Assessing Model Uncertainty for the Scaling Function Inversion of Potential Fields

Geophysics ◽  
2021 ◽  
pp. 1-39
Author(s):  
Mahak Singh Chauhan ◽  
Ivano Pierri ◽  
Mrinal K. Sen ◽  
Maurizio FEDI
Keyword(s):  
Simulated Annealing Algorithm ◽  
Scaling Function ◽  
Vertical Section ◽  
Gravity Data ◽  
Geometric Model ◽  
Salt Dome ◽  
The Body ◽  
Gravity Inversion ◽  
Geometrical Parameters ◽  
The Scaling Function

We use the very fast simulated annealing algorithm to invert the scaling function along selected ridges, lying in a vertical section formed by upward continuing gravity data to a set of altitudes. The scaling function is formed by the ratio of the field derivative by the field itself and it is evaluated along the lines formed by the zeroes of the horizontal field derivative at a set of altitudes. We also use the same algorithm to invert gravity anomalies only at the measurement altitude. Our goal is analyzing the different models obtained through the two different inversions and evaluating the relative uncertainties. One main difference is that the scaling function inversion is independent on density and the unknowns are the geometrical parameters of the source. The gravity data are instead inverted for the source geometry and the density simultaneously. A priori information used for both the inversions is that the source has a known depth to the top. We examine the results over the synthetic examples of a salt dome structure generated by Talwani’s approach and real gravity datasets over the Mors salt dome and the Decorah (USA) basin. For all these cases, the scaling function inversion yielded models with a better sensitivity to specific features of the sources, such as the tilt of the body, and reduced uncertainty. We finally analyzed the density, which is one of the unknowns for the gravity inversion and it is estimated from the geometric model for the scaling function inversion. The histograms over the density estimated at many iterations show a very concentrated distribution for the scaling function, while the density contrast retrieved by the gravity inversion, according to the fundamental ambiguity density/volume, is widely dispersed, this making difficult to assess its best estimate.

scholarly journals An Application of Inversion Technique to 1-Dimensional Gravity Data in Bayesian Framework using Monte Carlo, Metropolis, and Simulated Annealing Algorithm

2019 ◽  
Vol 30 (1) ◽  
pp. 1-5
Author(s):  
Adam Sukma Putra ◽  
Wahyu Srigutomo ◽  
Yuant Tiandho ◽  
Herlin Tarigan ◽  
Yanti Yanti
Keyword(s):  
Monte Carlo ◽  
Simulated Annealing ◽  
Simulated Annealing Algorithm ◽  
Gravity Data ◽  
Bayesian Framework ◽  
Gravity Inversion ◽  
Parameter Inversion ◽  
Inversion Methods ◽  
Dimensional Gravity ◽  
Annealing Algorithm

The purpose of this paper is to present a simulation to the inversion methods applied to geophysical exploration. Anapplication of Monte-Carlo, Metropolis, and Simulated Annealing techniques to 1-Dimensional gravity inversion inBayesian framework has been studied. Differences between these methods are observed in both single parameterinversion and simultaneous multi parameter inversion. After selecting the best inversion strategy from the three methods,a further investigation was investigated. Multi parameter inversion for two anomalies is simultaneously carried out andresults are observed. The synthetical data of GRAV2DC free source were used instead of observed data.

scholarly journals Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows

1975 ◽  
Vol 67 (4) ◽  
pp. 787-815 ◽  
Author(s):  
Allen T. Chwang ◽  
T. Yao-Tsu Wu
Keyword(s):  
Exact Solutions ◽  
Stokes Flow ◽  
Fundamental Solutions ◽  
The Body ◽  
Circular Cylinders ◽  
Geometrical Parameters ◽  
Flow Problems ◽  
Singularity Method ◽  
Wide Range ◽  
Body Shapes

The present study further explores the fundamental singular solutions for Stokes flow that can be useful for constructing solutions over a wide range of free-stream profiles and body shapes. The primary singularity is the Stokeslet, which is associated with a singular point force embedded in a Stokes flow. From its derivatives other fundamental singularities can be obtained, including rotlets, stresslets, potential doublets and higher-order poles derived from them. For treating interior Stokes-flow problems new fundamental solutions are introduced; they include the Stokeson and its derivatives, called the roton and stresson.These fundamental singularities are employed here to construct exact solutions to a number of exterior and interior Stokes-flow problems for several specific body shapes translating and rotating in a viscous fluid which may itself be providing a primary flow. The different primary flows considered here include the uniform stream, shear flows, parabolic profiles and extensional flows (hyper-bolic profiles), while the body shapes cover prolate spheroids, spheres and circular cylinders. The salient features of these exact solutions (all obtained in closed form) regarding the types of singularities required for the construction of a solution in each specific case, their distribution densities and the range of validity of the solution, which may depend on the characteristic Reynolds numbers and governing geometrical parameters, are discussed.

