ARCMH25: a hybrid seismic–isostatic approach for Moho structure and density contrast estimation in the Arctic

In this research, we present a local Moho model, named MOHV19, including Moho depth and Moho density contrast (or shortly Moho constituents) with corresponding uncertainties, which are mapped from altimetric and gravimetric data (DSNSC08) in addition to seismic tomographic (CRUST1.0) and Earth topographic data (Earth2014) to a resolution of 1° × 1° based on a solution of Vening Meinesz-Moritz’ theory of isostasy. The MOHV19 model covers the area of entire European plate along with the surrounding oceans, bounded by latitudes (30 °N–82 °N) and longitudes (40 °W–70 °E). The article aims to interpret the Moho model resulted via altimetric and gravimetric information from the geological and geophysical perspectives along with investigating the relation between the Moho depth and Moho density contrast. Our numerical results show that estimated Moho depths range from 7.5 to 57.9 km with continental and oceanic averages of 41.3 ± 4.9 km and 21.6 ± 9.2 km, respectively, and an overall average of 30.9 ± 12.3 km. The estimated Moho density contrast ranges from 60.2 to 565.8 kg/m3, with averages of 421.8 ± 57.9 and 284.4 ± 62.9 kg/m3 for continental and oceanic regions, respectively, with a total average of 350.3 ± 91.5 kg/m3. In most areas, estimated uncertainties in the Moho constituents are less than 3 km and 40 kg/m3, respectively, but they reach to much more significant values under Iceland, parts of Gulf of Bothnia and along the Kvitoya Island. Comparing the Moho depths estimated by MOHV19 and those derived by CRUST1.0, MDN07, GRAD09 and MD19 models shows that MOHV19 agree fairly well with CRUST1.0 but rather poor with other models. The RMS difference between the Moho density contrasts estimated by MOHV19 and CRUST1.0 models is 49.45 kg/m3.

We present a combined method for estimating a new global Moho model named KTH15C, containing Moho depth and Moho density contrast (or shortly Moho parameters), from a combination of global models of gravity (GOCO05S), topography (DTM2006) and seismic information (CRUST1.0 and MDN07) to a resolution of 1° × 1° based on a solution of Vening Meinesz-Moritz’ inverse problem of isostasy. This paper also aims modelling of the observation standard errors propagated from the Vening Meinesz-Moritz and CRUST1.0 models in estimating the uncertainty of the final Moho model. The numerical results yield Moho depths ranging from 6.5 to 70.3 km, and the estimated Moho density contrasts ranging from 21 to 650 kg/m3, respectively. Moreover, test computations display that in most areas estimated uncertainties in the parameters are less than 3 km and 50 kg/m3, respectively, but they reach to more significant values under Gulf of Mexico, Chile, Eastern Mediterranean, Timor sea and parts of polar regions. Comparing the Moho depths estimated by KTH15C and those derived by KTH11C, GEMMA2012C, CRUST1.0, KTH14C, CRUST14 and GEMMA1.0 models shows that KTH15C agree fairly well with CRUST1.0 but rather poor with other models. The Moho density contrasts estimated by KTH15C and those of the KTH11C, KTH14C and VMM model agree to 112, 31 and 61 kg/m3 in RMS. The regional numerical studies show that the RMS differences between KTH15C and Moho depths from seismic information yields fits of 2 to 4 km in South and North America, Africa, Europe, Asia, Australia and Antarctica, respectively.

