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1.
Reducing the bias of multitaper spectrum estimates   总被引：1，自引：0，他引：1  
The power spectral density of geophysical signals provides information about the processes that generated them. We present a new approach to determine power spectra based on Thomson's multitaper analysis method. Our method reduces the bias due to the curvature of the spectrum close to the frequency of interest. Even while maintaining the same resolution bandwidth, bias is reduced in areas where the power spectrum is significantly quadratic. No additional sidelobe leakage is introduced. In addition, our methodology reliably estimates the derivatives (slope and curvature) of the spectrum. The extra information gleaned from the signal is useful for parameter estimation or to compare different signals.  相似文献   

2.
The conductivity structure of the Earth's mantle was estimated using the induction method down to 2100  km depth for the Europe–Asia region. For this purpose, the responses obtained at seven geomagnetic observatories (IRT, KIV, MOS, NVS, HLP, WIT and NGK) were analysed, together with reliable published results for 11  yr variations. 1-D spherical modelling has shown that, beneath the mid-mantle conductive layer (600–800  km), the conductivity increases slowly from about 1  S  m−1 at 1000  km depth to 10  S  m−1 at 1900  km, while further down (1900–2100  km) this increase is faster. Published models of the lower mantle conductivity obtained using the secular, 30–60  yr variations were also considered, in order to estimate the conductivity at depths down to the core. The new regional model of the lower mantle conductivity does not contradict most modern geoelectrical sounding results. This model supports the idea that the mantle base, situated below 2100  km depth, has a very high conductivity.  相似文献   

3.
The ocean geoid can be inferred from the topography of the mean sea surface. Satellite altimeters transmit radar pulses and determine the return traveltime to measure sea-surface height. The ERS-1 altimeter stacks 51 consecutive radar reflections on board the satellite to a single waveform. Tracking the time shift of the waveform gives an estimate of the distance to the sea surface. We retrack the ERS-1 radar traveltimes using a model that is focused on the leading edge of the waveforms. While earlier methods regarded adjacent waveforms as independent statistical events, we invert a whole sequence of waveforms simultaneously for a spline geoid solution. Smoothness is controlled by spectral constraints on the spline coefficients. Our geoid solutions have an average spectral density equal to the expected power spectrum of the true geoid. The coherence of repeat track solutions indicates a spatial resolution of 31  km, as compared to 41  km resolution for the ERS-1 Ocean Product. While the resolution of the latter deteriorates to 47  km for wave heights above 2  m, our geoid solution maintains its resolution of 31  km for rough sea. Retracking altimeter waveform data and constraining the solution by a spectral model leads to a realistic geoid solution with significantly improved along-track resolution.  相似文献   

4.
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5.
We explore the inner dynamics of daily geoelectrical time series measured in a seismic area of the southern Apennine chain (southern Italy). Autoregressive models and the Higuchi fractal method are applied to extract maximum quantitative information about the time dynamics from these geoelectrical signals. First, the predictability of the geoelectrical measurements is investigated using autoregressive models. The procedure is based on two forecasting approaches: the global and the local autoregressive approximations. The first views the data as a realization of a linear stochastic process, whereas the second considers the data points as a realization of a deterministic process, which may be non-linear. Comparison of the predictive skills of the two techniques allows discrimination between low-dimensional chaos and stochastic dynamics. Our findings suggest that the physical systems governing electrical phenomena are characterized by a very large number of degrees of freedom and can be described only with statistical laws. Second, we investigate the stochastic properties of the same geoelectrical signals, searching for scaling laws in the power spectrum. The spectrum fits a power law P (  f )∝  f  −α , with the scaling exponent α a typical fingerprint of fractional Brownian processes. In this analysis we apply the Higuchi method, which gives a linear relationship between the fractal dimension D Σ and the spectral power law scaling index α : D Σ=(3− α )/2. This analysis highlights the stochastic nature of geoelectrical signals recorded in this seismic area of southern Italy.  相似文献   