GRAVITY AND MAGNETIC INVESTIGATIONS AT THE GRAND SALINE SALT DOME, VAN ZANDT CO., TEXAS

Geophysics ◽  
1945 ◽  
Vol 10 (3) ◽  
pp. 376-393 ◽  
Author(s):  
Jack W. Peters ◽  
Albert F. Dugan
Keyword(s):  
Physical Properties ◽  
Quantitative Evaluation ◽  
Gravity Data ◽  
Salt Dome ◽  
Salt Mine ◽  
Geological Data ◽  
East Texas ◽  
Additional Information ◽  
Theoretical Mass ◽  
Gravity And Magnetic

During May, 1944, detailed gravity and magnetic surveys were made at the Grand Saline Salt Dome to secure additional information on the physical properties of this typical East Texas salt dome. The results of the surface gravity and magnetic surveys, and the subsurface gravity survey in the Morton Salt Mine are illustrated and discussed. Densities and the available subsurface data were compiled and were utilized in a quantitative evaluation of the observed gravity data. The theoretical mass distribution which was determined by this quantitative evaluation is not intended to represent the unique solution of the geophysical and geological data; instead, it is offered as a possible solution based on relatively simple assumptions.

THE CONSTRUCTION OF A CLASS OF TRIVARIATE NONSEPARABLE COMPACTLY SUPPORTED WAVELETS

2009 ◽  
Vol 07 (03) ◽  
pp. 255-267 ◽  
Author(s):  
YONGDONG HUANG ◽  
SHOUZHI YANG ◽  
ZHENGXING CHENG
Keyword(s):  
General Theory ◽  
Mild Condition ◽  
Scaling Function ◽  
Moment Condition ◽  
Compactly Supported ◽  
Vanishing Moment ◽  
The Scaling Function

In this paper, under a mild condition, the construction of compactly supported [Formula: see text]-wavelets is obtained. Wavelets inherit the symmetry of the corresponding scaling function and satisfy the vanishing moment condition originating in the symbols of the scaling function. An example is also given to demonstrate the general theory.

scholarly journals P-wave velocity and density structure beneath Mt. Vesuvius: a magma body in the upper edifice?

2013 ◽  
Vol 56 (4) ◽  
Author(s):  
Paolo Capuano ◽  
Guido Russo ◽  
Roberto Scarpa
Keyword(s):  
High Resolution ◽  
Wave Velocity ◽  
Gravity Data ◽  
High Energy ◽  
P Wave ◽  
Gravity Inversion ◽  
Density Structure ◽  
Resolution Image ◽  
High Resolution Image ◽  
P Wave Velocity

<p>A high-resolution image of the compressional wave velocity and density structure in the shallow edifice of Mount Vesuvius has been derived from simultaneous inversion of travel times and hypocentral parameters of local earthquakes and from gravity inversion. The robustness of the tomography solution has been improved by adding to the earthquake data a set of land based shots, used for constraining the travel time residuals. The results give a high resolution image of the P-wave velocity structure with details down to 300-500 m. The relocated local seismicity appears to extend down to 5 km depth below the central crater, distributed into two clusters, and separated by an anomalously high Vp region positioned at around 1 km depth. A zone with high Vp/Vs ratio in the upper layers is interpreted as produced by the presence of intense fluid circulation alternatively to the interpretation in terms of a small magma chamber inferred by petrologic studies. In this shallower zone the seismicity has the minimum energy, whilst most of the high-energy quakes (up to Magnitude 3.6) occur in the cluster located at greater depth. The seismicity appears to be located along almost vertical cracks, delimited by a high velocity body located along past intrusive body, corresponding to remnants of Mt. Somma. In this framework a gravity data inversion has been performed to study the shallower part of the volcano. Gravity data have been inverted using a method suitable for the application to scattered data in presence of relevant topography based on a discretization of the investigated medium performed by establishing an approximation of the topography by a triangular mesh. The tomography results, the retrieved density distribution, and the pattern of relocated seismicity exclude the presence of significant shallow magma reservoirs close to the central conduit. These should be located at depth higher than that of the base of the hypocenter volume, as evidenced by previous studies.</p>

