This document describes a study investigating seismic velocity imaging of lithospheric delamination. The goal is to map pressure and temperature data from a numerical model of delamination to seismic velocities using the van Wijk method. This will allow imaging of a delamination similar to the Isabella anomaly in the Sierra Nevada mountains. The model includes different earth layers with varying densities and rheologies. Governing equations for the model are provided. Temperature and pressure profiles are interpolated onto a grid. Initial velocities are calculated from pressure and temperature at infinite frequency. Shear wave velocities are then calculated by including an attenuation factor. Compressional wave velocities are determined from shear wave velocities using Poisson's ratio. Velocity deviations from a reference value will be analyzed
This document summarizes a study on the effects of radiation on magnetohydrodynamic (MHD) free convection flow of a viscous fluid past an exponentially accelerated vertical plate. The governing equations are solved numerically using an implicit finite difference Crank-Nicolson method. It is found that the fluid velocity decreases with increasing magnetic field or radiation parameter. Fluid temperature also decreases with stronger radiation. Shear stress and heat transfer at the plate increase and decrease, respectively, with higher radiation or magnetic parameters.
Saturns fast spin_determined_from_its_gravitational_field_and_oblatenessSérgio Sacani
ARtigo descreve o novo método usado para determinar com precisão o período de rotação do planeta Saturno. Uma das grandes questões da astronomia. De acordo com o artigo o período de rotação de Saturno é de 10 horas 32 minutos e 45 segundos (+/- 46 segundos).
The document summarizes an empirical ground motion model developed as part of the PEER Next Generation Attenuation (NGA) project. Key points:
- The model predicts peak ground acceleration, velocity, displacement, and response spectra for shallow crustal earthquakes in active tectonic regions.
- It is based on over 1,500 recordings from 64 earthquakes ranging in magnitude from 4.3 to 7.9 and distances from 0.1 to 199 km.
- The model accounts for magnitude, distance, faulting style, depth, directivity, site conditions, and variability between events and recordings.
This document analyzes pore pressure generation and dissipation in cohesionless materials during seismic loading. It develops an efficient solution based on a multiple time scale analysis. The solution splits the problem into two sub-problems based on different time scales: 1) a fast time scale related to cyclic loading and 2) a slow time scale related to drainage. It presents the theoretical framework and describes implementing the solution in a finite element code to predict pore pressure development under a bridge pier foundation during an earthquake. The goal is to limit excessive pore pressure increase that could compromise foundation stability.
This document summarizes a research paper that examines the steady magnetohydrodynamic mass transfer flow of a polar fluid through a porous medium bounded by an infinite vertical porous plate. The paper presents the governing equations for the fluid flow, angular momentum, energy, and concentration considering effects such as magnetic field, thermal diffusion, and radiation. Exact solutions for the velocity, angular velocity, temperature, and concentration fields are obtained. The skin friction and heat transfer rate are also derived. Graphs illustrate the effects of various parameters on the flow behavior and transport properties.
Nanofluid Flow past an Unsteady Permeable Shrinking Sheet with Heat Source or...IJERA Editor
The consideration of nanofluids has been paid a good attention on the forced convection; the analysis focusing
nanofluids in porous media are limited in literature. Thus, the use of nanofluids in porous media would be very
much helpful in heat and mass transfer enhancement. In this paper, the influence of variable suction, Newtonian
heating and heat source or sink heat and mass transfer over a permeable shrinking sheet embedded in a porous
medium filled with a nanofluid is discussed in detail. The solutions of the nonlinear equations governing the
velocɨty, temperature and concentration profiles are solved numerically using Runge-Kutta Gill procedure
together with shooting method and graphical results for the resulting parameters are displayed and discussed.
The influence of the physical parameters on skin-friction coefficient, local Nusselt number and local Sherwood
number are shown in a tabulated form.
This document summarizes a study on the effects of radiation on magnetohydrodynamic (MHD) free convection flow of a viscous fluid past an exponentially accelerated vertical plate. The governing equations are solved numerically using an implicit finite difference Crank-Nicolson method. It is found that the fluid velocity decreases with increasing magnetic field or radiation parameter. Fluid temperature also decreases with stronger radiation. Shear stress and heat transfer at the plate increase and decrease, respectively, with higher radiation or magnetic parameters.
Saturns fast spin_determined_from_its_gravitational_field_and_oblatenessSérgio Sacani
ARtigo descreve o novo método usado para determinar com precisão o período de rotação do planeta Saturno. Uma das grandes questões da astronomia. De acordo com o artigo o período de rotação de Saturno é de 10 horas 32 minutos e 45 segundos (+/- 46 segundos).
The document summarizes an empirical ground motion model developed as part of the PEER Next Generation Attenuation (NGA) project. Key points:
- The model predicts peak ground acceleration, velocity, displacement, and response spectra for shallow crustal earthquakes in active tectonic regions.
- It is based on over 1,500 recordings from 64 earthquakes ranging in magnitude from 4.3 to 7.9 and distances from 0.1 to 199 km.
- The model accounts for magnitude, distance, faulting style, depth, directivity, site conditions, and variability between events and recordings.
This document analyzes pore pressure generation and dissipation in cohesionless materials during seismic loading. It develops an efficient solution based on a multiple time scale analysis. The solution splits the problem into two sub-problems based on different time scales: 1) a fast time scale related to cyclic loading and 2) a slow time scale related to drainage. It presents the theoretical framework and describes implementing the solution in a finite element code to predict pore pressure development under a bridge pier foundation during an earthquake. The goal is to limit excessive pore pressure increase that could compromise foundation stability.
This document summarizes a research paper that examines the steady magnetohydrodynamic mass transfer flow of a polar fluid through a porous medium bounded by an infinite vertical porous plate. The paper presents the governing equations for the fluid flow, angular momentum, energy, and concentration considering effects such as magnetic field, thermal diffusion, and radiation. Exact solutions for the velocity, angular velocity, temperature, and concentration fields are obtained. The skin friction and heat transfer rate are also derived. Graphs illustrate the effects of various parameters on the flow behavior and transport properties.
Nanofluid Flow past an Unsteady Permeable Shrinking Sheet with Heat Source or...IJERA Editor
The consideration of nanofluids has been paid a good attention on the forced convection; the analysis focusing
nanofluids in porous media are limited in literature. Thus, the use of nanofluids in porous media would be very
much helpful in heat and mass transfer enhancement. In this paper, the influence of variable suction, Newtonian
heating and heat source or sink heat and mass transfer over a permeable shrinking sheet embedded in a porous
medium filled with a nanofluid is discussed in detail. The solutions of the nonlinear equations governing the
velocɨty, temperature and concentration profiles are solved numerically using Runge-Kutta Gill procedure
together with shooting method and graphical results for the resulting parameters are displayed and discussed.
The influence of the physical parameters on skin-friction coefficient, local Nusselt number and local Sherwood
number are shown in a tabulated form.
