The uncertainty of CRUST1.0

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lars E. Sjöberg ◽  
Majid Abrehdary
Keyword(s):  
A Priori ◽  
Analytical Techniques ◽  
Moho Depth ◽  
Survey Method ◽  
Gravity Inversion ◽  
Contour Maps ◽  
Error Covariance ◽  
Crustal Structures ◽  
Simple Error ◽  
Priori Information

Abstract As crustal structure models based on seismic and other data are frequently used as a-priori information for further geophysical and geological studies and interpretations (e. g., for gravity inversion), it is important to accurately document their qualities. For instance, the uncertainties in published crustal structures deeply affect the accuracies of produced Moho contour maps. The qualities in seismic crustal models arise from several factors such as the survey method, the spatial resolution of the survey (for example the spacing of the shot points and the recording stations), and the analytical techniques utilized to process the data. It is difficult to determine the uncertainties associated with seismic based crustal depth/Moho depth (MD) models, and even more difficult to use such data for estimating the Moho density contrast (MDC) and its accuracy. However, there is another important observable available today, namely global satellite gravitational data, which are fairly homogeneous v. r. t. accuracy and distribution over the planet. For instance, we find by simple error propagation, using the error covariance matrix of the GOCE TIM5 gravitational model, that this model can determine the MD to a global RMS error of 0.8 km with a resolution of about 1° for a known MDC of 200  kg / m 3 \text{kg}/{\text{m}^{3}} . However, the uncertainty in the MDC will further deteriorate the result. We present a new method for estimating the MD and MDC uncertainties of one model by comparing it with another (correlated or uncorrelated) model with known uncertainty. The method is applied in estimating the uncertainty for the CRUST1.0 MD model from four global models (CRUST19, MDN07, GEMMA1.0, KTH15C), yielding mean standard errors varying between 2 and 4.9 km in ocean regions and between 3.2 and 6.0 km on land regions with overall means of 3.8±0.4 and 4.8 ± 0.6 km 4.8\pm 0.6\hspace{0.1667em}\text{km} , respectively. Also, starting from the KTH15C MDC model, the mean standard error of CRUST1.0 MDC was estimated to 47.4 and 48.3  kg / m 3 \text{kg}/{\text{m}^{3}} for ocean and land regions, respectively.

Generalized compact gravity inversion

Geophysics ◽  
1994 ◽  
Vol 59 (1) ◽  
pp. 57-68 ◽  
Author(s):  
Valeria Cristina F. Barbosa ◽  
João B. C. Silva
Keyword(s):  
Body Shape ◽  
Sedimentary Basin ◽  
A Priori ◽  
Gravity Inversion ◽  
A Priori Information ◽  
Magnetite Ore ◽  
Inversion Technique ◽  
True Value ◽  
Ore Body ◽  
Priori Information

Extending the compact gravity inversion technique by incorporating a priori information about the maximum compactness of the anomalous sources along several axes provides versatility. Thus, the method may also incorporate information about limits in the axes lengths or greater concentration of mass along one or more directions. The judicious combination of different constraints on the anomalous mass distribution allows the introduction of several kinds of a priori information about the (arbitrary) shape of the sources. This method is particularly applicable to constant, linear density sources such as mineralizations along faults and intruded sills, dikes, and laccoliths in a sedimentary basin. The correct source density must be known with a maximum uncertainty of 40 percent; otherwise, the inversion produces thicker bodies for densities smaller than the true value and vice‐versa. Because of the limitations of the inverse gravity problem, the proposed technique requires an empirical technique to analyze the sensitivity of solutions to uncertainties in the a priori information. The proposed technique is based on a finite number of acceptable solutions, presumably representative of the ambiguity region. By using standard statistical techniques, each parameter is assigned a coefficient measuring its uncertainty. The known hematite and magnetite ore body shape, in the vicinity of Iron Mountain, MO, was reproduced quite well using this inversion technique.

Three‐dimensional gravity inversion using simulated annealing: Constraints on the diapiric roots of allochthonous salt structures

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1438-1449 ◽  
Author(s):  
Seiichi Nagihara ◽  
Stuart A. Hall
Keyword(s):  
Simulated Annealing ◽  
Gulf Of Mexico ◽  
Gravity Data ◽  
A Priori ◽  
Gravity Inversion ◽  
Inversion Method ◽  
A Priori Information ◽  
Final Density ◽  
Smoothing Effects ◽  
Priori Information

