Structural joint inversion coupled with Euler deconvolution of isolated gravity and magnetic anomalies

Geophysics ◽  
2015 ◽  
Vol 80 (2) ◽  
pp. G67-G79 ◽  
Author(s):  
Emilia Fregoso ◽  
Luis A. Gallardo ◽  
Juan García-Abdeslem
Keyword(s):  
Joint Inversion ◽  
Structural Characteristics ◽  
A Priori ◽  
Real Field ◽  
Vertical Position ◽  
Euler Deconvolution ◽  
Data Set ◽  
Gravity And Magnetic ◽  
Structural Joint ◽  
Northwest Region

We generalized the Euler deconvolution method to a joint scheme, which consists of locating the horizontal and vertical positions of the top of potential-field 3D sources. These results were then used to constrain the depth to the top of the models obtained by cross-gradient joint 3D inversions, imposing fixed known values in the a priori models. The coupling of both methods produced more realistic density and magnetization models for separate and joint inversions, relative to those obtained by applying cross-gradient joint inversion only. This strategy was tested on a 3D synthetic experiment, and on a real field data set from the northwest region of the Baja California Peninsula, Mexico. After locating the vertical position of the source, the algorithm uses this information to obtain density and magnetization models that enhanced their structural compatibility and reduces the ambiguity on the interpretation of their structural characteristics laterally and at surface.

Structural joint inversion on irregular meshes

2019 ◽  
Vol 220 (3) ◽  
pp. 1995-2008 ◽  
Author(s):  
C Jordi ◽  
J Doetsch ◽  
T Günther ◽  
C Schmelzbach ◽  
H Maurer ◽  
...  
Keyword(s):  
Electrical Resistivity ◽  
Joint Inversion ◽  
A Priori ◽  
Structural Similarity ◽  
P Wave ◽  
Parameter Distribution ◽  
Data Sets ◽  
Inversion Algorithm ◽  
Structural Joint ◽  
Irregular Meshes

SUMMARY Structural joint inversion of several data sets on an irregular mesh requires appropriate coupling operators. To date, joint inversion algorithms are primarily designed for the use on regular rectilinear grids and impose structural similarity in the direct neighbourhood of a cell only. We introduce a novel scheme for calculating cross-gradient operators based on a correlation model that allows to define the operator size by imposing physical length scales. We demonstrate that the proposed cross-gradient operators are largely decoupled from the discretization of the modelling domain, which is particularly important for irregular meshes where cell sizes vary. Our structural joint inversion algorithm is applied to a synthetic electrical resistivity tomography and ground penetrating radar 3-D cross-well experiment aiming at imaging two anomalous bodies and extracting the parameter distribution of the geostatistical background models. For both tasks, joint inversion produced superior results compared with individual inversions of the two data sets. Finally, we applied structural joint inversion to two field data sets recorded over a karstified limestone area. By including geological a priori information via the correlation-based operators into the joint inversion, we find P-wave velocity and electrical resistivity tomograms that are in accordance with the expected subsurface geology.

scholarly journals Quantitative imaging of water, ice and air in permafrost systems through petrophysical joint inversion of seismic refraction and electrical resistivity data

2019 ◽  
Vol 219 (3) ◽  
pp. 1866-1875 ◽  
Author(s):  
F M Wagner ◽  
C Mollaret ◽  
T Günther ◽  
A Kemna ◽  
C Hauck
Keyword(s):  
Electrical Resistivity ◽  
Liquid Water ◽  
Field Data ◽  
Joint Inversion ◽  
A Priori ◽  
Seismic Refraction ◽  
Rock Matrix ◽  
Data Set ◽  
Water Ice ◽  
Borehole Temperatures