This document presents a nonlinear observer approach for estimating vehicle longitudinal and lateral velocity. It describes sensors used and a simplified vehicle model. A nonlinear observer is proposed using a tire-ground friction model. Examples are shown applying the observer to different vehicle maneuvers, like sinusoidal steering, braking in a turn, and lane changes. The next step is to develop an adaptive nonlinear observer that can estimate the maximum friction coefficient online without prior knowledge of road conditions.
Seismic data processing 13 stacking&migrationAmin khalil
1) Stacking involves correcting common midpoint (CMP) gathers for normal moveout (NMO) and then summing the traces to increase the signal-to-noise ratio. There are two types of stacking: horizontal and vertical.
2) While stacking improves signal-to-noise ratio, it averages over different incident angles and results in data only at zero offset.
3) Migration is needed to properly image dipping and irregular reflectors by removing wave phenomena like diffraction and properly locating reflections in the subsurface.
1) Conventional semblance analysis assumes no amplitude variation with offset (AVO), which can cause issues for events with strong AVO or polarity reversals. 2) The document proposes generalized semblance methods that incorporate AVO by modeling events with both hyperbolic moveout and amplitude variation. 3) It compares traditional, AB, and AK semblance on synthetic data, finding AK semblance maintains good velocity resolution while handling AVO better than traditional semblance.
This document outlines the key steps in a simple seismic data processing workflow, including: data initialization such as reformatting, geometry updates, and trace editing; amplitude processing; noise attenuation; deconvolution; multiple attenuation; velocity analysis and NMO; migration; stacking; and data makeup. Each processing step is briefly described and examples are provided of before and after visualizations. References and an opportunity for questions are provided at the end.
Quantitative and Qualitative Seismic Interpretation of Seismic Data Haseeb Ahmed
This document discusses quantitative and qualitative seismic interpretation techniques used to analyze seismic data and map subsurface geology. It compares traditional qualitative techniques to more modern quantitative techniques. It then focuses on unconventional seismic interpretation techniques used for unconventional reservoirs with low permeability, including AVO analysis, seismic inversion, seismic attributes, and forward seismic modeling. These techniques can help identify tight gas, shale gas, and gas hydrate reservoirs that conventional methods cannot easily detect. The document provides details on how each technique works and its advantages.
Seismic data interpretation aims to tell the geologic story contained in seismic data by correlating seismic features with known geological elements. The summary outlines key concepts including:
1. Reflection, velocity, P and S waves, polarity, phase, resolution and detectability which influence seismic interpretation.
2. Depositional environments, rock types, faults and folds are interpreted from seismic data to understand the subsurface petroleum system.
3. Structural and stratigraphic interpretation including seismic attributes, multi-attribute logging, direct hydrocarbon indicators, and AVO/impedance inversion are used to characterize reservoirs.
Greetings all,
This month’s newsletter is devoted to data assimilation and its application to Ocean Reanalyses.
Brasseur is introducing this newsletter telling us about the history of Ocean Reanalyses, the need for such Reanalyses for
MyOcean users in particular, and the perspective of Ocean Reanalyses coupled with biogeochemistry or regional systems for
example.
Scientific articles about Ocean Reanalyses activities are then displayed as follows: First, Cabanes et al. are presenting CORA, a
new comprehensive and qualified ocean in-situ dataset from 1990 to 2008, developped at the Coriolis Data Centre at IFREMER
and used to build Ocean Reanalyses. A more comprehensive article will be devoted to the CORA dataset in our next April 2010
issue. Then, Remy at Mercator in Toulouse considers large scale decadal Ocean Reanalysis to assess the improvement due to
the variational method data assimilation and show the sensitivity of the estimate to different parameters. She uses a light
configuration system allowing running several long term reanalysis. Third, Ferry et al. present the French Global Ocean
Reanalysis (GLORYS) project which aims at producing eddy resolving global Ocean Reanalyses with different streams spanning different time periods and using different technical choices. This is a collaboration between Mercator and French research
laboratories, and is a contribution to the European MyOcean project. Then, Masina et al. at CMCC in Italy are presenting the
implementation of data assimilation techniques into global ocean circulation model in order to investigate the role of the ocean on
climate variability and predictability. Fifth, Smith et al. are presenting the Ocean Reanalyses studies at ESSC in the U.K. which
aim at reconstructing water masses variability and ocean transports. Finally, Langlais et al. are giving an example of the various
uses of ocean reanalyses: they are using the Australian BlueLink Reanalysis in order to look into details at the various Southern
Ocean fronts.
The next April 2010 newsletter will introduce a new editorial line with a common newsletter between the Mercator
Ocean Forecasting Center in Toulouse and the Coriolis Data Center at Ifremer in Brest. Some papers will be
dedicated to observations only, when others will display collaborations between the 2 aspects: Observations and
Model. The idea is to wider and complete the subjects treated in our newsletter, as well as to trigger interactions
between observations and modeling communities. This common Mercator-Coriolis Newsletter is a test for which
we will take the opportunity to ask for your feedback.
We wish you a pleasant reading!
This document describes a numerical simulation of magnetohydrodynamic instabilities in nuclear fusion plasma. The simulation analyzed plasma characteristics like magnetic compression and tension. It found that strong initial internal and external magnetic fields can correct for natural MHD instabilities, increasing magnetic confinement time. The best configuration applied a poloidal field of similar magnitude to the toroidal field and a constant external vertical field, increasing confinement time by 400%.
1) The document analytically solves the nonisothermal Buckley-Leverett problem for two-phase immiscible flow in porous media including a tracer component and temperature effects.
2) Mass balances for the fluids and tracer and a convective heat balance equation are formulated and solved using the method of characteristics.
3) The solutions can be used to analyze pressure transients, interpret formation testing, calculate temperature front propagation during waterflooding, and benchmark simulators.
This document describes Evan Foley's senior research paper on simulating solitons of the sine-Gordon equation using variational approximations and Hamiltonian principles. It provides background on solitons and Hamilton's principle. It then applies a variational approximation method to the Korteweg-de Vries equation and modified Korteweg-de Vries equation, obtaining traveling wave solutions that closely match the exact solutions. This method is then extended to the sine-Gordon equation using Gaussian and odd oriented Gaussian trial functions to obtain both traveling wave and dynamic solutions.
This dissertation examines the stability and nonlinear evolution of an idealized hurricane model. The author uses the quasi-geostrophic shallow water equations to model the hurricane as a simple axisymmetric annular vortex with a predefined potential vorticity distribution. Both single-layered and two-layered models are considered. For the single-layer case, linear stability analysis reveals barotropic and baroclinic instabilities that depend on parameters like the potential vorticity within the core and the Rossby deformation length. Nonlinear simulations then show how the annular structure breaks down in different ways depending on these parameters. For the two-layer case, linear stability is found to be identical to the single-layer case, and phase diagrams
The document investigates the response of tropical cyclone activity and frequency to different perturbed climates using an aquaplanet configuration of a global climate model with 50-km horizontal resolution. It compares the direct response to solar and carbon dioxide forcing, sea surface temperature changes, and the combined response in slab-ocean model simulations. The results suggest that tropical cyclone frequency changes are greater in magnitude for increased carbon dioxide forcing compared to increased solar forcing, despite both having similar global-mean radiative forcing.
