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At least 19 records

Monte Carlo inversion of seismic data

The analytic solution to the linear inverse problem provides estimates of the uncertainty of the solution in terms of standard deviations of corrections to a particular solution, resolution of parameter adjustments, and information distribution among the observations. It is shown that Monte Carlo inversion, when properly executed, can provide all the same kinds of information for nonlinear problems. Proper execution requires a relatively uniform sampling of all possible models. The expense of performing Monte Carlo inversion generally requires strategies to improve the probability of finding passing models. Such strategies can lead to a very strong bias in the distribution of models examined unless great care is taken in their application.

Wiggins, R. A.↗

Computational methods for estimation of parameters in hyperbolic systems

Approximation techniques for estimating spatially varying coefficients and unknown boundary parameters in second order hyperbolic systems are discussed. Methods for state approximation (cubic splines, tau-Legendre) and approximation of function space parameters (interpolatory splines) are outlined and numerical findings for use of the resulting schemes in model "one dimensional seismic inversion' problems are summarized.

Banks, H. T.↗

Seismic analysis of the solar interior. I - Can opacity changes improve the theoretical frequencies?

The paper describes the application of seismic inverse theory to the deduction of properties of the solar interior using presently available measured frequencies of the solar oscillations. Only the solar opacity is included in this application. This study has used the spectral expansion method of Lanczos and Jackson to derive changes to the opacity which improve agreement between the theoretical and observed frequencies of oscillation. It is found that a family of opacity changes exists which yields models that improve the frequency agreement by amounts that are indistinguishable among the family members.

Korzennik, Sylvain G.↗

The Effect of Redox Conditions on Seismic Waves in Iron-Bearing Olivine: Implications for Understanding Planetary Interiros Through Seismilogy

Seismic data, inclusive of velocities and attenuation, can be utilized to elucidate the physical state of planetary interiors]. However, numerous micromechanical factors have been either experimentally demonstrated, or theoretically considered, to affect the propagation and dissipation of seismic energy within crystalline solids - including, but not limited to, changes in grain size, temperature, melt fraction, pressure and dislocation density. Thus, observed variations in seismic wave speeds and attenuation may be used to ultimately ‘map’ variations in physical properties, such as those listed above, within planetary bodies. But, in order to complete a successful inversion of seismic data into representations of physical properties, a first requirement is to obtain a fundamental laboratory based understanding of how each of these possible factors individually influences seismic waves. Here we conduct an experimental study with the initial objective to further understand one of the most commonly invoked, yet least studied, mechanisms that could alter intrinsic seismic wave attenuation: water content (occurring as chemically-bound hydroxyl). The historical basis for determining the effect of water on seismic properties was established predominantly through analogy with large-strain creep experiments conducted on olivine under water-saturated conditions. While these deformation experiments routinely demonstrate a weakening of olivine in the presence of water, they represent a fundamentally different deformation regime in comparison to the microstrains experienced due to a passing seismic wave. Thus, in order to directly assess the effects of water on seismic properties, small-strain experiments are required. Substantially modified seismic properties in the presence of water have been observed previously at low strains and low frequencies, but only in a single exploratory study conducted under water-saturated conditions. Thus, to properly test the theoretical predictions we conducted a systematic study of the seismic properties of olivine using low-frequency torsional oscillation on aggregates containing varying concentrations of bound hydroxyl, for the first time at under saturated conditions.

