G51C-0092 0800h
Gravity Data Analysis and Forward Modelling Along the Chilean Margin at 36-42\deg S
The Chilean margin between 36 and 42\deg S is the subject of new geological and geophysical research. The information about this area come from comprehensive gravity database, field geological observations, seismic reflection profiles (amphibious wide-angle seismic experiment across the subduction zone) at 36-38\deg S, and the integrated active and passive seismological experiment ISSA 2000 at 36-39\deg S, including also the receiver function study and the local earthquake tomography model. Based on these constraining data, the 3D density model has been developed within the framework of the German Collaborative Research Center 267 "Deformation Processes in the Andes" (SFB 267, task group F4). The convergent Andean margin, which is subject to some of the earth largest earthquakes, shows pronounced along-strike changes in the tectonic setting, deformation history and its morphological expression. The study area is characterized by much lower (on average less than 2000 meters) and narrower Main Cordillera than in the Central Andes (15-33\deg S), as well as by a thinner crust. The central part of the study region is the site of the large 1960 Valdivia earthquake, which occurred onshore the transition between the oceanic lithosphere generated at two different spreading centers. This region shows no gravity high, whereas a positive Bouguer gravity anomaly is an omnipresent feature along most of the coastline south of 10\deg S. The gravity data, combined under agreements from the oil industry data and other sources, as well as the own measurements, were reprocessed and show clearly a local scale segmentation of the region under study. The results of the forward density modelling show that the position of the Nazca plate and changes in its geometry controls the gravity field. Shallower oceanic plate below the forearc region at 36-39\deg S vs. deeper slab south of 39\deg S might also have its impact on the plate coupling between the subducting and overriding plates. The modelling also indicates a shallow crust beneath the Central Depression, which is observed as well in the earthquake tomography model, together with the high velocity and density anomaly in the mantle below the Central Depression.
http://userpage.fu-berlin.de/~geoinfhb/Welcome.html
G51C-0093 0800h
New Analytical Solution for Estimation of Flexural Rigidity
In the frame of a PHD-work in the subproject F1/F4 of the Collaborative Research Center "Deformation processes in the Andes" (SFB 267) the analytical solution for estimation of the flexural rigidity (equivalent the elastic thickness) of the lithosphere based on given topography and moho undulations e.g. taken from a 3D density model or computed by an inversion from gravity data, was developed. The flexural rigidity is the parameter that governs the flexural response of the lithosphere in the meaning of a theoretical thin plate flexure model. This proposed analytical solution is an alternative methode to the widely used calculation of admittance of topography and gravity and the coherence methode, with some good advantages. Instabilities of the numerical admittance evaluation in wavenumber domain with low spectral energy of topography are overcome. The analysis can be made over an area which is much smaller than 350 km comparable to the coherence methode. The proposed methode allows a higher space resolution of elastic thickness than any other spectral methode. Instead of calculating the admittance function using spectral analysis, a set of point-load response functions is used in order to retrieve the optimal flexure parameter. Essential for the modeling is furthermore the isostatic flexure model, which is evaluated in terms of a convolutional approach (Braitenberg), thus overcoming the problems connected with a spectral analysis. This convolution methode was successfully applied in South China Sea and the Eastern Alps. Now the analytical solution is included within this convolution approach and was for the validation compared with the FFT-solution after Vening-Meinesz. This new methode has been applied in the SFB 267 working area of the Central Andes (15-$33\deg$S) and Southern Andes (36-$42\deg$S). Based on this Database the gravity field over the Andes has been used to construct 3D density models (IGMAS, Schmidt and G\"{o}tze) from which the crustal thickness variations are obtained. Constraining data of this density models come from results of other projects of the SFB 267 e.g. the crust-mantle interface depth values recovered from seismic studies, reciever function study and the shipborne bathymetry measurements. The computation of spatial variations of the flexural rigidity leads us to understand the differences between the northern and the southern part of the Andes and to distinguish e.g. some tectonical provinces. The analytical computed flexure model and the gravity model of moho depth variations agree very well over all the areas.