SUMMARY Quantitative estimation of pore fractions filled with liquid water, ice and air is crucial for a process-based understanding of permafrost and its hazard potential upon climate-induced degradation. Geophysical methods offer opportunities to image distributions of permafrost constituents in a non-invasive manner. We present a method to jointly estimate the volumetric fractions of liquid water, ice, air and the rock matrix from seismic refraction and electrical resistivity data. Existing approaches rely on conventional inversions of both data sets and a suitable a priori estimate of the porosity distribution to transform velocity and resistivity models into estimates for the four-phase system, often leading to non-physical results. Based on two synthetic experiments and a field data set from an Alpine permafrost site (Schilthorn, Bernese Alps and Switzerland), it is demonstrated that the developed petrophysical joint inversion provides physically plausible solutions, even in the absence of prior porosity estimates. An assessment of the model covariance matrix for the coupled inverse problem reveals remaining petrophysical ambiguities, in particular between ice and rock matrix. Incorporation of petrophysical a priori information is demonstrated by penalizing ice occurrence within the first two meters of the subsurface where the measured borehole temperatures are positive. Joint inversion of the field data set reveals a shallow air-rich layer with high porosity on top of a lower-porosity subsurface with laterally varying ice and liquid water contents. Non-physical values (e.g. negative saturations) do not occur and estimated ice saturations of 0–50 per cent as well as liquid water saturations of 15–75 per cent are in agreement with the relatively warm borehole temperatures between −0.5  and 3 ° C. The presented method helps to improve quantification of water, ice and air from geophysical observations.

Particle swarm optimization of 2D magnetotelluric data

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. E125-E141 ◽  
Author(s):  
Francesca Pace ◽  
Alessandro Santilano ◽  
Alberto Godio
Keyword(s):  
Inverse Problem ◽  
Particle Swarm Optimization ◽  
A Priori ◽  
Particle Swarm ◽  
Stability And Convergence ◽  
Real Field ◽  
A Priori Information ◽  
Data Set ◽  
Swarm Optimization ◽  
Priori Information

We implement the particle swarm optimization (PSO) algorithm for the two-dimensional (2D) magnetotelluric (MT) inverse problem. We first validate PSO on two synthetic models of different complexity and then apply it to an MT benchmark for real-field data, the COPROD2 data set (Canada). We pay particular attention to the selection of the PSO input parameters to properly address the complexity of the 2D MT inverse problem. We enhance the stability and convergence of the solution of the geophysical problem by applying the hierarchical PSO with time-varying acceleration coefficients (HPSO-TVAC). Moreover, we parallelize the code to reduce the computation time because PSO is a computationally demanding global search algorithm. The inverse problem was solved for the synthetic data both by giving a priori information at the beginning and by using a random initialization. The a priori information was given to a small number of particles as the initial position within the search space of solutions, so that the swarming behavior was only slightly influenced. We have demonstrated that there is no need for the a priori initialization to obtain robust 2D models because the results are largely comparable with the results from randomly initialized PSO. The optimization of the COPROD2 data set provides a resistivity model of the earth in line with results from previous interpretations. Our results suggest that the 2D MT inverse problem can be successfully addressed by means of computational swarm intelligence.

Joint inversion of Rayleigh-wave dispersion and P-wave refraction data for laterally varying layered models

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. EN49-EN59 ◽  
Author(s):  
Daniele Boiero ◽  
Laura Valentina Socco
Keyword(s):  
Rayleigh Wave ◽  
Joint Inversion ◽  
A Priori ◽  
P Wave ◽  
Inversion Method ◽  
Model Parameters ◽  
Data Set ◽  
Wave Refraction ◽  
Velocity Models ◽  
Refraction Data

We implemented a joint inversion method to build P- and S-wave velocity models from Rayleigh-wave and P-wave refraction data, specifically designed to deal with laterally varying layered environments. A priori information available over the site and any physical law to link model parameters can be also incorporated. We tested and applied the algorithm behind the method. The results from a field data set revealed advantages with respect to individual surface-wave analysis (SWA) and body wave tomography (BWT). The algorithm imposed internal consistency for all the model parameters relaxing the required a priori assumptions (i.e., Poisson’s ratio level of confidence in SWA) and the inherent limitations of the two methods (i.e., velocity decreases for BWT).

scholarly journals A Traveler’s Guide to the Multiverse: Promises, Pitfalls, and a Framework for the Evaluation of Analytic Decisions

2021 ◽  
Vol 4 (1) ◽  
pp. 251524592095492
Author(s):  
Marco Del Giudice ◽  
Steven W. Gangestad
Keyword(s):  
Degrees Of Freedom ◽  
A Priori ◽  
Simulated Data ◽  
Style Analysis ◽  
Data Set ◽  
Scant Attention ◽  
Equivalence Type ◽  
The Impact ◽  
Biased Estimates