In the northern continental slope of the Gulf of Mexico, large oil and gas reservoirs are often found beneath sheetlike, allochthonous salt structures that are laterally extensive. Some of these salt structures retain their diapiric feeders or roots beneath them. These hidden roots are difficult to image seismically. In this study, we develop a method to locate and constrain the geometry of such roots through 3‐D inverse modeling of the gravity anomalies observed over the salt structures. This inversion method utilizes a priori information such as the upper surface topography of the salt, which can be delineated by a limited coverage of 2‐D seismic data; the sediment compaction curve in the region; and the continuity of the salt body. The inversion computation is based on the simulated annealing (SA) global optimization algorithm. The SA‐based gravity inversion has some advantages over the approach based on damped least‐squares inversion. It is computationally efficient, can solve underdetermined inverse problems, can more easily implement complex a priori information, and does not introduce smoothing effects in the final density structure model. We test this inversion method using synthetic gravity data for a type of salt geometry that is common among the allochthonous salt structures in the Gulf of Mexico and show that it is highly effective in constraining the diapiric root. We also show that carrying out multiple inversion runs helps reduce the uncertainty in the final density model.

scholarly journals Seismic Constrained Gravity Inversion: A Reliable Tool to Improve Geophysical Models Away from Seismic Information

Geosciences ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 467
Author(s):  
Daniele Sampietro ◽  
Martina Capponi
Keyword(s):  
High Resolution ◽  
Gravity Field ◽  
A Priori ◽  
Geophysical Methods ◽  
Real Life ◽  
Gravity Inversion ◽  
Seismic Surveys ◽  
Real Model ◽  
Gravity Fields ◽  
Priori Information

The exploitation of gravity fields in order to retrieve information about subsurface geological structures is sometimes considered a second rank method, in favour of other geophysical methods, such as seismic, able to provide a high resolution detailed picture of the main geological horizons. Within the current work we prove, through a realistic synthetic case study, that the gravity field, thanks to the availability of freely of charge high resolution global models and to the improvements in the gravity inversion methods, can represent a valid and cheap tool to complete and enhance geophysical modelling of the Earth’s crust. Three tests were carried out: In the first one a simple two-layer problem was considered, while in tests two and three we considered two more realistic scenarios in which the availability on the study area of constraints derived from 3D or 2D seismic surveys were simulated. In all the considered test cases, in which we try to simulate real-life scenarios, the gravity field, inverted by means of an advanced Bayesian technique, was able to obtain a final solution closer to the (simulated) real model than the assumed a priori information, typically halving the uncertainties in the geometries of the main geological horizons with respect to the initial model.

Isostatic constraint for 2D nonlinear gravity inversion on rifted margins

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. G17-G34
Author(s):  
B. Marcela S. Bastos ◽  
Vanderlei C. Oliveira Jr.
Keyword(s):  
Gravity Data ◽  
A Priori ◽  
Petroleum Industry ◽  
Synthetic Data ◽  
Gravity Inversion ◽  
Rifted Margins ◽  
Isostatic Equilibrium ◽  
Priori Information ◽  
Pelotas Basin ◽  
Nonlinear Gravity

We have developed a nonlinear gravity inversion for simultaneously estimating the basement and Moho geometries, as well as the depth of the reference Moho along a profile crossing a passive rifted margin. To obtain stable solutions, we impose smoothness on basement and Moho, force them to be close to previously estimated depths along the profile and also impose local isostatic equilibrium. Different from previous methods, we evaluate the information of local isostatic equilibrium by imposing smoothness on the lithostatic stress exerted at depth. Our method delimits regions that deviate and those that can be considered in local isostatic equilibrium by varying the weight of the isostatic constraint along the profile. It also allows controlling the degree of equilibrium along the profile, so that the interpreter can obtain a set of candidate models that fit the observed data and exhibit different degrees of isostatic equilibrium. Our method also differs from earlier studies because it attempts to use isostasy for exploring (but not necessarily reducing) the inherent ambiguity of gravity methods. Tests with synthetic data illustrate the effect of our isostatic constraint on the estimated basement and Moho reliefs, especially at regions with pronounced crustal thinning, which are typical of passive volcanic margins. Results obtained by inverting satellite data over the Pelotas Basin, a passive volcanic margin in southern Brazil, agree with previous interpretations obtained independently by combining gravity, magnetic, and seismic data available to the petroleum industry. These results indicate that combined with a priori information, simple isostatic assumptions can be very useful for interpreting gravity data on passive rifted margins.

scholarly journals Practical Tips for 3D Regional Gravity Inversion

Geosciences ◽  
2019 ◽  
Vol 9 (8) ◽  
pp. 351 ◽  
Author(s):  
Daniele Sampietro ◽  
Martina Capponi
Keyword(s):  
Spatial Resolution ◽  
Mass Density ◽  
A Priori ◽  
Regional Scale ◽  
Gravity Inversion ◽  
A Priori Information ◽  
Numerical Examples ◽  
Priori Information ◽  
Regional Gravity ◽  
The Ideal

To solve the inverse gravimetric problem, i.e., to estimate the mass density distribution that generates a certain gravitational field, at local or regional scale, several parameters have to be defined such as the dimension of the 3D region to be considered for the inversion, its spatial resolution, the size of its border, etc. Determining the ideal setting for these parameters is in general difficult: theoretical solutions are usually not possible, while empirical ones strongly depend on the specific target of the inversion and on the experience of the user performing the computation. The aim of the present work is to discuss empirical strategies to set these parameters in such a way to avoid distortions and errors within the inversion. In particular, the discussion is focused on the choice of the volume of the model to be inverted, the size of its boundary, its spatial resolution, and the spatial resolution of the a-priori information to be used within the data reduction. The magnitude of the possible effects due to a wrong choice of the above parameters is also discussed by means of numerical examples.