The Mohorovicic discontinuity is the boundary between the Earth’s crust and mantle. Several isostatic hypotheses exist for estimating the crustal thickness and density variation of the Earth’s crust from gravity anomalies. The goal of this article is to compare the Airy-Heiskanen and Vening Meinesz-Moritz (VMM) gravimetric models for determining Moho depth, with the seismic Moho (CRUST2.0 or SM) model. Numerical comparisons are performed globally as well as for some geophysically interesting areas, such as Fennoscandia, Persia, Tibet, Canada and Chile. These areas are most complicated areas in view of rough topography (Tibet, Persia and Peru and Chile), post-glacial rebound (Fennoscandia and Canada) and tectonic activities (Persia). The mean Moho depth provided by CRUST2.0 is 22.9 ± 0.1 km. Using a constant Moho density contrast of 0.6 g/cm3, the corresponding mean values for Airy-Heiskanen and VVM isostatic models become 25.0 ± 0.04 km and 21.6 ± 0.08 km, respectively. By assuming density contrasts of 0.5 g/cm2 and 0.35 g/cm3 for continental and oceanic regions, respectively, the VMM model yields the mean Moho depth 22.6 ± 0.1 km. For this model the global rms difference to CRUST2.0 is 7.2 km, while the corresponding difference between Airy-Heiskanen model and CRUST2.0 is 11 km. Also for regional studies, Moho depths were estimated by selecting different density contrasts. Therefore, one conclusion from the study is that the global compensation by the VMM method significantly improves the agreement with the CRUST2.0 vs. the local compensation model of Airy-Heiskanen. Also, the last model cannot be correct in regions with ocean depth larger than 9 km (e.g., outside Chile), as it may yield negative Moho depths. This problem does not occur with the VMM model. A second conclusion is that a realistic variation of density contrast between continental and oceanic areas yields a better fit of the VMM model to CRUST2.0. The study suggests that the VMM model can primarily be used to densify the CRUST2.0 Moho model in many regions based on separate data by taking advantage of dense gravity data. Finally we have found also that the gravimetric terrain correction affects the determination of the Moho depth by less than 2 km in mean values for test regions, approximately. Hence, for most practical applications of the VMM model the simple Bouguer gravity anomaly is sufficient.

The determination of the oceanic Moho (or crust-mantle) density contrast derived from seismic acquisitions suffers from severe lack of data in large parts of the oceans, where have not yet been sufficiently covered by such data. In order to overcome this limitation, gravitational field models obtained by means of satellite altimetry missions can be proficiently exploited, as they provide global uniform information with a sufficient accuracy and resolution for such a task. In this article, we estimate a new Moho density contrast model named MDC2018, using the marine gravity field from satellite altimetry in combination with a seismic-based crustal model and Earth’s topographic/bathymetric data. The solution is based on the theory leading to Vening Meinesz-Moritz’s isostatic model. The study results in a high-accuracy Moho density contrast model with a resolution of 1° × 1° in oceanic areas. The numerical investigations show that the estimated density contrast ranges from 14.2 to 599.7 kg/m3 with a global average of 293 kg/m3. In order to evaluate the accuracy of the MDC2018 model, the result was compared with some published global models, revealing that our altimetric model is able to image rather reliable information in most of the oceanic areas. However, the differences between this model and the published results are most notable along the coastal and polar zones, which are most likely due to that the quality and coverage of the satellite altimetry data are worsened in these regions.

Modelling the density contrast and depth of the Moho discontinuity by seismic and gravimetric–isostatic methods with an application to Africa

Due to different structures of the Earth’s crust and mantle, there is a significant density contrast at their boundary, the Moho Density Contrast (or shortly MDC). Frequently one assumes that the MDC is about 600 kg/m3, but seismic and gravimetric data show a considerable variation from region to region, and today there are few such studies, and global models are utterly rare. This research determines a new global model, called MDC21, which is a weighted least-squares combination of three available MDC models, pixel by pixel at a resolution of 1° × 1°. For proper weighting among the models, the study starts by estimating lacking standard errors and (frequently high) correlations among them. The numerical investigation shows that MDC21 varies from 21 to 504 kg/m3 in ocean areas and ranges from 132 to 629 kg/m3 in continental regions. The global average is 335 kg/m3. The standard errors estimated in ocean regions are mostly less than 40 kg/m3, while for continental regions it grows to 80 kg/m3. Most standard errors are small, but they reach to notable values in some specific regions. The estimated MDCs (as well as Moho depths) at mid-ocean ridges are small but show significant variations and qualities.