Cline, C. J., II↗

The 26 December 2004 tsunami source estimated from satellite radar altimetry and seismic waves

The 26 December 2004 Indian Ocean tsunami was the first earthquake tsunami of its magnitude to occur since the advent of both digital seismometry and satellite radar altimetry. Both have independently recorded the event from different physical aspects. The seismic data has then been used to estimate the earthquake fault parameters, and a three-dimensional ocean-general-circulation-model (OGCM) coupled with the fault information has been used to simulate the satellite-observed tsunami waves. Here we show that these two datasets consistently provide the tsunami source using independent methodologies of seismic waveform inversion and ocean modeling. Cross-examining the two independent results confirms that the slip function is the most important condition controlling the tsunami strength, while the geometry and the rupture velocity of the tectonic plane determine the spatial patterns of the tsunami.

ocean general circulation model (OGCM)↗

GRAIL Refinements to Lunar Seismic Structure

Joint interpretation of disparate geophysical datasets helps to reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly co‐located at one corner. Due to this limited geographical extent, near‐surface ray coverage from moonquakes is low, but increases with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefore well suited to joint inversion, since the complementary information reduces inherent model ambiguity. Previous joint inversions of the Apollo seismic data (seismic phase arrival times) and Clementine‐ or Lunar Prospector‐derived gravity data (mass and moment of inertia) attempted to recover the subsurface structure of the Moon by focusing on hypothetical lunar compositions that explore the density/velocity relationship. These efforts typically search for the best fitting thermodynamically calculated velocity/density model, allowing variables like core size, velocity, and/or composition to vary freely. Seismic velocity profiles previously derived from the Apollo seismic data through inversion of travel times vary both in the depth of the crust and mantle layers, and the seismic velocities and densities assigned to those layers. The lunar mass and moment of inertia likewise only constrain gross variations in the density profile beyond that of a uniform density sphere. As a result, composition and structure models previously obtained by jointly inverting these data retain the original uncertainties inherent in the input data sets. We will perform a joint inversion of Apollo seismic delay times and gravity data collected by the GRAIL lunar gravity mission, in order to recover seismic velocities and density as a function of latitude, longitude, and depth within the Moon. We will relate density to seismic velocity using a linear relationship that is allowed to be depth‐dependent. The corresponding coefficient (B) can reflect a variety of material properties that vary with depth, including temperature and composition. The inversion seeks to recover the set of density, velocity, and B‐coefficient perturbations that minimize (in a least‐squares sense) the difference between the observed and calculated data.

Weber, Renee C.↗

Analysis of Lunar Seismic Signals: Determination of Instrumental Parameters and Seismic Velocity Distributions

Inverse filters were designed to correct the effect of instrumental response, coupling of the seismometer to the ground, and near surface structures. The least squares technique was used to determine the instrumental constants and the transfer functions of the long period lunar seismographs. The influence of noise and the results of these calculations are discussed.

Horvath, P.↗

GRAIL Refinements to Lunar Seismic Structure

Joint interpretation of disparate geophysical datasets helps reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly co-located at one corner. Due to this limited geographical extent, near-surface ray coverage from moonquakes is low, but increases with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefore well suited to joint inversion, since the complementary information reduces inherent model ambiguity. Previous joint inversions of the Apollo seismic data (seismic phase arrival times) and Clementine- or Lunar Prospector-derived gravity data (mass and moment of inertia) attempted to recover the subsurface structure of the Moon by focusing on hypothetical lunar compositions that explored the density/velocity relationship. These efforts typically searched for the best fitting thermodynamically calculated velocity/density model, and allowed variables like core size, velocity, and/or composition to vary freely. Seismic velocity profiles derived from the Apollo seismic data through travel time inversion vary both in the depth of the crust and mantle layers, and the seismic velocities and densities assigned to those layers. The lunar mass and moment of inertia likewise only constrain gross variations in the density profile beyond that of a uniform density sphere. As a result, composition and structure models previously obtained by jointly inverting these data retain the original uncertainties inherent in the input data sets. We perform a joint inversion of Apollo seismic delay times and gravity data collected by the GRAIL lunar gravity mission, in order to recover seismic velocity and density as a function of latitude, longitude, and depth within the Moon. We relate density (p) to seismic velocity (v) using a depth-dependent linear relationship. The corresponding coefficient (B) can reflect a variety of material properties, including temperature and composition. The inversion seeks to recover the set of p, v, and B perturbations that minimize (in a least-squares sense) the difference between the observed and calculated data.