Decisions made by researchers while analyzing data (e.g., how to measure variables, how to handle outliers) are sometimes arbitrary, without an objective justification for choosing one alternative over another. Multiverse-style methods (e.g., specification curve, vibration of effects) estimate an effect across an entire set of possible specifications to expose the impact of hidden degrees of freedom and/or obtain robust, less biased estimates of the effect of interest. However, if specifications are not truly arbitrary, multiverse-style analyses can produce misleading results, potentially hiding meaningful effects within a mass of poorly justified alternatives. So far, a key question has received scant attention: How does one decide whether alternatives are arbitrary? We offer a framework and conceptual tools for doing so. We discuss three kinds of a priori nonequivalence among alternatives—measurement nonequivalence, effect nonequivalence, and power/precision nonequivalence. The criteria we review lead to three decision scenarios: Type E decisions (principled equivalence), Type N decisions (principled nonequivalence), and Type U decisions (uncertainty). In uncertain scenarios, multiverse-style analysis should be conducted in a deliberately exploratory fashion. The framework is discussed with reference to published examples and illustrated with the help of a simulated data set. Our framework will help researchers reap the benefits of multiverse-style methods while avoiding their pitfalls.

scholarly journals MAX-DOAS observations of aerosols, formaldehyde and nitrogen dioxide in the Beijing area: comparison of two profile retrieval approaches

2015 ◽  
Vol 8 (2) ◽  
pp. 941-963 ◽  
Author(s):  
T. Vlemmix ◽  
F. Hendrick ◽  
G. Pinardi ◽  
I. De Smedt ◽  
C. Fayt ◽  
...  
Keyword(s):  
Standard Deviation ◽  
A Priori ◽  
Systematic Bias ◽  
Aerosol Extinction ◽  
Data Set ◽  
Near Surface ◽  
Beijing Area ◽  
Least Squares Fit ◽  
Relative Differences ◽  
Good Agreement

Abstract. A 4-year data set of MAX-DOAS observations in the Beijing area (2008–2012) is analysed with a focus on NO2, HCHO and aerosols. Two very different retrieval methods are applied. Method A describes the tropospheric profile with 13 layers and makes use of the optimal estimation method. Method B uses 2–4 parameters to describe the tropospheric profile and an inversion based on a least-squares fit. For each constituent (NO2, HCHO and aerosols) the retrieval outcomes are compared in terms of tropospheric column densities, surface concentrations and "characteristic profile heights" (i.e. the height below which 75% of the vertically integrated tropospheric column density resides). We find best agreement between the two methods for tropospheric NO2 column densities, with a standard deviation of relative differences below 10%, a correlation of 0.99 and a linear regression with a slope of 1.03. For tropospheric HCHO column densities we find a similar slope, but also a systematic bias of almost 10% which is likely related to differences in profile height. Aerosol optical depths (AODs) retrieved with method B are 20% high compared to method A. They are more in agreement with AERONET measurements, which are on average only 5% lower, however with considerable relative differences (standard deviation ~ 25%). With respect to near-surface volume mixing ratios and aerosol extinction we find considerably larger relative differences: 10 ± 30, −23 ± 28 and −8 ± 33% for aerosols, HCHO and NO2 respectively. The frequency distributions of these near-surface concentrations show however a quite good agreement, and this indicates that near-surface concentrations derived from MAX-DOAS are certainly useful in a climatological sense. A major difference between the two methods is the dynamic range of retrieved characteristic profile heights which is larger for method B than for method A. This effect is most pronounced for HCHO, where retrieved profile shapes with method A are very close to the a priori, and moderate for NO2 and aerosol extinction which on average show quite good agreement for characteristic profile heights below 1.5 km. One of the main advantages of method A is the stability, even under suboptimal conditions (e.g. in the presence of clouds). Method B is generally more unstable and this explains probably a substantial part of the quite large relative differences between the two methods. However, despite a relatively low precision for individual profile retrievals it appears as if seasonally averaged profile heights retrieved with method B are less biased towards a priori assumptions than those retrieved with method A. This gives confidence in the result obtained with method B, namely that aerosol extinction profiles tend on average to be higher than NO2 profiles in spring and summer, whereas they seem on average to be of the same height in winter, a result which is especially relevant in relation to the validation of satellite retrievals.