Effects of shale volume distribution on the elastic properties of reserviors ...DR. RICHMOND IDEOZU
Shale volume (Vsh) estimation has been carried out on three selected reservoirs (Nan.1, Nan.2, and Nan.4) distributed across four wells (01, 03, 06, and 12) in Nantin Field, using petrophysical analysis and reservoir modeling techniques with a view to understanding the reservoir elastic properties. Materials utilized for this research work include: Well Log data (Gamma Ray Log, Resistivity Log, Sonic Log, Density Log, Neutron porosity log), and a 3-D Seismic volume were used for the study. Sand and shale were the prevalent lithologies in Nantin Field. Nan. 1 reservoir was thickest in Nantin well 12 (29.7ft), Nantin 2 reservoir was thickest in Nantin Well 12 (30.9ft) while Nantin 4 reservoir was thickest in Well 3 (72ft). Correlation well panel across the Field showed that Nantin 4 reservoir, was thicker than Nan 1 and Nan 2 Reservoir respectively. Normal and synthetic Faults were also mapped, the trapping system in the field includes anticlines in association with fault closures. The thicknesses and lateral extents of these reservoirs were delineated into three zones (1, 2, and 3) which were modeled appropriately. Petrophysical and some elasticity parameters such as Poisson ratio (PR), Acoustic Impedance (AI), and Reflectivity Coefficient (RC) were evaluated for the wells. The results from elasticity evaluation showed a high Poisson Ratio of 0.40 in Nantin 2 reservoir of Well 12 based on high shale volume distribution of 0.70 indicating high stress level and possible boundary to hydraulic fracture. The lowest Poisson Ratio was evaluated in Nantin reservoir of Well 1 with lowest shale volume of 0.18 which indicates weak zones and may not constrain a fracturing job. Results from Acoustic impedance showed a high AI value of 7994.3 in Nan 2 Reservoir compared to Nan.1 which has the least AI value of 7447.3 because of low shale volume. A higher Reflectivity Coefficient of 0.01 was recorded in Nan.2 reservoir indicating bright spot while a lower RC of -0.00023 was recorded in Nan.4 Reservoir indicating dim spot. Hydrocarbon volume estimate of the three reservoirs showed 163mmstb in Nan.1 reservoir, 169mmstb, in Nantin 2 reservoir and 115mmstb in Nan. 4 Reservoir. The reservoirs encountered were faulted and laterally extensive. Nantin 2 reservoir was more prolific with a STOIIP of 169 mmstb compared to Nan. 1 with a STOIP of 163 mmstb and Nantin.4 with a STOIP of 115 mmstb, because of its good petrophysical values, facies quality and low shale volume distributions.
This document describes a C++ program called CRadtran that calculates microwave radiance from the atmosphere. It presents the radiative transfer equation that models how intensity changes as light travels through atmospheric layers. The atmosphere is divided into thin slices where temperature, pressure, and attenuation are constant. The change in intensity is calculated for each slice using the radiative transfer equation, accounting for emission and absorption. Integrating the intensity changes across all slices allows determining the upwelling microwave radiance from the top of the atmosphere. This program improves on an older FORTRAN model by being more readable and usable.
This document provides lecture notes on the topic of geophysics. It introduces gravimetry, which detects tiny differences in gravitational force to differentiate underground structures based on density variations. Key points covered include Newton's law of gravitation, factors that influence the gravity field of Earth, methods for reducing gravity data to correct for these factors (such as latitude, elevation, topography, tides, and subsurface density variations), and applications of gravimetry in geological mapping and exploration.
This document is an internship report submitted by Yiteng Dang to the École Normale Supérieure on applying mean-field theory to study charge density waves in rare-earth nickelates. Chapter 1 provides theoretical background, discussing concepts like density of states calculations, the nearly free electron model, mean-field theory applied to ferromagnetism and antiferromagnetism, and Green's functions. Chapter 2 focuses on nickelates, introducing a low-energy two-orbital Hamiltonian and applying mean-field theory to obtain results like a phase diagram at half-filling and quarter-filling. Numerical methods are used throughout to solve problems in condensed matter theory.
This document describes a heat exchanger design project. It provides theory on heat exchanger design including heat transfer rate calculations. It then details the CFD simulation process used to model and analyze different heat exchanger designs. This included an initial 2D model, mesh refinement studies to determine optimal mesh size, and modeling variations in pipe spacing, flow direction, and a 3D design. Results were analyzed using temperature, turbulence, and velocity contours to evaluate design performance.
This document describes a PhD thesis that analyzes water isotope diffusion in firn layers to improve paleoclimatic interpretations of ice core records. It presents background on water isotopes, the global water cycle, and post-depositional processes in firn. It then describes using a diffusion model and NorthGRIP ice core data to estimate past temperatures. Laboratory diffusion experiments are also presented to measure firn diffusivity. Finally, a model is used to interpret tritium records from Spitsbergen ice cores and understand meltwater percolation effects. The overall aim is to better account for post-depositional processes and improve ice core proxy climate reconstructions.
The October 2004 Mw=7.1 Nicaragua earthquake: Rupture process, aftershock loc...Gus Alex Reyes
The subduction zone off the Nicaragua
coastline has been the site of several large
earthquakes in the past decades, including
the 1992 tsunami earthquake that was
anomalous in the size of the tsunami relative
to moment release [Kanamori and
Kikuchi, 1993]. As a focus site for both
the MARGINS-SEIZE and SubFac initiatives,
it is an area of keen interest for
scientists interested in earthquake rupture
and volcanic processes.
PSY2G: moving towards
global operational oceanography
By Nicolas Ferry
Introduction
In just a few years, Mercator has developed 3 ocean analysis and forecasting systems for the
North Atlantic. Today a new stage has been reached with PSY2G, Mercator’s first low resolution (2°),
global ocean analysis system.
Each week, the PSY2G system does operational analysis of the global ocean by assimilating all
available altimetry observations in an identical way to the work being done with PSY1v1 and PSY2v1.
PSY2G thus provides weekly ocean bulletins which are used, in particular, for seasonal forecasting by
Météo France. Mercator has thus shown its determination to contribute to GODAE (the Global Ocean
Data Assimilation Experiment).
In terms of objectives, PSY2G, due to its horizontal resolution, is of course not designed to
assimilate mesoscale processes like PSY1 or PSY2 but rather to assimilate global scale climate
signals. This is also a significant technical stage before the migration towards PSY3 (global to ¼°) and
the setting up of global mode multivariate assimilation (SAM1v2).
In this newsletter, we shall be describing the PSY2G prototype in detail. The system’s
performances are discussed by referring to a global ocean reanalysis for an 11 year period (1993 to
2003).