NEW AMY AND DELPHI MULTIPLICITY DATA AND THE LOGNORMAL DISTRIBUTION

1991 ◽  
Vol 06 (03) ◽  
pp. 245-257 ◽  
Author(s):  
R. SZWED ◽  
G. WROCHNA ◽  
A.K. WRÓBLEWSKI
Keyword(s):  
Energy Dependence ◽  
Lognormal Distribution ◽  
Scaling Function ◽  
Average Multiplicity ◽  
Linear Functions ◽  
The Mean ◽  
Multiplicity Distributions ◽  
The Scaling Function ◽  
Skewness And Kurtosis

Multiplicity distributions for e+e−→ hadrons recently reported by the AMY and DELPHI collaborations are compared with the data obtained at lower energies. It is proven that the new data obey the KNO-G scaling and the scaling function can be described by the lognormal distribution. The dispersions are linear functions of the mean as for the data measured at lower energies and the standardized moments (such as skewness and kurtosis) are independent of the energy. The energy dependence of the average multiplicity is described by <nch>=β sα−1.

Architecture and dynamics of the magmatic system feeding the 2018 offshore Mayotte eruption from satellite gravity data

2021 ◽  
Author(s):  
Hélène Le Mével ◽  
Craig A. Miller ◽  
Yan Zhan
Keyword(s):  
Gravity Data ◽  
System Structure ◽  
Constant Thickness ◽  
Gravity Inversion ◽  
Model Parameters ◽  
Low Density ◽  
Submarine Eruption ◽  
Magmatic System ◽  
Magma Flow ◽  
Marine Gravity

&lt;p&gt;In May 2018, a submarine eruption started offshore Mayotte (Comoros archipelago, Indian Ocean), and was first detected as a series of earthquake swarms. Since then, at least 6.4 km&lt;sup&gt;3&lt;/sup&gt; of lava has erupted from a newly mapped volcanic edifice (MAYOBS campaigns), about 50 km east of Mayotte island. Since the onset of the eruption, GNSS stations on the island have recorded subsidence (up to 17 cm) and eastward displacement (up to 23 cm). We combine marine gravity data derived from satellite altimetry with finite element models to examine the magmatic system structure and its dynamics. First, we calculate the Mantle Bouguer Anomaly (MBA) by taking into account the gravitational effect of the bathymetry and the Moho interfaces, assuming a crust of constant thickness of 17.5 km and correction densities of 2.8 g/cm&lt;sup&gt;3&lt;/sup&gt; and 3.3 g/cm&lt;sup&gt;3&lt;/sup&gt; for the crust and mantle, respectively. We then invert the MBA to determine the anomalous density structures within the lithosphere, using the mixed Lp-norm inversion and Gauss-Newton optimization implemented in the SimPEG framework. The gravity inversion reveals two zones of low density, east of Mayotte island. The first is located NE of Petite Terre island between ~15 and 35 km depth, and the second is located further east, south of La Jumelle seamounts and extends from ~25 to 35 km depth. We interpret these low density regions as regions of partial melt stored in the lithosphere and estimate the volume of stored magma. Finally, we use the newly imaged low density bodies to constrain the magma reservoir geometry and simulate magma flow from this reservoir to the eruptive vent in a 3D, time-dependent, numerical model. The model parameters are adjusted by minimizing the misfit between the modeled surface displacement and that measured at the 6 GPS sites, between May 2018 and 2020. The deformation modeling reveals the temporal evolution of the magma flux during the eruption, and the resulting stress distribution in the crust explains the patterns of recorded seismicity. Together with the existing seismic and geodetic studies, the gravity data analysis and FEM models bring new constraints on the architecture of the magma plumbing system and the magmatic processes behind the largest submarine eruption ever documented.&lt;/p&gt;

Joint receiver function and gravity inversion for new constraints on the Ivrea body structure: a 2D high-resolution view along the Val Sesia profile (N. Italy).