We compare three different numerical schemes of treating the Moho density contrast in gravimetric inverse problems for finding the Moho depths. The results are validated using the global crustal model CRUST2.0, which is determined based purely on seismic data. Firstly, the gravimetric recovery of the Moho depths is realized by solving Moritz’s generalization of the Vening-Meinesz inverse problem of isostasy while the constant Moho density contrast is adopted. The Pratt-Hayford isostatic model is then facilitated to estimate the variable Moho density contrast. This variable Moho density contrast is subsequently used to determine the Moho depths. Finally, the combined least-squares approach is applied to estimate jointly the Moho depths and density contract based on ap riorierror model. The EGM2008 global gravity model and the DTM2006.0 global topographic/bathymetric model are used to generate the isostatic gravity anomalies. The comparison of numerical results reveals that the optimal isostatic inverse scheme should take into consideration both the variable depth and density of compensation. This is achieved by applying the combined least-squares approach for a simultaneous estimation of both Moho parameters. We demonstrate that the result obtained using this method has the best agreement with the CRUST2.0 Moho depths. The numerical experiments are conducted at the regional study area of New Zealand’s continental shelf.

In gravimetric methods for a determination of the Moho geometry, the constant value of the Moho density contract is often adopted. Results of gravimetric and seismic studies, however, showed that the Moho density contrast varies significantly. The assumption of a uniform density contrast thus might yield large errors in the estimated Moho depths. In this study we investigate these errors by comparing the Moho depths determined globally for the uniform and variable models of the Moho density contrast. These two gravimetric results are obtained based on solving the Vening Meinesz-Moritz’s inverse problem of isostasy. The uniform model of the Moho density contrast is defined individually for the continental and oceanic lithosphere to better reproduce the reality. The global data of the lower crust and upper mantle retrieved from the CRUST1.0 seismic crustal model are used to define the variable Moho density contrast. This seismic model is also used to validate both gravimetric solutions. Results of our numerical experiment reveals that the consideration of the variable Moho density contrast improves the agreement between the gravimetric and seismic Moho models; the RMS of differences is 5.4 km (for the uniform density contrast) and 4.7 km (for the variable density contrast).

A constant value of the Moho density contrast is often assumed in the gravimetric methods used for determination of Moho geometry. This assumption might be sufficient in regional studies with a relatively homogenous lithospheric structure (and, consequently, small lateral variations in Moho density contrast). In global studies, however, this assumption is not reasonable, because not only the Moho depth but also the Moho density contrast vary substantially, and are, thus, likely to result in systematic errors in Moho geometry determined globally from gravity data. In this study we address this issue by investigating the effect of variable Moho density contrast on Moho geometry. We demonstrate that assumption of variable Moho density contrast (instead of a uniform model) substantially improves agreement between the global gravimetric and seismic Moho models by approximately 30 %.

According to Vening Meinesz-Moritz (VMM) global inverse isostatic problem, either the Moho density contrast (crust-mantle density contrast) or the Moho geometry can be estimated by solving a non-linear Fredholm integral equation of the first kind. Here solutions to the two Moho parameters are presented by combining the global geopotential model (GOCO-03S), topography (DTM2006) and a seismic crust model, the latter being the recent digital global crustal model (CRUST1.0) with a resolution of 1o×1o. The numerical results show that the estimated Moho density contrast varies from 21 to 637 kg/m3, with a global average of 321 kg/m3, and the estimated Moho depth varies from 6 to 86 km with a global average of 24 km. Comparing the Moho density contrasts estimated using our leastsquares method and those derived by the CRUST1.0, CRUST2.0, and PREM models shows that our estimate agrees fairly well with CRUST1.0 model and rather poor with other models. The estimated Moho depths by our least-squares method and the CRUST1.0 model agree to 4.8 km in RMS and with the GEMMA1.0 based model to 6.3 km.