Weber, Renee C.↗

GRAIL Refinements to Lunar Seismic Structure

Joint interpretation of disparate geophysical datasets helps reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly co-located at one corner. Due to this limited geographical extent, near-surface ray coverage from moonquakes is low, but increase with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefor well suited to joint inversion, since the complementary information reduces inherent model ambiguity. We will perform a joint inversion of Apollo seismic delay times and gravity data collected by GRAIL lunar gravity mission, in order to recover seismic velocity and density as a function of latitude, longitude and depth within the Moon. We will relate density (rho) to seismic velocity (v) using a linear relationship that is allowed to be depth-dependent. The corresponding coefficient (B) can reflect a variety of material properties that vary with depth, including temperature and composition. The inversion seeks to recover the set of rho, v, and B perturbations that minimize (in a least-squares sense) the difference between the observed and calculated data.

Weber, Renee C.↗

Grail Refinements to Lunar Seismic Structure

To probe a planet's interior, seismology provides the most direct constraints on the variables that govern the dynamic properties of the body. However, the GRAIL (Gravity Recovery and Interior Laboratory) mission's high-resolution measurements of the lunar gravity field provide constraints on crustal thickness, mantle structure, core radius and stratification, and core state (solid vs. molten). These data complement seismic investigations, and joint interpretation permits improved constraints on the Moon's internal structure. Joint interpretation of disparate geophysical datasets helps reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly co-located at one corner. Due to this limited geographical extent, near-surface ray coverage from moonquakes is low, but increase with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefor well suited to joint inversion, since the complementary information reduces inherent model ambiguity. We will perform a joint inversion of Apollo seismic delay times and gravity data collected by GRAIL lunar gravity mission, in order to recover seismic velocity and density as a function of latitude, longitude and depth within the Moon. We will relate density (rho) to seismic velocity (v) using a linear relationship that is allowed to be depth-dependent. The corresponding coefficient (B) can reflect a variety of material properties that vary with depth, including temperature and composition. The inversion seeks to recover the set of rho, v, and B perturbations that minimize (in a least-squares sense) the difference between the observed and calculated data.

Weber, Renee C.↗

GRAIL Refinements to Lunar Seismic Structure

The present ]day internal structure of the Moon provides insight not only into its own formation and evolution, but also that of all rocky planetary bodies. The most direct way to probe a planet fs interior structure is through seismology. As part of the Apollo lunar missions, four seismometers were deployed on the nearside surface of the Moon between the years 1969 and 1972. These instruments operated continuously until 1977, forming the only substantial extraterrestrial seismic data set in existence. These data have been used to constrain various aspects of the seismic velocity and density structure of the Moon. Typical 1-D models recognize a 30-60 km thick crust overlying a nearly constant ]velocity mantle, and extend to a depth of approximately 1000 km, below which the lack of penetrating moonquake ray ]paths precludes the seismic determination of deeper structure. Previously, the lack of observed moonquakes from the far side of the Moon has been used to infer the presence of a highly attenuating (possibly molten) core. Indirect geophysical measurements such as moment of inertia, magnetic induction, lunar laser ranging, and elemental abundances of mare basalts also place varying constraints on core size and state. In combination with seismic studies, these indirect measurements have been used to arrive at a commonly accepted model of the Moon's deepest interior that includes a solid inner and fluid outer core, overlain by a partial melt boundary layer. We recently applied modern array seismology techniques to the Apollo data and revealed detailed core structure, including the first direct confirmation of the presence of a solid inner core. Our study focused on the identification of core ]reflected phases in deep moonquake seismograms. The resulting model of the Moon fs innermost structure was found to be consistent with the commonly accepted model. However, the modeled layer radii may vary by tens of kilometers, as is expected when accounting for uncertainties such as moonquake location, timing errors, and potential seismic heterogeneities. In addition, the modeled velocities may vary with a 1-to-1 trade ]off with the modeled reflector depth. The GRAIL (Gravity Recovery and Interior Laboratory) mission, launched in Sept. 2011, placed two nearly identical spacecraft in lunar orbit. The two satellites make extremely high-resolution measurements of the lunar gravity field, which can be used to constrain the interior structure of the Moon using a "crust to core" approach. GRAIL fs constraints on crustal thickness, mantle structure, core radius and stratification, and core state (solid vs. molten) will complement seismic investigations in several ways. Here we present a progress report on our efforts to advance our knowledge of the Moon fs internal structure using joint gravity and seismic analyses. We will focus on methodology, including 1) refinements to the seismic core constraint accomplished through array processing of Apollo seismic data, made by applying a set of travel time corrections based on GRAIL structure estimates local to each Apollo seismic station; 2) modeling deep lunar structure through synthetic seismograms, to test whether the seismic core model can reproduce the core reflections observed in the Apollo seismograms; and 3) a joint seismic and gravity inversion in which we attempt to fit a family of seismic structure models with the gravity constraints from GRAIL, resulting in maps of seismic velocities and densities that vary from a nominal model both laterally and with depth.