This document is a thesis submitted by Yishi Lee to Embry-Riddle Aeronautical University for the degree of Master of Science in Engineering Physics. The thesis developed a new 3-D model of the high-latitude ionosphere to study the coupling between the ionosphere, magnetosphere, and neutral atmosphere. The model consists of equations describing the conservation of mass, momentum, and energy for six ionospheric constituents, as well as an electrostatic potential equation. The thesis was prepared under the direction of Dr. Matthew Zettergren and other committee members. It uses the 3-D model to examine ion heating, plasma structuring due to perpendicular transport, ion upflow, molecular ion generation, and neutral wave forcing in
The document discusses the Vainshtein mechanism, which is a screening mechanism that allows a scalar field coupled to matter to have a negligible effect as a fundamental force on matter within a specific scale. This is important for explaining the cosmological constant problem, which is that the observed acceleration of the universe requires a cosmological constant that is much smaller than predicted by quantum field theory. The Vainshtein mechanism introduces a scalar field while maintaining the accuracy of general relativity at solar system scales by making the new force negligible at those scales. The document explores how such a screening mechanism for a general scalar field could maintain Newtonian gravity results within the solar system and potentially explain the observed acceleration of the universe.
This document presents a nonlinear observer approach for estimating vehicle longitudinal and lateral velocity. It describes sensors used and a simplified vehicle model. A nonlinear observer is proposed using a tire-ground friction model. Examples are shown applying the observer to different vehicle maneuvers, like sinusoidal steering, braking in a turn, and lane changes. The next step is to develop an adaptive nonlinear observer that can estimate the maximum friction coefficient online without prior knowledge of road conditions.
Seismic data processing 13 stacking&migrationAmin khalil
1) Stacking involves correcting common midpoint (CMP) gathers for normal moveout (NMO) and then summing the traces to increase the signal-to-noise ratio. There are two types of stacking: horizontal and vertical.
2) While stacking improves signal-to-noise ratio, it averages over different incident angles and results in data only at zero offset.
3) Migration is needed to properly image dipping and irregular reflectors by removing wave phenomena like diffraction and properly locating reflections in the subsurface.
1) Conventional semblance analysis assumes no amplitude variation with offset (AVO), which can cause issues for events with strong AVO or polarity reversals. 2) The document proposes generalized semblance methods that incorporate AVO by modeling events with both hyperbolic moveout and amplitude variation. 3) It compares traditional, AB, and AK semblance on synthetic data, finding AK semblance maintains good velocity resolution while handling AVO better than traditional semblance.
This document outlines the key steps in a simple seismic data processing workflow, including: data initialization such as reformatting, geometry updates, and trace editing; amplitude processing; noise attenuation; deconvolution; multiple attenuation; velocity analysis and NMO; migration; stacking; and data makeup. Each processing step is briefly described and examples are provided of before and after visualizations. References and an opportunity for questions are provided at the end.
Quantitative and Qualitative Seismic Interpretation of Seismic Data Haseeb Ahmed
This document discusses quantitative and qualitative seismic interpretation techniques used to analyze seismic data and map subsurface geology. It compares traditional qualitative techniques to more modern quantitative techniques. It then focuses on unconventional seismic interpretation techniques used for unconventional reservoirs with low permeability, including AVO analysis, seismic inversion, seismic attributes, and forward seismic modeling. These techniques can help identify tight gas, shale gas, and gas hydrate reservoirs that conventional methods cannot easily detect. The document provides details on how each technique works and its advantages.
Seismic data interpretation aims to tell the geologic story contained in seismic data by correlating seismic features with known geological elements. The summary outlines key concepts including:
1. Reflection, velocity, P and S waves, polarity, phase, resolution and detectability which influence seismic interpretation.
2. Depositional environments, rock types, faults and folds are interpreted from seismic data to understand the subsurface petroleum system.
3. Structural and stratigraphic interpretation including seismic attributes, multi-attribute logging, direct hydrocarbon indicators, and AVO/impedance inversion are used to characterize reservoirs.
Greetings all,
This month’s newsletter is devoted to data assimilation and its application to Ocean Reanalyses.
Brasseur is introducing this newsletter telling us about the history of Ocean Reanalyses, the need for such Reanalyses for
MyOcean users in particular, and the perspective of Ocean Reanalyses coupled with biogeochemistry or regional systems for
example.
Scientific articles about Ocean Reanalyses activities are then displayed as follows: First, Cabanes et al. are presenting CORA, a
new comprehensive and qualified ocean in-situ dataset from 1990 to 2008, developped at the Coriolis Data Centre at IFREMER
and used to build Ocean Reanalyses. A more comprehensive article will be devoted to the CORA dataset in our next April 2010
issue. Then, Remy at Mercator in Toulouse considers large scale decadal Ocean Reanalysis to assess the improvement due to
the variational method data assimilation and show the sensitivity of the estimate to different parameters. She uses a light
configuration system allowing running several long term reanalysis. Third, Ferry et al. present the French Global Ocean
Reanalysis (GLORYS) project which aims at producing eddy resolving global Ocean Reanalyses with different streams spanning different time periods and using different technical choices. This is a collaboration between Mercator and French research
laboratories, and is a contribution to the European MyOcean project. Then, Masina et al. at CMCC in Italy are presenting the
implementation of data assimilation techniques into global ocean circulation model in order to investigate the role of the ocean on
climate variability and predictability. Fifth, Smith et al. are presenting the Ocean Reanalyses studies at ESSC in the U.K. which
aim at reconstructing water masses variability and ocean transports. Finally, Langlais et al. are giving an example of the various
uses of ocean reanalyses: they are using the Australian BlueLink Reanalysis in order to look into details at the various Southern
Ocean fronts.
The next April 2010 newsletter will introduce a new editorial line with a common newsletter between the Mercator
Ocean Forecasting Center in Toulouse and the Coriolis Data Center at Ifremer in Brest. Some papers will be
dedicated to observations only, when others will display collaborations between the 2 aspects: Observations and
Model. The idea is to wider and complete the subjects treated in our newsletter, as well as to trigger interactions
between observations and modeling communities. This common Mercator-Coriolis Newsletter is a test for which
we will take the opportunity to ask for your feedback.
We wish you a pleasant reading!
This document describes a numerical simulation of magnetohydrodynamic instabilities in nuclear fusion plasma. The simulation analyzed plasma characteristics like magnetic compression and tension. It found that strong initial internal and external magnetic fields can correct for natural MHD instabilities, increasing magnetic confinement time. The best configuration applied a poloidal field of similar magnitude to the toroidal field and a constant external vertical field, increasing confinement time by 400%.
1) The document analytically solves the nonisothermal Buckley-Leverett problem for two-phase immiscible flow in porous media including a tracer component and temperature effects.
2) Mass balances for the fluids and tracer and a convective heat balance equation are formulated and solved using the method of characteristics.
3) The solutions can be used to analyze pressure transients, interpret formation testing, calculate temperature front propagation during waterflooding, and benchmark simulators.