6.
The C -response connects the magnetic vertical component and the horizontal gradient of the horizontal components of electromagnetic variations and forms the basis for deriving the conductivitydepth profile of the Earth. Time-series of daily mean values at 42 observatories typically with 50 years of data are used to estimate C -responses for periods between 1 month and 1  yr. The Z : Y method is applied, which means that the vertical component is taken locally whereas the horizontal components are used globally by expansion in a series of spherical harmonics.
In combination with results from previous analyses, the method yields consistent results for European observatories in the entire period range from a few hours to 1  yr, corresponding to penetration depths between 300 and 1800  km.
1-D conductivity models derived from these results show an increase in conductivity with depth z to about 2  S  m-1 at z =800  km, and almost constant conductivity between z =800 and z =2000  km with values of 310  S  m-1, in good agreement with laboratory measurements of mantle material. Below 2000  km the conductivity is poorly resolved. However, the best-fitting models indicate a further increase in conductivity to values between 50 and 150  S  m-1.  相似文献   

7.
We derive both 3-D and 2-D Fréchet sensitivity kernels for surface-wave group-delay and anelastic attenuation measurements. A finite-frequency group-delay exhibits 2-D off-ray sensitivity either to the local phase-velocity perturbation  δ c / c   or to its dispersion  ω(∂/∂ω)(δ c / c )  as well as to the local group-velocity perturbation  δ C / C   . This dual dependence makes the ray-theoretical inversion of measured group delays for 2-D maps of  δ C / C   a dubious procedure, unless the lateral variations in group velocity are extremely smooth.  相似文献   

8.
Micromagnetic modelling with a Monte Carlo method was performed to obtain 2-D micromagnetic structures of pseudo-single-domain (PSD) magnetite (0.2–2.5  μm). Cubic model grains were subdivided into a 2-D array with a maximum of 100×100 cells. In order to find an appropriate cell size, the variation of the self-consistency parameter ( S ) with cell size was examined. We regard solutions with S >0.95, which corresponds to cell sizes ≤0.03  μm, as representing realistic micromagnetic structures. For saturation remanence states, we found vortex structures for small PSD grains (≤0.25  μm) and closure domain structures for larger PSD grains (0.6–2.5  μm). Between 0.25 and 0.6  μm, structures remained chaotic even after a very large number of Monte Carlo steps. In grains with a closure domain structure, domain walls were usually subdivided into several segments with opposite polarities of magnetization rotation.  相似文献   

9.
The Narmada zone in central India is a zone of weakness that separates the region of Vindhyan (Meso-Neoproterozoic) deposition to the north from Gondwana (Permo-Carboniferous–lower Cretaceous) deposits to the south. The reinterpretation of analogue seismic refraction data, acquired during the early 1980s, using 2-D ray-tracing techniques reveals a basement (velocity 5.8–6.0 km s−1 ) topography suggesting that the Narmada zone, bounded by the Narmada North and Narmada South faults is a region of basement uplift. A layer of anomalously high velocity (6.5–6.7 km s−1 ) at depths between 1.5 and 9.0 km appears to be present in the entire region. Within the Narmada zone this layer occurs at shallower depths than outside the Narmada zone. At two places within the Narmada zone this layer is at a depth of about 1.5 km. This layer cannot be considered as the top of the lower crust because in this case it should have produced large positive gravity anomalies at the shallowest parts. Instead, these parts correspond to Bouguer gravity lows. Furthermore, lower crust at such shallow depths has not been reported from any other part of the Indian shield. Therefore, this layer is likely to represent the top of a high-velocity mafic body that has different thicknesses in different places.  相似文献   

10.
Array techniques are particularly well‐suited for detecting and quantifying the complex seismic wavefields associated with volcanic activity such as volcanic tremor and long‐period events. The methods based on the analysis of the signal in the frequency domain, or spectral methods, have the main advantages of both resolving closely spaced sources and reducing the necessary computer time, but may severely fail in the analysis of monochromatic, non‐stationary signals. Conversely, the time‐domain methods, based on the maximization of a multichannel coherence estimate, can be applied even for short‐duration pulses. However, for both the time and the frequency domain approaches, an exhaustive definition of the errors associated with the slowness vector estimate is not yet available. Such a definition become crucial once the slowness vector estimates are used to infer source location and extent. In this work we develop a method based on a probabilistic formalism, which allows for a complete definition of the uncertainties associated with the estimate of frequency–slowness power spectra from measurement of the zero‐lag cross‐correlation. The method is based on the estimate of the theoretical frequency–slowness power spectrum, which is expressed as the convolution of the true signal slowness with the array response pattern. Using a Bayesian formalism, the a posteriori probability density function for signal slowness is expressed as the difference, in the least‐squares sense, between the model spectrum and that derived from application of the zero‐lag cross‐correlation technique. The method is tested using synthetic waveforms resembling the quasi‐monochromatic signals often associated with the volcanic activity. Examples of application to data from Stromboli volcano, Italy, allow for the estimate of source location and extent of the explosive activity.  相似文献   