SUMMARY Before inverting Moho topography, the traditional Parker–Oldenburg method requires the determination of two important hyperparameters, the average Moho depth and Moho density contrast. The selection of these two hyperparameters will directly affect the inversion results. In this paper, a new method for estimating hyperparameters is proposed which is used to improve the Parker–Oldenburg method. The new method is improved by using simulated annealing to accurately estimate the average Moho depth and Moho density contrast based on the relationship between Moho depths and corresponding gravity anomalies at seismic control points. Synthetic tests show that compared to the improved Bott's method and the trial and error method, our method reduces the error in Moho density contrast and average Moho depth by 0.83 and 1.81 per cent, respectively. In addition, compared with the trial and error method, our method greatly improves the computational efficiency. In a practical example, we apply this method to invert the Moho topography in the northern South China Sea. The inversion results show that the Moho topography in the northern South China Sea ranges from 8.2 to 33 km. The root mean squared error between our Moho topography and the seismic validation points is 0.94 km. Compared with the CRUST 1.0 model, our Moho topography is more accurate.

A constant value of the Moho density contrast is often assumed in methods for a gravimetric determination of the Moho geometry. This assumption might be sufficient in some regional studies. In global studies, however, this assumption is not reasonable due to the fact that the Moho density contrast vary significantly. Large errors then can be expected in the Moho geometry determined globally from gravity data. In this study we utilize a generalized compensation scheme based on variable depth and density of compensation. The Moho depths are determined based on assuming the variable Moho density contrast. We demonstrate that this assumption (instead of a uniform model) significantly improves the agreement between the global gravimetric and seismic Moho models; the RMS fit of the gravimetric result with the CRUST1.0 seismic Moho model is 4.5 km (for a uniform model) and 3.0 km (for a variable model).

Moho modeling in spatial domain: A case study under Tibet

Two hyperparameters, the mean Moho depth and the Moho density contrast, must be specified before the gravity inversion of Moho. Incorrect estimation will impact inversed Moho morphology. The purpose of this study is to present a new gravimetric Moho inversion method. The key improvement of the new method is to accurately estimate the Moho density contrast, based on a linear relationship between the depth of known points and gravity observations. The method is illustrated by a synthetic experiment where the estimated density contrast differs from the true value by only 0.0011 , showing a 93% improvement compared to the initial estimate. The results of processing the noise data show that, our method's accuracy is minimally affected by noise, but is sensitive to the number of known points. Nevertheless, when using only 10 known points, there is still a 50% probability of obtaining a solution with a root mean square (RMS) less than 1 km. When the number of points is greater than 64, the effect of the uniformity of the point distribution is almost negligible. In the real case, we employed the proposed method to invert the South China Sea (SCS) Moho depth. The Moho model reveals that, there is a distinct zoning feature at Moho depth in the SCS, and the 13.5 km isodepth line indicates the continent‐ocean boundary. Furthermore, the RMS of the difference between the gravimetric Moho model and the seismological data is 1.64 km, which is primarily attributed to the lateral variation of the density contrast.

Seismic data are primarily used in studies of the Earth’s inner structure. Since large parts of the world are not yet sufficiently covered by seismic surveys, products from the Earth’s satellite observation systems have more often been used for this purpose in recent years. In this study we use the gravity-gradient data derived from the Gravity field and steady-state Ocean Circulation Explorer (GOCE), the elevation data from the Shuttle Radar Topography Mission (SRTM) and other global datasets to determine the Moho density contrast at the study area which comprises most of the Eurasian plate (including parts of surrounding continental and oceanic tectonic plates). A regional Moho recovery is realized by solving the Vening Meinesz-Moritz’s (VMM) inverse problem of isostasy and a seismic crustal model is applied to constrain the gravimetric solution. Our results reveal that the Moho density contrast reaches minima along the mid-oceanic rift zones and maxima under the continental crust. This spatial pattern closely agrees with that seen in the CRUST1.0 seismic crustal model as well as in the KTH1.0 gravimetric-seismic Moho model. However, these results differ considerably from some previously published gravimetric studies. In particular, we demonstrate that there is no significant spatial correlation between the Moho density contrast and Moho deepening under major orogens of Himalaya and Tibet. In fact, the Moho density contrast under most of the continental crustal structure is typically much more uniform.