This document describes Evan Foley's senior research paper on simulating solitons of the sine-Gordon equation using variational approximations and Hamiltonian principles. It provides background on solitons and Hamilton's principle. It then applies a variational approximation method to the Korteweg-de Vries equation and modified Korteweg-de Vries equation, obtaining traveling wave solutions that closely match the exact solutions. This method is then extended to the sine-Gordon equation using Gaussian and odd oriented Gaussian trial functions to obtain both traveling wave and dynamic solutions.
This dissertation examines the stability and nonlinear evolution of an idealized hurricane model. The author uses the quasi-geostrophic shallow water equations to model the hurricane as a simple axisymmetric annular vortex with a predefined potential vorticity distribution. Both single-layered and two-layered models are considered. For the single-layer case, linear stability analysis reveals barotropic and baroclinic instabilities that depend on parameters like the potential vorticity within the core and the Rossby deformation length. Nonlinear simulations then show how the annular structure breaks down in different ways depending on these parameters. For the two-layer case, linear stability is found to be identical to the single-layer case, and phase diagrams
The document investigates the response of tropical cyclone activity and frequency to different perturbed climates using an aquaplanet configuration of a global climate model with 50-km horizontal resolution. It compares the direct response to solar and carbon dioxide forcing, sea surface temperature changes, and the combined response in slab-ocean model simulations. The results suggest that tropical cyclone frequency changes are greater in magnitude for increased carbon dioxide forcing compared to increased solar forcing, despite both having similar global-mean radiative forcing.
Effects of shale volume distribution on the elastic properties of reserviors ...DR. RICHMOND IDEOZU
Shale volume (Vsh) estimation has been carried out on three selected reservoirs (Nan.1, Nan.2, and Nan.4) distributed across four wells (01, 03, 06, and 12) in Nantin Field, using petrophysical analysis and reservoir modeling techniques with a view to understanding the reservoir elastic properties. Materials utilized for this research work include: Well Log data (Gamma Ray Log, Resistivity Log, Sonic Log, Density Log, Neutron porosity log), and a 3-D Seismic volume were used for the study. Sand and shale were the prevalent lithologies in Nantin Field. Nan. 1 reservoir was thickest in Nantin well 12 (29.7ft), Nantin 2 reservoir was thickest in Nantin Well 12 (30.9ft) while Nantin 4 reservoir was thickest in Well 3 (72ft). Correlation well panel across the Field showed that Nantin 4 reservoir, was thicker than Nan 1 and Nan 2 Reservoir respectively. Normal and synthetic Faults were also mapped, the trapping system in the field includes anticlines in association with fault closures. The thicknesses and lateral extents of these reservoirs were delineated into three zones (1, 2, and 3) which were modeled appropriately. Petrophysical and some elasticity parameters such as Poisson ratio (PR), Acoustic Impedance (AI), and Reflectivity Coefficient (RC) were evaluated for the wells. The results from elasticity evaluation showed a high Poisson Ratio of 0.40 in Nantin 2 reservoir of Well 12 based on high shale volume distribution of 0.70 indicating high stress level and possible boundary to hydraulic fracture. The lowest Poisson Ratio was evaluated in Nantin reservoir of Well 1 with lowest shale volume of 0.18 which indicates weak zones and may not constrain a fracturing job. Results from Acoustic impedance showed a high AI value of 7994.3 in Nan 2 Reservoir compared to Nan.1 which has the least AI value of 7447.3 because of low shale volume. A higher Reflectivity Coefficient of 0.01 was recorded in Nan.2 reservoir indicating bright spot while a lower RC of -0.00023 was recorded in Nan.4 Reservoir indicating dim spot. Hydrocarbon volume estimate of the three reservoirs showed 163mmstb in Nan.1 reservoir, 169mmstb, in Nantin 2 reservoir and 115mmstb in Nan. 4 Reservoir. The reservoirs encountered were faulted and laterally extensive. Nantin 2 reservoir was more prolific with a STOIIP of 169 mmstb compared to Nan. 1 with a STOIP of 163 mmstb and Nantin.4 with a STOIP of 115 mmstb, because of its good petrophysical values, facies quality and low shale volume distributions.
This document describes a C++ program called CRadtran that calculates microwave radiance from the atmosphere. It presents the radiative transfer equation that models how intensity changes as light travels through atmospheric layers. The atmosphere is divided into thin slices where temperature, pressure, and attenuation are constant. The change in intensity is calculated for each slice using the radiative transfer equation, accounting for emission and absorption. Integrating the intensity changes across all slices allows determining the upwelling microwave radiance from the top of the atmosphere. This program improves on an older FORTRAN model by being more readable and usable.
This document provides lecture notes on the topic of geophysics. It introduces gravimetry, which detects tiny differences in gravitational force to differentiate underground structures based on density variations. Key points covered include Newton's law of gravitation, factors that influence the gravity field of Earth, methods for reducing gravity data to correct for these factors (such as latitude, elevation, topography, tides, and subsurface density variations), and applications of gravimetry in geological mapping and exploration.
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3. Abstract
This report investigates the seismic anomaly produced in the event of a lithospheric de-
lamination. Lithospheric delamination is a convective removal process of the lithosphere
in the subsurface. It’s overall environmental impact is linked to volcanism events and
local topographic variations. As one of the lesser documented and understood earth re-
cycling processes, this report investigate the ability to image a seismic velocity anomaly
indicative of a lithospheric delamination utilizing the van Wijk et al. approach. In or-
der to accomplish this I use a geodynamic model of delamination and convert the model
pressure-temperature structure into seismic velocity. The results demonstrate consistent
seismic velocities deviations to the Isabella anomaly in the Sierra Nevada mountain range
of California. The ability to successfully reconstruct seismic anomaly continues to sup-
port the validity of seismic studies in pursuit of further understanding the delamination
process. Though successful in this approach, future improvements to the start model in
terms of overall complexity is required. The performed sensitivity analysis emphasizes
the impact of attenuation, specifically, in the proper definition mantle water content as
well as grain size. In conclusion I find the van Wijk method a good approximation to
converting pressure and temperature to seismic velocities, however, in order to obtain
better results mantle heterogeneity and anisotropy will need to be further studied.
4. Chapter 1
Introduction
1.1 Motivation
The lithosphere delamination phenomenon is a best perhaps described as a method for
the earth to recycle crustal and continental mantle lithosphere material. The principal
mechanisms for crustal recycling are subduction at plate margins as well as lithospheric
delamination and drip mechanisms [1]. While subduction is a well understood process
that is essential to the plate tectonic engine of planet earth, delamination, on the other
hand requires recycling via convective removal of the lower parts of the lithosphere and
is more difficult to detect [1]. Delamination is a form of vertically and spatially localized
tectonics which often generate amoeba-like or circular surface topography effects that are
regional results of tectono-magmatic processes at convergent plate margins[1]. Simply
put, lithospheric delamination is crustal and lithospheric removal by peeling a mechanism
driven by convective mantle fluids and a density instability. This process is formally
depicted in figure 1.1.