11.
A 3-D density model was created for the Central Balkans area down to a depth of 670  km on the basis of seismic (both artificial sources and earthquakes) and gravity data. This model is based on density columns constructed for the main geological units of the study region. The densities for these columns were obtained using the density variation method. This method makes it possible to extrapolate the density distribution from the well-studied uppermost layers to the deeper levels of the Earth. The constructed 3-D density model was interpreted in relation to the available data on the heat flow and the seismicity of the region. The subdivision of the region by the Maritza fault into two parts—the southern part including the Rhodope massif and the northern part including the structures of Alpine activation of Srednogorie and the Balkanides—was confirmed. The upraised position of the 400  km boundary within the upper mantle, which was established from the density modelling, is assumed to be a sign of development of recent geodynamical processes over the Srednogorie block. From the viewpoint of seismicity prediction, a finding of mantle inhomogeneities orthogonal to the Maritza suture is of great importance.  相似文献   

12.
From ACH tomographic models to absolute velocity models   总被引：2，自引：0，他引：2  
The ACH method, a widely used tomographic inverse method, is characterized by the use of relative residuals in order to avoid possible biases coming from outside the target volume. The ACH method thus does not really retrieve the 3-D structure of the target volume, but instead leads to velocity contrasts relative to the layer average of the velocity, this average value remaining unknown ( Aki et al. 1977 ). Two artefacts derive from this particularity: (1) velocity contrasts are known only in the horizontal direction and it is not possible, in a strict mathematical sense, to estimate the contrasts in the vertical direction with ACH alone; (2) negative anomalies are often interpreted as low velocities, whereas negative anomalies may correspond to high velocities if the average value of the corresponding layer is sufficiently high. The converse is true of positive anomalies. We show with synthetic data how these artefacts can affect the interpretation of tomographic images. We propose to correct the artefacts by reintroducing the 1-D regional average model, and show in synthetic experiments how effective this correction can be.
  The application of this procedure to data recorded in the Kunlun region shows that the retrieval of the absolute values of the 3-D velocity model is helpful for interpreting the tomographic images and better defining which features are anomalous.  相似文献   

13.
The magnitude and frequency of normal-fault palaeoearthquakes are usually determined by trenching studies that ascertain the size and number of colluvial wedges along the fault. Such information can be invaluable in predicting the seismic hazard and potential for a future earthquake in that region. Digging trenches across normal faults, however, is environmentally intrusive, expensive and limited in the penetration depth. To overcome these problems we propose the use of 3-D seismic tomography as a means to identify the shapes and sizes of colluvial wedges along normal faults. As an example,2-D and 3-D seismic surveys were conducted across the Oquirrh fault, Utah with the purpose of imaging the normal-fault structure to a depth of about 10  m. Results show that the 3-D tomogram clearly delineates the fault zone and a colluvial wedge, both of which correlate extremely well with the geological cross-section interpreted from an adjacent trench. The thickness of the colluvial wedge image is used in conjunction with a seismic section to compute an estimate of a 6.8 moment magnitude earthquake for the most recent event on this fault, which is in close agreement with the 7.0 estimate based on a nearby trenching study. These tomographic results demonstrate, for the first time, that seismic imaging methods can be used in some cases to estimate unambiguously the shapes of colluvial wedges and the sizes of prehistoric earthquakes. Thus, seismic tomography has the possibility of providing cheaper, deeper and wider, but less resolved, images of fault systems than the intrusive excavation of trenches across faults.  相似文献   