Magnetotelluric static shift: Estimation and removal using the cokriging method

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. F25-F34 ◽  
Author(s):  
Benoit Tournerie ◽  
Michel Chouteau ◽  
Denis Marcotte
Keyword(s):  
Apparent Resistivity ◽  
A Priori ◽  
Shift Factor ◽  
Static Shift ◽  
Geostatistical Model ◽  
Data Set ◽  
Resistivity Sounding ◽  
The Difference ◽  
Cross Variogram

We present and test a new method to correct for the static shift affecting magnetotelluric (MT) apparent resistivity sounding curves. We use geostatistical analysis of apparent resistivity and phase data for selected periods. For each period, we first estimate and model the experimental variograms and cross variogram between phase and apparent resistivity. We then use the geostatistical model to estimate, by cokriging, the corrected apparent resistivities using the measured phases and apparent resistivities. The static shift factor is obtained as the difference between the logarithm of the corrected and measured apparent resistivities. We retain as final static shift estimates the ones for the period displaying the best correlation with the estimates at all periods. We present a 3D synthetic case study showing that the static shift is retrieved quite precisely when the static shift factors are uniformly distributed around zero. If the static shift distribution has a nonzero mean, we obtained best results when an apparent resistivity data subset can be identified a priori as unaffected by static shift and cokriging is done using only this subset. The method has been successfully tested on the synthetic COPROD-2S2 2D MT data set and on a 3D-survey data set from Las Cañadas Caldera (Tenerife, Canary Islands) severely affected by static shift.

Character selection and the quantification of morphological disparity

Paleobiology ◽  
2016 ◽  
Vol 43 (1) ◽  
pp. 68-84 ◽  
Author(s):  
Bradley Deline ◽  
William I. Ausich
Keyword(s):  
A Priori ◽  
Morphological Diversity ◽  
Small Subset ◽  
Early Paleozoic ◽  
Data Set ◽  
Rarefaction Analysis ◽  
Morphological Studies ◽  
Body Regions ◽  
Scientific Hypotheses

AbstractA priori choices in the detail and breadth of a study are important in addressing scientific hypotheses. In particular, choices in the number and type of characters can greatly influence the results in studies of morphological diversity. A new character suite was constructed to examine trends in the disparity of early Paleozoic crinoids. Character-based rarefaction analysis indicated that a small subset of these characters (~20% of the complete data set) could be used to capture most of the properties of the entire data set in analyses of crinoids as a whole, noncamerate crinoids, and to a lesser extent camerate crinoids. This pattern may be the result of the covariance between characters and the characterization of rare morphologies that are not represented in the primary axes in morphospace. Shifting emphasis on different body regions (oral system, calyx, periproct system, and pelma) also influenced estimates of relative disparity between subclasses of crinoids. Given these results, morphological studies should include a pilot analysis to better examine the amount and type of data needed to address specific scientific hypotheses.

scholarly journals Robust Bayesian Joint Inversion of Gravimetric and Muographic Data for the Density Imaging of the Puy de Dôme Volcano (France)

2021 ◽  
Vol 8 ◽  
Author(s):  
Anne Barnoud ◽  
Valérie Cayol ◽  
Peter G. Lelièvre ◽  
Angélie Portal ◽  
Philippe Labazuy ◽  
...  
Keyword(s):  
Joint Inversion ◽  
A Priori ◽  
Constant Density ◽  
Acquisition Duration ◽  
Regularization Parameters ◽  
Absolute Density ◽  
Gravimetric Data ◽  
Ill Posed ◽  
Leave One Out

Imaging the internal structure of volcanoes helps highlighting magma pathways and monitoring potential structural weaknesses. We jointly invert gravimetric and muographic data to determine the most precise image of the 3D density structure of the Puy de Dôme volcano (Chaîne des Puys, France) ever obtained. With rock thickness of up to 1,600 m along the muon lines of sight, it is, to our knowledge, the largest volcano ever imaged by combining muography and gravimetry. The inversion of gravimetric data is an ill-posed problem with a non-unique solution and a sensitivity rapidly decreasing with depth. Muography has the potential to constrain the absolute density of the studied structures but the use of the method is limited by the possible number of acquisition view points, by the long acquisition duration and by the noise contained in the data. To take advantage of both types of data in a joint inversion scheme, we develop a robust method adapted to the specificities of both the gravimetric and muographic data. Our method is based on a Bayesian formalism. It includes a smoothing relying on two regularization parameters (an a priori density standard deviation and an isotropic correlation length) which are automatically determined using a leave one out criterion. This smoothing overcomes artifacts linked to the data acquisition geometry of each dataset. A possible constant density offset between both datasets is also determined by least-squares. The potential of the method is shown using the Puy de Dôme volcano as case study as high quality gravimetric and muographic data are both available. Our results show that the dome is dry and permeable. Thanks to the muographic data, we better delineate a trachytic dense core surrounded by a less dense talus.

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