G51C-0094 0800h
Clarification of the NS-trending faults by analysis of borehole data and gravity inversion using the Monte Carlo method in northwestern Shikoku, Japan.
In northwestern Shikoku, Japan, several EW-trending faults related to the median tectonic line (MTL) have been investigated. However, the existence of the NS-trending faults has not yet been demonstrated as being estimated from its lineaments. On the basis of gravity data and borehole data, we investigate the basement structure and Quaternary stratigraphy under the Horie lowland, the narrow and NNW-SSE-trending alluvial lowland at the north of the Matsuyama Plain, northwestern Shikoku. We developed the gravity inversion method using the Monte Carlo method in order to estimate these underground density structures. The borehole data indicates a discontinuous change of depth on the basement surface along the western margin of the lowland. The depth of the basement surface is approximately 200 m on the east side of the step and 0-20 m on the west side. The length of the step is horizontally distributed for more than 1 km. The deposits under the Horie lowland can be categorized into five formations based on the sedimentary faces. They are composed mainly of gravel, sand, silt and clay that are intercalated with thin tuff beds. Lower formations located eastward from the step are tilted to the west at an angle of 98/1000 at a maximum, which decrease in ascending order. The Bouguer anomaly distribution was demonstrated by the gravity data of approximately 2500 points. Based on this distribution, a regional anomaly is assumed by the upward continuation method (continuation height = 2 km). This distribution shows a negative anomaly belt (minimum -3.3 mGal) in the same region of the Horie lowland. A high inclination of the anomaly value is distributed at the same location of the step of depth. A density structure was estimated by gravity inversion using the Monte Carlo method that employed known surface geology data and the density value of the basement rock and sediment as a constrained condition. The result shows the high inclined belt of the basement surface, which dip has an angle of 66 degree, distributed through the Horie Lowland. Further, its EW cross-section exhibits an asymmetric shape of the basement surface. These results are in good agreement with the basin structure on the basis of the borehole data. The existence of step of the basement surface and the anomaly tilt of the basal formation suggest fault movements by a NNW-SSE-trending fault, i.e., the Horie fault, along the western margin of the Horie lowland. It is inferred that the fault has been active during the Quaternary. The asymmetric shape of the basin and the tilted formations under the Horie lowland indicate that it is a half-graben due to an E-W extension stress. This graben can be traced for the distribution zone of the MTL active fault system on the basis of Bouguer anomaly.
G51C-0095 0800h
New Gravity and Magnetic Maps of the San Juan Volcanic Field, Southwestern Colorado
A very large simple Bouguer anomaly gravity low, about 100 km by 150 km in map view and reaching values less than -350 mGals, lies over the Oligocene San Juan volcanic field in southwestern Colorado. Roughly 15-18 different calderas represent the eruptive sources of the andesitic-rhyolitic rocks of this large volcanic field, and most are located within two swarms: the Silverton-Lake City (western) caldera complex, and the central complex that includes the Creede, Bachelor, and La Garita calderas. The prominent gravity low over the region has been previously interpreted to be due to the presence a low-density granitic batholith that underlies the volcanic field in the upper crust. However, there are complicating issues in this interpretation. First, many of the volcanic rocks are notably less dense than the Bouguer reduction density of 2.67 g/cc used for processing of the gravity data, meaning that those rocks exposed at the surface could account for a significant portion of the gravity low. Second, the extreme topographic relief in the region requires that terrain corrections (always positive algebraically) be applied. To meet these needs, a new complete Bouguer gravity map of the volcanic field has been prepared using the new traditionally terrain corrected U. S. gravity database. Modeling these data show that the caldera fill is a major contributor to the gravity low but that an upper crustal batholith is also required to satisfy the observed data. In addition, a second map is being prepared. It is derived by applying a new complex Bouguer correction that takes geologically reasonable surface densities and digital elevation data into account, and as a result will provide a much clearer picture of the nature of the subsurface batholith. A new aeromagnetic map of the region has also been completed. This represents a significant improvement over previous merging efforts in southwestern Colorado, as numerous and previously under-utilized high-resolution aeromagnetic datasets were used in the compilation. The new map is highly complex in detail, as it is largely dominated by numerous short-wavelength anomalies sourced by volcanic rocks. A pseudogravity transformation of the aeromagnetic anomalies reveals prominent highs associated with the western and central caldera swarms, possibly representing structural and/or petrologic variations within the sub-caldera upper crust.