Tectonics events lead to crustal shortening or extention. During shortening, duc-
tile delamination of continental lower lithosphere via Rayleigh-Taylor instabilities can
produce continental magmatism with a range of major- and trace-element compositions
and volatile contents [2]. It doesn’t take much to produce these effects either. Density
contrasts as small as 1% are sufficient to drive gravitational Rayleigh-Taylor instabilities
[2]. These events have been noted to have occurred in the past in the southern Sierra
Nevada. Where the Sierra Nevada is a mountain range located in between the Central
Valley and Basin and Range Province of California [3]. during the Pliocene, at roughly
3.5 Ma, small volumes of high potassium magmas were erupted through the granodior-
ites [4]. Thus, understanding and detecting delamination events may lead to a better
understanding of not only the past but may perhaps increase the prevention of environ-
mental hazards linked to magmatic intrusions. The removal of mantle lithosphere from
beneath continental crust has been called on to explain a number of tectonic features,
including volcanism and anomalous heat flow, upper mantle seismic velocity and gravity
anomalies, extensional tectonism, and both positive and negative topographic transients
[5]. The process may also play a significant role in continental crust becoming more felsic
as denser mafic material recycles back into the mantle [6]. Currently seismic tomogra-
2
5. (a) Earth (b) Lithosphere Asthenosphere Boundary
(c) Convection Driven Removal (d) Complete Lithosphere detachment
Figure 1.1: The Convective Removal Process
phy models show an inclined region of high velocities at roughly 3-8% higher than the
surrounding mantle) [17]. These are velocity deviations are interpreted to represent a
slab of delaminating lithosphere.
1.1.1 Objective
The goal of this project is to further examine the ability to accurately detect delami-
nation events with the use of seismic tomography. Seismic imaging is currently utilized
to study various economical and environmental methods. Its most prominent usage is
currently in the oil and gas and resource mining industries. During my 3 month study
I utilize a numerical model of delamination consisting of pressure (P) and temperature
(T), with the aim of mapping them to seismic velocity such that P,T ⇐⇒ V (P, T).
The hope is that the velocity anomalies seen in our forward model will accurately rep-
resent the delamination process. The conversion will take place following the van Wijk
method [8]. In particular this report looks to image a delamination similar to the Sierra
Nevada’s Isabella anomaly. Figure 1.2 shows the geographical location of the seismic
anomaly (Isabella) of interest.
3
7. 1.2 Previous Work
In order to simulate the temporal evolution of the delamination, I utilize a previously
built geological model consisting of a dense root with weak zone, mantle lithosphere,crust
and asthenosphere. Listed in table 1.1 are the densities and rheology of the model
shown also below in figure 1.3. The L-shape weak zone controls the asymmetry of the
delamination process.
Earth Zone Density (ρ0)
kg
m3
Rheology
Crust 2800 WQx5
Mantle Lithosphere 3250 WOx5
Root 3350 WOx1
Weak Zone 3250 1019
(Pa · s)
Table 1.1: Model Parameters
Notes:
• WQ: Wet Quartz
• WO: Wet Olivine
• Multiplicity is indicative of dryer and mechanically stronger zones
Figure 1.3: Geological Model
5
8. 1.2.1 Governing Equations
For the given geological model described above. We require solutions to the following
equations.
Please note that ALL variable definitions and values that are defined in Appendix B of
this paper.
Density Equation:
ρ (T) = ρ0 [1 − α (T − T0)] (1.1)
where: α = 3 × 10−5
, T0 = 900K
Mass Continuity Equation:
∂ρ
∂t
+ · (ρu) = 0 (1.2)
Conservation of momentum:
∂ρui
∂t
+
∂
∂xj
[ρuiuj] =
∂σij
∂xj
+ ρgi (1.3)
Conservation of energy (heat equation):
∂Φ
∂t
+ · (Φu) − · k T − H = 0 (1.4)
where: Φ = ρcpT → heat per unit volume
1.2.2 Solution Methodology
These equations were solved using a SOPALE code using a finite element solver for a
2D thermal mechanical evolution [19]. Figure 1.4 demonstrates the model evolution.
6
9. (a) time 0 ma (b) time 0.76 ma
(c) time 1.08 ma
Figure 1.4: Geological Model Evolution
7
10. Chapter 2
Problem Foundation
2.1 Framework
In order to handle the model data a 2D (x-distance, depth) uniform spatial Eulerian
grid was created utilizing Matlab. The original synthetic was not uniformly spaced so
this new grid uses a linear interpolation scheme with grid size of 25x1(km). The final
model space represents a range of 0-400(km) in depth, while laterally, the model covers
0-800(km).
2.1.1 Pressure and Temperature Cross-Section Modeling
For the grid at hand temperature and pressure are both strictly a 1D function of depth
at the start of the model. Both profiles are plotted below in figure 2.1.
8
11. 0 2 4 6 8 10 12 14
0
50
100
150
200
250
300
350
400
Pressure Gradient
Pressure (GPa)
Depth(Km)
(a) Pressure Gradient
200 400 600 800 1000 1200 1400 1600 1800
0
50
100
150
200
250
300
350
400
Temperature Gradient
Temperature (K)
Depth(Km)
(b) Temperature Gradient
Pressure (GPa) Cross Section
Distance (km)
Depth(km)
0 100 200 300 400 500 600 700 800
50
100
150
200
250
300
350
400
2
4
6
8
10
12
(c) Pressure Grid
Distance (km)
Depth(km)
Temperature (K) Cross Section
0 100 200 300 400 500 600 700 800
50
100
150
200
250
300
350
400
400
600
800
1000
1200
1400
1600
(d) Temperature Grid
Figure 2.1: Temperature and Pressure Profiles
2.2 Velocity Conversion
Van Wijk [8] gives an approach for calculating synthetic seismic velocities were they are
predicted from model temperatures and pressures. The approach also includes elastic
and anelastic effects and variations of mineral phase composition with pressure and
temperature [8]. Seismic anomalies are relative to the model horizontal average to a
regional reference [8]. I convert my temperature and pressure models to seismic velocities
utilizing this approach. After converting my velocities I qualitatively infer on potential
error sources and improvement methods. The conversion from pressure and temperature
data will take place in four steps.
1. T and P → Velocity (V ) at infinite frequency V∞
9
12. V∞(T, P) = 4.77 + 0.038P − 0.000378(T − 300) (2.1)
2. V∞ → to Vshear(s) with the addition of an attenuation factor
3. Vs → to Vcompressional(p) utilizing Poisson’s ratio
4. Calculate velocity deviation for Vp from background field Vp → Vdiff
Vdiff =
(Vp − Vref )
Vref
× 100% (2.2)
Figure 2.2 demonstrates the initial velocity conversion at infinite frequency, the model
space shown ignores the crust for simplicity, thus, the depth shown is the depth from
the base of the crust (40km) down. Furthermore I also neglect attenuation effects at
this stage, the figure 2.2 shown represents the converted geological model at time = 0.76
ma.