2021 ◽  
Author(s):  
Matteo Scarponi ◽  
György Hetényi ◽  
Jaroslava Plomerová ◽  
Stefano Solarino
Keyword(s):  
High Resolution ◽  
Velocity Structure ◽  
Receiver Function ◽  
Joint Inversion ◽  
Gravity Data ◽  
Rock Physics ◽  
Receiver Functions ◽  
Gravity Inversion ◽  
European Alps ◽  
Horizontal Distance

&lt;p&gt;We present results from a joint inversion study of new seismic and gravity data to constrain a 2D high-resolution image of one of the most prominent geophysical anomalies of the European Alps: the Ivrea geophysical body (IGB). Our work exploits both new data and multidisciplinary a priori constraints, to better resolve the shallow crustal structure in the Ivrea-Verbano zone (IVZ), where the IGB is known to reach anomalously shallow depths and partially outcrop at the surface.&lt;/p&gt;&lt;p&gt;A variety of previous studies, ranging from gravity surveys to vintage refraction seismics and recent local earthquake tomographies (Solarino et al. 2018, Diehl et al. 2009), provide comprehensive but spatially sparse information on the IGB structure, which we aim at investigating at higher resolution, along a linear profile crossing the IVZ. To this purpose, we deployed 10 broadband seismic stations (MOBNET pool, IG CAS Prague), 5 km spaced along a linear West-East profile, along Val Sesia and crossing Lago Maggiore. This network operated for 27 months and allowed us to produce a new database of ca. 1000 seismic high-quality receiver functions (RFs). In addition, we collected new gravity data in the IVZ, with a data coverage of 1 gravity point every 1-2 km along the seismic profile. The newly collected data was used to set up an inversion scheme, in which RFs and gravity anomalies are jointly used to constrain the shape and the physical property contrasts across the IGB interface.&lt;/p&gt;&lt;p&gt;We model the IGB as a single interface between far-field constraints, whose geometry is defined by the coordinates of four nodes which may vary in space, and &amp;#160;density and V&lt;sub&gt;S&lt;/sub&gt; shear-wave velocity contrasts associated with the interface itself, varying independently. A Markov chain Monte Carlo (MCMC) sampling method with Metropolis-Hastings selection rule was implemented to efficiently explore the model space, directing the search towards better fitting areas.&lt;/p&gt;&lt;p&gt;For each model, we perform ray-tracing and RFs migration using the actual velocity structure both for migration and computation of synthetic RFs, to be compared with the observations via cross-correlation of the migration images. Similarly, forward gravity modelling for a 2D density distribution is implemented and the synthetic gravity anomaly is compared with the observations along the profile. The joint inversion performance is the product of these two misfits.&lt;/p&gt;&lt;p&gt;The inversion results show that the IGB reaches the shallowest depths in the western part of the profile, preferentially locating the IGB interface between 3 and 7 km depth over a horizontal distance of ca. 20 km (between Boccioleto and Civiasco, longitudes 8.1 and 8.3). Within this segment, the shallowest point reaches up to 1 km below sea level. The found density and velocity contrasts are in agreement with rock physics properties of various units observed in the field and characterized in earlier studies.&lt;/p&gt;

OFF THE CRITICAL POINT BY PERTURBATION (II): THE ISING MODEL SPIN-SPIN CORRELATOR IN A MAGNETIC FIELD

1990 ◽  
Vol 04 (05) ◽  
pp. 1039-1047 ◽  
Author(s):  
Vl. S. Dotsenko
Keyword(s):  
Magnetic Field ◽  
Correlation Function ◽  
Ising Model ◽  
Scaling Function ◽  
Spin Correlation ◽  
Regularization Technique ◽  
Spin Correlation Function ◽  
Analytic Regularization ◽  
Spin Correlator ◽  
The Scaling Function

An extension of the analytic regularization technique based on the conform 1 theory is suggested for the case of the spin-spin correlation function of the Ising model in a magnetic field, <σ0σR>h=F(t)/(R)1/4, t=hR15/8. Several first terms of the expansion of the scaling function F(t) are given.

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