G51C-0096 0800h
Integrated Three-Dimensional Gravity Modelling in Different Types of Geological Environments
Three-dimensional (3-D) interactive modelling permits an integrated processing and interpretation of geoid, gravity and magnetic fields, yielding an improved geologic interpretation. Generally 3-D models are constructed by triangulated polyhedra to which constant density and/or induced and remnant susceptibility are assigned. Interactive modifications of model parameters (geometry, density, susceptibility), access to the numerical modelling process, and direct visualization of both calculated and measured fields of gravity and magnetics, enable the interpreter to design the model as realistic as possible (forward modelling). An approach is described to integrate constraining data into the interactive modelling process by means of visualizing and combining geodata with the density/susceptibility model. This visual combination of different 2- and 3-D models enables a quantitative comparison and adjustment, and results in a model comprising as much independently derived information as possible. The definition of 'geo-objects', which link geoscientific vocabulary with geometrical elements of the model, provides a comfort environment for interpretational discussions in front of the computer monitor. We present different cases of three dimensional density modelling using an object oriented GIS module (IGMAS); from 1) Subduction zone (Andes), 2) Collision zone (Alps), 3) Transform zone (Dead Sea Rift and Aqaba), 4) Sedimentary basins (North west Germany), and 5) Continental Rift systems (East African Rift). The modelling helped to shed some light on variations of subduction geometries and crustal thickness along the Andes, on the collision and interaction of the European and Adriatic plates, basin structures and sedimentary thickness in Germany and underlying rift structures in the Afro-Arabian rift system. The results demonstrate the capability and robustness of three-dimensional potential field modelling to study major geological processes that constantly change our planet.
http://www.geophysik.uni-kiel.de/~sabine/Sabine_IGMAS.html
G51C-0097 0800h
Three algorithms for the computation of tidal loading and their numerical accuracy
In this paper the efficiency and numerical accuracy of three algorithms to compute tidal loading is reviewed. The interest goes to vertical deformations and the self attraction and loading effect caused by ocean tides. Load calculations require evaluation of convolution integrals over the sphere. In order to assess the numerical accuracy of a load calculation procedure we recall that there exists an almost exact point-wise integration method. This recipe is suitable for computations at individual stations, unfortunately the algorithm is rather expensive for evaluations on a global grid. The other two algorithms are fast implementations of this procedure, the first relies on the use of spherical harmonics and multiplication in the spectral domain of ocean tide spherical harmonic coefficients times the Green function coefficients expanded in a series of zonal Legendre functions. An alternative is a new method that only relies on rotational symmetry on the sphere. The performance of both field methods deteriorates near coastal boundaries where the average error is about 3 mm, while some part of this error is radiating outward into nearby coastal seas and continents. In rare extreme cases there are localized errors reaching 10 mm. The conclusion is that accurate load and SAL tides in coastal area's should be computed with a point-wise method rather than a field method, that the FFT method is compatible to the spherical harmonics method, and that all field methods are capable of tidal dissipation errors in coastal seas as large as 100 $\mbox{mWatt/m} ^2$ whereas open ocean dissipation errors are typically a factor 100 smaller.