Weber, Renee↗

Large-scale sparse singular value computations

Four numerical methods for computing the singular value decomposition (SVD) of large sparse matrices on a multiprocessor architecture are presented. Lanczos and subspace iteration-based methods for determining several of the largest singular triplets (singular values and corresponding left and right-singular vectors) for sparse matrices arising from two practical applications: information retrieval and seismic reflection tomography are emphasized. The target architectures for implementations are the CRAY-2S/4-128 and Alliant FX/80. The sparse SVD problem is well motivated by recent information-retrieval techniques in which dominant singular values and their corresponding singular vectors of large sparse term-document matrices are desired, and by nonlinear inverse problems from seismic tomography applications which require approximate pseudo-inverses of large sparse Jacobian matrices.

Berry, Michael W.↗

A statistical technique for processing radio interferometer data

The output of a radio interferometer is the Fourier transform of the object under investigation. Due to the limited coverage of the Fourier plane, the reconstruction of the image of the source is blurred by the beam of the synthesized array. A maximum-likelihood processing technique is described which uses the statistical properties of the received noise-like signals. This technique has been used extensively in the processing of large-aperture seismic arrays. This inversion method results in a synthesized beam that is more uniform, has lower sidelobes, and higher resolution than the normal Fourier transform methods. The maximum-likelihood method algorithm was applied successfully to very long baseline and short baseline interferometric data.

Papadopoulos, G. D.↗

Backus-Gilbert inversion of travel time data

Application of the Backus-Gilbert theory for geophysical inverse problems to the seismic body wave travel-time problem is described. In particular, it is shown how to generate earth models that fit travel-time data to within one standard error and having generated such models how to describe their degree of uniqueness. An example is given to illustrate the process.

Johnson, L. E.↗

On the joint inversion of geophysical data for models of the coupled core-mantle system

Joint inversion of magnetic, earth rotation, geoid, and seismic data for a unified model of the coupled core-mantle system is proposed and shown to be possible. A sample objective function is offered and simplified by targeting results from independent inversions and summary travel time residuals instead of original observations. These data are parameterized in terms of a very simple, closed model of the topographically coupled core-mantle system. Minimization of the simplified objective function leads to a nonlinear inverse problem; an iterative method for solution is presented. Parameterization and method are emphasized; numerical results are not presented.

Voorhies, Coerte V.↗

The distribution of seismic velocities and attenuation in the earth

Estimates of the radial distribution of seismic velocities and density and of seismic attenuation within the earth are obtained through inversion of body wave, surface wave, and normal mode data. The effect of attenuation related dispersion on gross earth structure, and on the reliability of eigenperiod identifications is discussed. The travel time baseline discrepancies between body waves and free oscillation models are examined and largely resolved.

Hart, R. S.↗