14.
We present a spectral-finite-element approach to the 2-D forward problem for electromagnetic induction in a spherical earth. It represents an alternative to a variety of numerical methods for 2-D global electromagnetic modelling introduced recently (e.g. the perturbation expansion approach, the finite difference scheme). It may be used to estimate the effect of a possible axisymmetric structure of electrical conductivity of the mantle on surface observations, or it may serve as a tool for testing methods and codes for 3-D global electromagnetic modelling. The ultimate goal of these electromagnetic studies is to learn about the Earth's 3-D electrical structure.
Since the spectral-finite-element approach comes from the variational formulation, we formulate the 2-D electromagnetic induction problem in a variational sense. The boundary data used in this formulation consist of the horizontal components of the total magnetic intensity measured on the Earth's surface. In this the variational approach differs from other methods, which usually use spherical harmonic coefficients of external magnetic sources as input data. We verify the assumptions of the Lax-Milgram theorem and show that the variational solution exists and is unique. The spectral-finite-element approach then means that the problem is parametrized by spherical harmonics in the angular direction, whereas finite elements span the radial direction. The solution is searched for by the Galerkin method, which leads to the solving of a system of linear algebraic equations. The method and code have been tested for Everett & Schultz's (1995) model of two eccentrically nested spheres, and good agreement has been obtained.  相似文献   

15.
The discrimination between electrolytic and electronic conductors is highly relevant to geological modelling as it allows conclusions to be drawn about the formation and mineral composition of rocks. The induced polarization (IP) method, which compares the electric current injected into the ground with the corresponding earth potential differences can be used for this purpose.
  This paper describes a new method based on the theory that non-linear electrochemical processes on the surface of electronic conductors are responsible for non-linear IP (NLIP) phenomena. This results in multiples of the fundamental frequency being observed in the telluric voltage spectra when a monochromatic current signal is fed into the ground. The non-linearity of the current–voltage characteristic is most effectively described by a spectral method.
  A laboratory experiment was carried out, using an electrolytic trough with a small graphite cylinder serving as an electronic conductor, which clearly demonstrated the validity of the method. A field experiment was undertaken at a borehole of approximately 450  m depth, located in the transition zone of the Tepla-Barrandium and Moldanubicum in East Bavaria. A sinusoidal current was injected into the ground using a logging tool at depths varying between 150 and 450  m. The corresponding potential differences were simultaneously observed along a profile on the surface. Field and laboratory results show a striking similarity. It can be concluded that an extensive electronic conductor—probably graphite—is steeply dipping southwards meeting the borehole at approximately 310  m depth.  相似文献   

16.
We present a 3-D radially anisotropic S velocity model of the whole mantle (SAW642AN), obtained using a large three component surface and body waveform data set and an iterative inversion for structure and source parameters based on Non-linear Asymptotic Coupling Theory (NACT). The model is parametrized in level 4 spherical splines, which have a spacing of ∼ 8°. The model shows a link between mantle flow and anisotropy in a variety of depth ranges. In the uppermost mantle, we confirm observations of regions with   VSH > VSV   starting at ∼80 km under oceanic regions and ∼200 km under stable continental lithosphere, suggesting horizontal flow beneath the lithosphere. We also observe a   VSV > VSH   signature at ∼150–300 km depth beneath major ridge systems with amplitude correlated with spreading rate for fast-spreading segments. In the transition zone (400–700 km depth), regions of subducted slab material are associated with   VSV > VSH   , while the ridge signal decreases. While the mid-mantle has lower amplitude anisotropy (<1 per cent), we also confirm the observation of radially symmetric   VSH > VSV   in the lowermost 300 km, which appears to be a robust conclusion, despite an error in our previous paper which has been corrected here. The 3-D deviations from this signature are associated with the large-scale low-velocity superplumes under the central Pacific and Africa, suggesting that   VSH > VSV   is generated in the predominant horizontal flow of a mechanical boundary layer, with a change in signature related to transition to upwelling at the superplumes.  相似文献   

17.
Geological studies show evidence for temporal clustering of large earthquakes on individual fault systems. Since post-seismic deformation due to the inelastic rheology of the lithosphere may result in a variable loading rate on a fault throughout the interseismic period, it is reasonable to expect that the rheology of the non-seismogenic lower crust and mantle lithosphere may play a role in controlling earthquake recurrence times. We study this phenomenon using a 2-D, finite element method continuum model of the lithosphere containing a single strike-slip fault. This model builds on a previous study using a 1-D spring-dashpot-slider analogue of a single fault system to study the role of Maxwell viscoelastic relaxation in producing non-periodic earthquakes. In our 2-D model, the seismogenic portion of the fault slips when a predetermined yield stress is exceeded; stress accumulated on the seismogenic fault is shed to the viscoelastic layers below and recycled back to the seismogenic fault through viscoelastic relaxation. We find that random variation of the fault yield stress from one earthquake to the next can cause the earthquake sequence to be clustered; the amount of clustering depends on a non-dimensional number, W , called the Wallace number defined as the standard deviation of the randomly varied fault yield stress divided by the effective viscosity of the system times the tectonic loading rate. A new clustering metric based on the bimodal distribution of interseismic intervals allows us to investigate clustering behaviour of systems over a wide range of model parameters and those with multiple viscoelastic layers. For models with   W ≥ 1  clustering increases with increasing W , while those with   W ≤ 1  are unclustered, or quasi-periodic.  相似文献   