G51C-0098 0800h
Gravity Inversion Predicts Sediment Thickness in the Norwegian-Greenland Sea
The Norwegian-Greenland Sea has formed by the Eurasia and Greenland plates separating across the Mohn and Knipovich ridges since the earliest Eocene. Whereas the Lofoten Basin on the Norwegian side is relatively well mapped by multi-channel (MCS) and wide-angle seismic data, few details are known about sediments in the Greenland and Boreas basins offshore Greenland. However, the gravity field of the entire sea is freely available from satellite altimetry, as is the bathymetry from the International Bathymetric Chart of the Arctic Ocean. We therefore explore the feasibility of using these gridded datasets along with prior geological knowledge in a 3-D prediction of sediment thickness beyond seismic calibration points. Although this problem is similar to other workers$\'{}$ predictions of bathymetry or crustal thickness, we find it difficult to separate the gravity signal of deep-ocean sediments from that of the underlying basement. Moreover, the thermal mantle structure beneath midocean ridges and continental margins is only in part compensated by the crustal topography, thus gravity modeling of only shallow surfaces may be misleading. We mitigate these problems by first assuming that the oceanic crust has constant density and thickness. Second, we approximate the thermal gravity field by the field calculated for a stack of 2-D finite-difference models of the seafloor spreading and cooling. The inversion is carried out by an iterative scheme where 1) the bottom of the sediment layer is calculated by damped downward continuation of the residual gravity; and 2) an updated residual is forward calculated from the Parker formula. The model space is further constrained by depths and density estimates from boreholes and an extensive velocity database. The maximum-likelihood solution predicts sediment basins on spatial scales greater than 20-25 km. It broadly agrees with existing MCS profiles in areas where the oceanic crust follows our assumptions, but is less accurate near seamounts and submarine ridges. We expect that our method can be used as a rapid 3-D exploration tool in frontier areas where seismic data are sparse due to logistic challenges or previous lack of commercial interest, notably in the Arctic Ocean.
G51C-0099 0800h
Spherical Harmonic Representation of Very High Resolution Global Datasets
Spherical harmonics have traditionally been used to represent potential fields of the Earth such as gravity and magnetic fields. This allows a convenient way of storing information about the field in terms of spectral coefficients of the spherical harmonic transform and reproducing it using the inverse spherical harmonic transform. As more data are obtained, especially from satellites, the spectral coefficients can be recomputed to better define precision and resolution of the field. Recently, spherical harmonics have also been used to model topography and other observable properties of the Earth and other planets. The dense global datasets can be preserved properly by using very high degree and order spherical harmonics. This, however, presents two challenges. First, the numerical stability of computations and second, the computational efforts required. For kilometer scale resolution, this research has explored both challenges for analysis and synthesis, and proposes solutions using Chebychev quadrature and recent advances in 64-bit arithmetic as well as parallel and grid computations. The developed algorithms are computationally efficient and numerically stable for all kinds of applications.
G51C-0100 0800h
Improved Global Marine Gravity Field From Reprocessing of Geosat and ERS-1 Radar Altimeter Waveforms
The Geosat and ERS-1 radar altimeter satellites have mapped the global marine gravity field down to 20 to 30 km full wavelengths with errors of 3 to 8 milliGals (mGal). This mapping is adequate to reveal the main features of the ocean floor but we would like to resolve more detail. At shorter wavelengths the altimeter error budget is dominated by random errors caused by ocean waves. We have reprocessed nearly one billion radar waveforms returned to the Geosat and ERS1 spacecraft from the ocean surface, using an algorithm designed to minimize the sea surface slope error and decouple it from significant wave height (SWH) error. Standard waveform retracking algorithms include 5 parameters - sea surface height, SWH, return amplitude, pre-return noise, and decay caused by attitude excursion. We model Geosat waveforms using all 5 parameters while ERS-1 needs only a 3-parameter model because pre-return noise is truncated and nadir pointing is accurately maintained. In both cases, the least-squares objective function is non-linear in sea surface height and SWH, and we find maximum-likelihood weighting increases the correlation of errors in these two parameters. To minimize the noise caused by ocean waves, we fit a multi-parameter model to each waveform, smooth the parameters along track, and then refit the height parameter only while fixing the other parameters to smoothed values. The result yields sea surface slope errors 40% smaller than previously obtained, and relatively insensitive to SWH. Sandwell and Smith [this meeting] show the improved resolution of seamounts. While our method is optimized for gravity field recovery, it may also improve the resolution of sea surface height signals of interest in physical oceanography and global sea level rise [Lillibridge et al, this meeting]. Our dataset also eliminates the along-track phase shift inherent in the on-board tracker.