Vinf, t=0.76 ma
Distance (km)
Depth(km)
0 100 200 300 400 500 600 700 800
100
150
200
250
300
350
400
Velocity [Km/s]
4.35
4.4
4.45
4.5
4.55
4.6
4.65
4.7
Figure 2.2: Velocity at infinite frequency Seismic Model (Note: Depth is Depth from
the base of crust ie below 40km
2.2.1 S-Wave Conversion
Most of the seismological observations are made at low frequencies (ω ≤ 1Hz) and con-
tributions from anelastic (including viscoelastic) effects become important, particularly
for shear waves, when temperature is high [9]. At this point I introduce a seismic qual-
ity factor Q. Here Q−1
will represent the anelastic attenuation effect with respect to
the shear wave seismic velocities. As source energy propagates into the earth it loses
10
13. energy to the medium through which it is propagating, while changing mediums, energy
is transmitted and reflected at the interface. This transition then acts to further loses
in energy. This loss in wave energy is most often lost nowas heat [10]. At this point
I’ve neglected the oscillatory behavior of seismic waves and therefore neglected effect of
frequency of elastic waves. In order to account for the thermodynamic effect of energy
loss I will use equation 2.3 which includes anelastic attenuation.
Vs = Vinf(T, P)[1 − F · Q−1
(ω, T, P, COH, d)] (2.3)
Q−1
(ω, T, P, COH, d) = Bd−pQ
ω−1
exp −
(EQ + PVQ)
RT
α
(2.4)
The overall effect of anelasticity is to significantly increase the temperature derivative
of seismic wave velocities. This implies that the temperature anomalies associated with
low velocity anomalies should be significantly smaller [9].
B = B0d
PQ−PQref
Qref
COH
COH(Qref)
rQ
exp
(EQ + PQref VQ) − (EQref + PQref VQref )
RTQref
(2.5)
Shear Vel With attenuation Factor Q t=0.76 ma
Distance (km)
Depth(km)
0 100 200 300 400 500 600 700 800
100
150
200
250
300
350
400
Velocity [Km/s]
4.35
4.4
4.45
4.5
4.55
4.6
4.65
Figure 2.3: S-Wave Converted Seismic Model with Attenuation at model time 0.76 ma
2.2.2 P-Wave Conversion
In order to convert the velocities from S-waves to P-waves I use Poisson’s relationship.
Poissons ratio is known to be sensitive to lithology and Vp/Vs ratio is used in exploration
11
14. geophysics. In this case Poisson’s ratio ranges from 0.23 to 0.25 and is calculated as
function of compressional and shear wave velocity Poissons ratio is calculated from the
seismic velocity by the well-known formula 2.6. The Poisson’s ratio used to convert to
compressional velocity for the rest of this report is ν = 0.25 which is the upper bound
defined for an decompressed mantle (0.23 ≤ ν ≤ 0.25) as proposed by Poirier et al. [11].
ν =
(Vp/Vs)2
− 2
2(Vp/Vs)2 − 2
(2.6)
The values of and Vp and Vs are taken from various recent regional seismological
models.
Vp = Vs
1 − ν
(1/2) − ν
(2.7)
Utilizing equation 2.7 I convert a shear wave at a model time of 0.76 ma. The
attenuation parameters assume a dry mantle which is 50
H
106Si
with a grain size of
1(cm) as suggested by Ducea and Saleeby [14].
Pwave Vel, t=0.76 ma with Poisson, =0.25
Distance (km)
Depth(km)
0 100 200 300 400 500 600 700 800
100
150
200
250
300
350
400
Velocity [Km/s]
7.6
7.7
7.8
7.9
8
8.1
Figure 2.4: P-Wave Convertion of attenuated shear wave Seismic Model
12
15. Chapter 3
Results
3.1 Sensitivity Analysis
In order to investigate potential sources of error I conduct sensitivity tests isolating
parameters in order to view their overall effect on seismic velocities. In particular I
investigate the effect of water content, grain size.
3.1.1 Water Effect
In the attenuation parameter Q−1
I include factor B which introduces the effect of
water content in the mantle. We notice that an increase in mantle water content greatly
affects the seismic velocity. The overall effect is that an increase in water content acts
to slow seismic velocities, specifically it enhances the attenuation term in equation 2.5.
In figure 3.1 we notice the effect of mantle wetness has a greater impact to the change in
velocity than the effect of grain size variation. This result is consistent with the studies
found by (Behn et al. [12]) in which he notes that difference in water content has a
greater effect on Vs than does the calculated change in grain size. The most important
effects to seismic velocity accuracy are (i)enhancement of anelasticity, leading to higher
attenuation of seismic waves and lower seismic wave velocities and (ii) modification
of lattice preferred orientation, leading to changes in seismic anisotropy [13]. Overall,
water enhances anelasticity and that the effects of water on anelasticity can be quantified
through the effects of water on creep that modifies the relaxation time. It follows that
Q−1
depends on temperature, pressure and water content [13].
3.1.2 Grain Size Variation
In order to properly define our attenuation parameter we account for the effect of grain
size in the mantle. For simplicity I assume a homogeneous mantle with respect to grain
size of 1cm as analyzed from xenoliths in the Sierra Nevada [14]. Although ignoring
the effect of grain size simplifies our problem by greatly reducing computational re-
quirements they also preclude effects such as shear localisation and transient changes
in rheology associated with phase transitions, which have the potential to fundamen-
tally change flow patterns in the mantle [15]. It is therefore inferred that much of the
seismic wave attenuation in the upper mantle may be attributed to grain-size-sensitive
13
16. 400 600 800 1000 1200 1400 1600
3
3.2
3.4
3.6
3.8
4
4.2
4.4
4.6
4.8
5
Attenuation Effect Due to Mantle Water Content, grain size = 0.01(m)
Temperature (K)
ShearWaveVelocity(km/s)
Vinf
Coh=50
Coh=500
Coh=1000
Coh=3000
(a) Grain size = 0.01 (m)
400 600 800 1000 1200 1400 1600
3
3.2
3.4
3.6
3.8
4
4.2
4.4
4.6
4.8
5
Attenuation Effect Due to Mantle Water Content, grain size = 0.0075(m)
Temperature (K)
ShearWaveVelocity(km/s)
Vinf
Coh=50
Coh=500
Coh=1000
Coh=3000
(b) Grain size = 0.0075 (m)
400 600 800 1000 1200 1400 1600
3
3.2
3.4
3.6
3.8
4
4.2
4.4
4.6
4.8
5
Attenuation Effect Due to Mantle Water Content, grain size = 0.005(m)
Temperature (K)
ShearWaveVelocity(km/s)
Vinf
Coh=50
Coh=500
Coh=1000
Coh=3000
(c) Grain size = 0.005 (m)
400 600 800 1000 1200 1400 1600
3
3.2
3.4
3.6
3.8
4
4.2
4.4
4.6
4.8
5
Attenuation Effect Due to Mantle Water Content, grain size = 0.001(m)
Temperature (K)
ShearWaveVelocity(km/s)
Vinf
Coh=50
Coh=500
Coh=1000
Coh=3000
(d) Grain size = 0.001 (m)
Figure 3.1: The effect of Grain Size
diffusional processes occurring in the absence of melt, notably elastically and diffusion-
ally accommodated grain boundary sliding [16]. The effect of varying grain size in my
particular case be seen in figure 3.1 the effects of decreasing the grain size are consistent
with the expected theory as decreasing the grain size leads to a decrease in the shear
wave velocity.