3D gravity inversion with Euler deconvolution as a priori information

2007 ◽  
Vol 38 (1) ◽  
pp. 44-49 ◽  
Author(s):  
Hyoungrae Rim ◽  
Yeong-Sue Park ◽  
Mutaek Lim ◽  
Sung Bon Koo ◽  
Byung Doo Kwon
Keyword(s):  
A Priori ◽  
Gravity Inversion ◽  
A Priori Information ◽  
Euler Deconvolution ◽  
3D Gravity ◽  
Priori Information

Practical applications of uniqueness theorems in gravimetry: Part II—Pragmatic incorporation of concrete geologic information

Geophysics ◽  
2002 ◽  
Vol 67 (3) ◽  
pp. 795-800 ◽  
Author(s):  
Valéria C. F. Barbosa ◽  
João B. C. Silva ◽  
Walter E. Medeiros
Keyword(s):  
Gravity Data ◽  
A Priori ◽  
Gravity Inversion ◽  
Solution Stability ◽  
Practical Applications ◽  
Density Distributions ◽  
Alternative Method ◽  
True Source ◽  
Priori Information ◽  
Simply Connected

We illustrate the importance of establishing solution uniqueness through mathematical restrictions reflecting a source attribute. We also illustrate the validity and utility of a guideline derived in an accompanying paper for constructing sound gravity inversion methods for the class of sources presenting either homogeneous or depth‐independent density distributions. The two‐part guideline is (1) to introduce a priori information favoring uniqueness, either by assuming that a nonnull density distribution depending only on x and y is confined to the interior of a horizontal slab with known position or by limiting the class of possible solutions to homogeneous, simply connected polygons (or polyhedra) with known density, displaying no fancy shapes and no curling apophyses at their borders, and (2) to introduce information favoring solution stability by estimating only the features of the source which may be resolved by the data. Following the guideline, we apply different methods to gravity data using interpretation models consisting of a grid of cells on the x‐y and x‐z planes. In both cases the estimates are very close to the true synthetic source. The data produced by the distribution varying with x and z are also inverted using the method, which minimizes the norm of the first‐order derivative of the density. This constraint does not reflect a true source attribute but is strong enough to stabilize the solution and to guarantee its uniqueness. Because of the strong bias imposed to the solution, the estimated distribution, although unique and stable, is far from the true source, concentrating most of the anomalous mass at the surface. Finally, we present an alternative method which redistributes the estimated anomalous mass downward. To be effective, this technique requires prior knowledge about the source depth to the top. In addition, the source should not be too small and deep. Although being able to produce good results, this alternative method requires a great dose of the interpreter's art.

Practical applications of uniqueness theorems in gravimetry: Part I—Constructing sound interpretation methods

Geophysics ◽  
2002 ◽  
Vol 67 (3) ◽  
pp. 788-794 ◽  
Author(s):  
João B. C. Silva ◽  
Walter E. Medeiros ◽  
Valéria C. F. Barbosa
Keyword(s):  
Inverse Problem ◽  
A Priori ◽  
Stable Solution ◽  
Gravity Inversion ◽  
Uniqueness Theorems ◽  
A Priori Information ◽  
Practical Applications ◽  
Inversion Methods ◽  
Geological Information ◽  
Priori Information

To obtain a unique and stable solution to the gravity inverse problem, a priori information reflecting geological attributes of the gravity source must be used. Mathematical conditions to obtain stable solutions are established in Tikhonov's regularization method, where the a priori information is introduced via a stabilizing functional, which may be suitably designed to incorporate some relevant geological information. However, there is no unifying approach establishing general uniqueness conditions for a gravity inverse problem. Rather, there are many theorems, usually establishing just abstract mathematical conditions and making it difficult to devise the type of geological information needed to guarantee a unique solution. In Part I of these companion papers, we show that translating the mathematical uniqueness conditions into geological constraints is an important step not only in establishing the type of geological setting where a particular method may be applied but also in designing new gravity inversion methods. As an example, we analyze three uniqueness theorems in gravimetry restricted to the class of homogeneous bodies with known density and show that the uniqueness conditions established by them are more probably met if the solution is constrained to be a compact body without curled protrusions at their borders. These conditions, together with stabilizing conditions (assuming a simple shape for the source), form a guideline to construct sound gravity inversion methods. A historical review of the gravity interpretation methods shows that several methods implicitly follow this guideline. In Part II we use synthetic examples to illustrate the theoretical results derived in Part I. We also illustrate that the presented guideline is not the only way to design sound inversion methods for the class of homogeneous bodies. We present an alternative approach which produces good results but whose design requires a good dose of the interpreter's art.

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