18.
We have been developing an accurate and efficient numerical scheme, which uses the finite-difference method (FDM) in spherical coordinates, for the computation of global seismic wave propagation through laterally heterogeneous realistic Earth models. In the field of global seismology, traditional axisymmetric modeling has been used widely as an efficient approach since it can solve the 3-D elastodynamic equation in spherical coordinates on a 2-D cross-section of the Earth, assuming structures to be invariant with respect to the axis through the seismic source. However, it has the severe disadvantages that asymmetric structures about the axis cannot be incorporated and the source mechanisms with arbitrary shear dislocation have not been attempted for a long time. Our scheme is based on the framework of axisymmetric modeling but has been extended to treat asymmetric structures, arbitrary moment-tensor point sources, anelastic attenuation, and the Earth center which is a singularity of wave equations in spherical coordinates. All these types of schemes which solve 3-D wavefields on a 2-D model cross-section are classified as 2.5-D modeling, so we have named our scheme the spherical 2.5-D FDM. In this study, we compare synthetic seismograms calculated using our FDM scheme with three-component observed long-period seismograms including data from stations newly installed in Antarctica in conjunction with the International Polar Year (IPY) 2007–2008. Seismic data from inland Antarctica are expected to reveal images of the Earth's deep interior with enhanced resolution because of the high signal-to-noise ratio and wide extent of this region, in addition to the rarity of sampling paths along the rotation axis of the Earth. We calculate synthetic seismograms through the preliminary reference earth model (PREM) including attenuation using a moment-tensor point source for the November 9, 2009 Fiji earthquake. Our results show quite good agreement between synthetic and observed seismograms, which indicates the accuracy of observations in the Antarctica, as well as the feasibility of the spherical 2.5-D modeling scheme.  相似文献   

19.
Geophysical observables are generally related to earth structure and source parameters in a complicated non-linear way. Consequently, a large number of forward modelling processes are commonly necessary to obtain a satisfactory estimate of such parameters from observed data. The most time-consuming part of the forward modelling is the computation of the Green's functions of the different earth models to be tested. In this study, we present a fast converging algorithm: the differential transform method for the computation of Green's functions in terms of spherical or cylindrical harmonics. In this method, a deconvolutable high-pass filter is used to enhance the numerical significance of the far-field spectrum of Green's functions. Compared with existing fast converging algorithms such as the Kummer's transformation and the disc factor method, the differential transform method is more efficient except for the extremely near-source region. The new method can be used to suppress numerical phases (non-physical seismic signals) associated with the aliasing effect that may arise in synthetic seismograms when the latter are computed from a windowed wavenumber (or slowness) spectrum. The numerical efficiency of the new method is demonstrated via two representative tests.  相似文献   

20.
We present a method for the retrieval of the phase velocities of surface-wave overtones. The 'single-station' method is successful for several Love and Rayleigh overtone branches (up to at least four) in mode-specific period ranges between 40 and 200 s. It uses mode-branch cross-correlation functions and relies on adjusting the phase and amplitude of the mode branches one at a time. A standard statistical optimization technique is used. We discuss in detail the a priori information that is added to stabilize the retrieval procedure. In addition, we present a technique to estimate the reliability of individual phase and amplitude measurements. The retrieval method and the technique to estimate reliabilities can be used together in a highly automated way, making the methods especially suited for studying the large volume of digital data now available.
We include several applications to synthetic and recorded waveforms. We will discuss in detail an experiment with 90 waveforms that have travelled along very similar paths from Vanuatu to California. For this path, we will present average overtone phase velocities and an average 1-D velocity structure.  相似文献   

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