, the NCCs can be calculated directly from the filtered data covariance matrix. This approach is applied to a 1.02 h data set of ambient noise recorded by a permanent reservoir monitoring receiver array installed on the seabed. The power spectral density indicates that the noise recordings were contaminated by strong directional noise over nearly half of the whole observation period. Beamforming and crosscorrelation results indicate that the interference still exists even after applying traditional temporal and spectral normalization techniques, whereas the adapted eigenvalue-based filter can significantly attenuate it and help to obtain improved crosscorrelations. The approach makes it possible to retrieve reliable approximations of Green’s functions over a much shorter recording time.

Green’s function implementation of common‐offset, wave‐equation migration

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1813-1821 ◽  
Author(s):  
Andreas Ehinger ◽  
Patrick Lailly ◽  
Kurt J. Marfurt
Keyword(s):  
Wave Equation ◽  
Green's Functions ◽  
Wave Equations ◽  
Green’S Functions ◽  
Data Set ◽  
Kirchhoff Migration ◽  
Migration Velocity Analysis ◽  
Standard Wave ◽  
The Cost ◽  
Wavefield Extrapolation

Common‐offset migration is extremely important in the context of migration velocity analysis (MVA) since it generates geologically interpretable migrated images. However, only a wave‐equation‐based migration handles multipathing of energy in contrast to the popular Kirchhoff migration with first‐arrival traveltimes. We have combined the superior treatment of multipathing of energy by wave‐equation‐based migration with the advantages of the common‐offset domain for MVA by implementing wave‐equation migration algorithms via the use of finite‐difference Green’s functions. With this technique, we are able to apply wave‐equation migration in measurement configurations that are usually considered to be of the realm of Kirchhoff migration. In particular, wave‐equation migration of common offset sections becomes feasible. The application of our wave‐equation, common‐offset migration algorithm to the Marmousi data set confirms the large increase in interpretability of individual migrated sections, for about twice the cost of standard wave‐equation common‐shot migration. Our implementation of wave‐equation migration via the Green’s functions is based on wavefield extrapolation via paraxial one‐way wave equations. For these equations, theoretical results allow us to perform exact inverse extrapolation of wavefields.

Forward and inverse self-potential modeling in mineral exploration

Geophysics ◽  
2008 ◽  
Vol 73 (1) ◽  
pp. F33-F43 ◽  
Author(s):  
Carlos Alberto Mendonça
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Mineral Exploration ◽  
Current Source ◽  
Target Surface ◽  
Gold Deposits ◽  
Source Terms ◽  
Data Set ◽  
Inert Electrode ◽  
Self Potential

Natural self-potential (SP) fields observed in the vicinity of conductive orebodies can be explained in terms of electrochemical reactions in which the conductors participate. Battery-like models assume that a buried conductor creates an anode-cathode pair by conveying a flow of electrons to oxidizing areas in the shallow subsurface from reducing areas at depth. For conductors with invariant composition (behaving as an inert electrode), a quantitative formulation is already available. Numerical Green’s functions are used to allow one-step evaluation of SP fields from an inert electrode model. The model is used to simulate geoelectric targets in mineral exploration and to test a procedure to obtain current source terms by inverting an SP data set. Data inversion is constrained by charge conservation and prescribes source terms at the target surface. A background resistivity model is assumed to be known and is used to recognize interfaces and evaluate numerical Green’s functions in forward and inverse modeling. The inversion procedure is applied to interpret 2D data from two gold deposits of the Yanacocha district, Peru.

A simple method to calculate Green's functions for elastic layered media

1981 ◽  
Vol 71 (4) ◽  
pp. 959-971
Author(s):  
Michel Bouchon
Keyword(s):  
Point Source ◽  
Green's Functions ◽  
Layered Medium ◽  
Time Window ◽  
Green’S Functions ◽  
Great Accuracy ◽  
Two Dimensional ◽  
Double Integral ◽  
Simple Method ◽  
Infinite Set

abstract Green's functions for an elastic layered medium can be expressed as a double integral over frequency and horizontal wavenumber. We show that, for any time window, the wavenumber integral can be exactly represented by a discrete summation. This discretization is achieved by adding to the particular point source an infinite set of specified circular sources centered around the point source and distributed at equal radial interval. Choice of this interval is dependent on the length of time desired for the point source response and determines the discretized set of horizontal wavenumbers which contribute to the solution. Comparisons of the results obtained with those derived using the two-dimensional discretization method (Bouchon, 1979) are presented. They show the great accuracy of the two methods.

Target-oriented wave-equation least-squares migration/inversion with phase-encoded Hessian

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCA95-WCA107 ◽  
Author(s):  
Yaxun Tang
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Green's Functions ◽  
Green’S Functions ◽  
Random Phase ◽  
Inverse Filtering ◽  
Data Set ◽  
Phase Encoding ◽  
Hessian Operator ◽  
Least Squares Migration

Prestack depth migration produces blurred images resulting from limited acquisition apertures, complexities in the velocity model, and band-limited characteristics of seismic waves. This distortion can be partially corrected using the model-space least-squares migration/inversion approach, where a target-oriented wave-equation Hessian operator is computed explicitly and then inverse filtering is applied iteratively to deblur or invert for the reflectivity. However, one difficulty is the cost of computing the explicit Hessian operator, which requires storing a large number of Green’s functions, making it challenging for large-scale applications. A new method to compute the Hessian operator for the wave-equation-based least-squares migration/inversion problem modifies the original explicit Hessian formula, enabling efficient computation of this operator. An advantage is that the method eliminates disk storage of Green’s functions. The modifications, however, also introduce undesired crosstalk artifacts. Two different phase-encoding schemes, plane-wave-phase encoding and random-phase encoding, suppress the crosstalk. When the randomly phase-encoded Hessian operator is applied to the Sigsbee2A synthetic data set, an improved subsalt image with more balanced amplitudes is obtained.

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.

Double-plane-wave reverse time migration in the frequency domain

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. S367-S382 ◽  
Author(s):  
Zeyu Zhao ◽  
Mrinal K. Sen ◽  
Paul L. Stoffa
Keyword(s):  
Plane Wave ◽  
Frequency Domain ◽  
Green's Functions ◽  
Green’S Functions ◽  
Plane Waves ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Time Migration ◽  
Double Plane

We have developed an efficient, accurate, and flexible plane-wave migration algorithm in the frequency domain by using a compressed and coupled-plane-wave data set, known as the double-plane-wave (DPW) data set. The DPW data set obtained by slant stacking of seismic shot profiles over source and receiver/offset represents seismic data in a fully decomposed plane-wave domain, which is called the DPW domain. A new DPW migration algorithm is derived under the Born approximation in the frequency domain, and it is referred to as the frequency-domain DPW reverse time migration (RTM). Frequency plane-wave Green’s functions need to be constructed and used during the migration. Time dips in shot profiles help to estimate the range of plane-wave decomposition. Therefore, the number of frequency plane-wave Green’s functions required for migration is limited. Furthermore, frequency plane-wave Green’s functions can be used for imaging each set of plane waves — either source or receiver/offset plane waves. As a result, the computational burden of computing Green’s function is substantially reduced; this results in increasing the migration efficiency. A selected range of plane-wave components can be migrated independently to image specific targets. Ray-parameter common-image gathers can be generated after migration without extra effort. The algorithm was tested on several synthetic data sets to show its feasibility and usefulness. The frequency-domain DPW RTM can also include anisotropy by constructing plane-wave Green’s function in anisotropic media.

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