G51C-0101 0800h
Improving gravity field models on short wavelength with the help of non-gravitational observations
Geoid models over oceanic areas are determined on the basis of a combination of satellite, air-borne and ship-borne gravity-related observations. Inconsistencies between the different data-types and the different observational campaigns introduce significant errors affecting particularly shorter wavelengths. The marine geoid is closely linked to sea surface height and the dynamic topography of the sea surface. Therefore, independent observations of the sea surface height and the dynamic topography can be used to identify errors in the geoid models and eventually help to remove inconsistencies in the database leading to these errors. However, sea surface heights determined from satellite altimetry and dynamic topography models determined from oceanographic observations or ocean circulation models have their own error characteristics which need to be taken into account in studying the quality of the geoid models. We will focus on the methodology to analysis the quality and errors of different models for the marine geoid, mean dynamic topography and mean sea surface heights through consistency studies utilising their interrelation. Based on spatial correlation coefficients, a large number of models of the three quantities given for the North Atlantic will be intercompared and their degree of consistency quantified. As a result, the geographical locations of areas with high probability for inconsistencies in the database used for geoid computation will be discussed.
G51C-0102 0800h
Spatiospectral concentration and spectral analysis of potential fields on the sphere
Physical properties, such as the elastic strength or the magnetization depth of a planetary lithosphere can be estimated from the cross-spectral properties of potential fields. Such data are most commonly available as bandlimited spherical harmonic coefficients, measured by artificial satellites or spacecraft. In many if not most applications, planetary curvature prohibits the use of locally flat approximations. Thus, the determination of spatially localized estimates of planetary properties requires spatiospectral localization methods that go beyond those available in the plane. Single spherical windows or tapers have been developed and applied in a number of recent studies; however, these are neither optimally concentrated, nor as reliable as an orthogonal family of multitapers in the extraction of robust localized statistical information from bandlimited spherical data. Here, we pose and solve the analogue of Slepian's time-frequency concentration problem on the surface of the unit sphere to determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of the sphere, or, alternatively, of strictly spacelimited functions that are optimally concentrated within the spherical harmonic domain. Such a basis of simultaneously spatially and spectrally concentrated functions should be a useful data analysis and representation tool in a variety of geophysical and planetary applications, as well as in medical imaging, computer science, cosmology and numerical analysis. The spherical Slepian functions can be found either by solving an algebraic eigenvalue problem in the spectral domain or by solving a Fredholm integral equation in the spatial domain. The associated eigenvalues are a measure of the spatiospectral concentration. When the concentration region is an axisymmetric polar cap the spatiospectral projection operator commutes with a Sturm-Liouville operator; this enables the eigenfunctions to be computed extremely accurately and efficiently, even when their area-bandwidth product, or Shannon number, is large. In the asymptotic limit of a small concentration region and a large spherical harmonic bandwidth the spherical concentration problem approaches its planar equivalent, which exhibits self-similarity when the Shannon number is kept invariant. Our examples show families of bandlimited spherical harmonic expansions that are localized to Earth's continents. In a related presentation, we investigate the ability of our orthogonal data tapers to obtain spectral estimates by analyzing the bias and variance properties of the multitaper estimator constructed using our windows.
http://www.frederik.net