3.2 Qualitative Validation
Since the inversion data for the Isabella anomaly is not currently available to me for direct
analysis it is not possible to conduct a rigorous quantitative data misfit. However, I am
able to make first order qualitative error analysis of the velocity anomalies. I compare
to the delamination in the Isabella anomaly using the paper from Craig Jones [16] which
provides P-wave tomography of the Sierra Nevada’s. Figure 3.2 demonstrates a velocity
14
17. contrast on the order of 3-7% and a size of roughly 220(km) from surface.
Figure 3.2: E-W Tomography Sierra Nevada (Isabella Anomaly) [16]
Looking deeper in the inversion the ray path’s 3.3, there are zones of noticeable
sparsity which leads to further questioning of the actual tomography results. Various
inversion methodologies also lead to greatly varying results. So there are multiple sources
that should be investigated prior to determining a proper reference model. Figure 3.3
demonstrate p-wave inversion tomography along with its ray path’s which most closely
match the rough shape of my delamination model in the 0.86 ma frame from figure 3.5.
15
18. Figure 3.3: E-W Tomography Sierra Nevada ray path’s [16]
In the paper by Jones et. [16] al they utilize a reference velocity as prescribed by the
Incorporated Research Institutions for Seismology (IRIS), model IASP91. The iasp91
reference model is a parametrised velocity model that has been constructed to be a
summary of the travel time characteristics of the main seismic phases [17]. When I used
this as my background I observe an inconsistent anomaly utilizing equation 2.2, this
error is due to the fact that there is an inconsistency in the velocity model in terms
of depth as shown in figure 3.4. In order to utilize the IASP91 reference model a bulk
shift correction with respect to velocity would need to be applied to the model. It is not
discussed and would have been intriguing to see how it was applied in the Jones et.al
paper [17].
16
19. Velocity Contrast to IRIS with Attenuation, and Poisson = 0.25
Distance (km)
Depth(km)
0 100 200 300 400 500 600 700 800
100
150
200
250
300
350
400
Velocity Deviation [%]
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
Figure 3.4: IASP91 Reference Velocity Anomaly
Figure 3.5 shows the velocity deviation from the background field using a simple
percent deviation as prescribed in equation 2.2. The background or reference veloc-
ity field in these is the p-wave converted seismic velocity at time 0. More specifically
the attenuation parameters utilized include the grain size at 1 cm and water content
50
H
106Si
representative of a dry mantle. We notice that at time 0.86 ma we have the
best agreement with the Isabella anomaly with a velocity contrast of about 4.3% and
slab size of roughly 135 km from the base of the crust. Given the simplicity of our model
the ability to retrieve such successful results is quite encouraging. Increasing the mantle
water content from the dry 50
H
106Si
case (COH) = 500,100,3000
H
106Si
, yields
respective velocity contrast anomalies of 4.9%,6.2%,12.3% and size of 142 km, 151 km,
169 km. The grain size variation from 1 cm to 0.75 cm, 0.5 cm and 1 mm result in
velocity contrast anomalies of 4.4%,4.5%,5% and size of 135 km, 135 km, 135 km. These
results confirms that mantle water content has a much more substantial impact on the
size and velocity contrast of our delamination.
The initial geological model parameters could be ”tweaked” in order to more accu-
rately replicate the velocity anomaly. For example the size weak zone and dense root
could be modified such that the slab size is more consistent to the Isabella slab observed.
Accurately reconstructing the model parameters would be a crucial step for further in-
terpretation of accuracy in the conversion. At this point increases imaging the anomaly
would require a shift to quantitative error analysis. However, qualitatively agreement
of the model provides optimism for more in-depth analysis, as I already can observe a
17
21. Chapter 4
Conclusion
In summary, this report demonstrates the ability to utilize a generic model of delam-
ination and at least, to first order, fit the observed velocity anomalies for the Sierra
Nevada mountain range in California. The results demonstrate a removed lithosphere
with a velocity contrast of 4% for a dry mantle and 1 cm grain size, with its size on the
order of about 130 km. This supports the idea that the Isabella anomaly may represent
lithosphere that is in the process of delamination.
4.1 Future Works
In order to refine the accuracy of this method it would be beneficial to apply a correction
or bulk shift to the IRIS reference velocity in order to use a consistent reference velocity
model. Having access to the ray path’s as well as the inversion scheme used by Jones
et al. [17] may also provide improvement to my results. The problem can be progressed
by adding complexity to the model in the form of anisotropy which would then require
additional sensitivity analysis. In converting my shear wave velocity to compressional
velocity I assumed a constant 0.25 Poisson’s ratio and grain size 1 cm for the entire
model space. Ideally I would like to extend my Poisson’s ratio usage to a function
of the form ν(T) such that a compressional velocity for a non uniform Poisson’s ratio
could be obtained. To extend the model to a more realistic state which would include a
heterogeneous and anisotropic mantle and lithosphere in the next step for this study.
4.2 Acknowledgements
The work of Huilin Wang for the geological model used in this project is greatly ap-
preciated. I would also like to acknowledge Dr. Claire Currie for her mentorship and
supervision during my project.
19
23. Appendix A
Matlab Codes
Appendix A contains the codes utilized to complete this project. All codes where made
by Karl-Yvan Mome using MATLAB.
A.1 Temperature and Pressure Mesh
Figure A.1: Eulerian Grid Part 1
21
32. Appendix B
Parameter Definitions and Values
Variable Description Value Units
ρ density see table 1.1
Kg
m3
α non dimensional constant 3 × 10−5
unitless
T temperature N/A Kelvin (K)
u velocity N/A
m
s
t time N/A s
x distance N/A m
σ stress N/A Pa
g gravity 9.81
m
s2
H heat source N/A Kelvin(K)
P Pressure N/A GPa
F constant (1/2) cot(πα/2) s
Q−1
attenuation factor N/A s
w frequency 1/8.2 s
COH olivine water concentration N/A
H
106Si
d grain size N/A m
dQref reference grain size 1.24 × 10−5
m
TQref reference temperature 1538 Kelvin(K)
PQref reference pressure 0.3 GPa
COH(Qref) reference water content in olivine 50
H
106Si
EQref reference activation energy 505
kJ
mol
VQref reference activation volume 1.2 × 10−5 m3
mol
PQref reference grain size exponent 1.09 unitless
Bo prefactor for Q for ω = 0.122Hz 1.28 × 108 mpQ
s
EQ activation energy 420
kJ
mol
VQ activation volume 1.2 × 10−5 m3
mol
pQ grain size exponent 1 unitless
rQ water content exponent 1.2 unitless
30
33. Chapter 5
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32