The study of Moho structures can provide crucial information for applications in geology, geophysics, and geodesy. For example, such information is useful in geodynamic studies of the Earth’s interior, in unraveling the gravitational signals of anomalous subsurface distributions and in understanding geoid anomalies (e.g., Abrehdary 2016). Models of the Moho depth (MD) are resolved either by seismic, isostatic compensation or gravimetric-isostatic techniques. Typically, seismic data are generated by the travel-time of seismic waves from ground-based man-made explosions reflected at the denser Moho boundary and returned to the Earth’s surface. As this method is expensive, particularly at sea, such data become sparse, inhomogeneous and/or interpolated, which leads to low resolution and accuracy in the process. Hence, over large parts of the world, particularly at high seas, with little or no coverage of seismic data, methods based on gravimetric-isostatic techniques, and in combinations with seismic data (combined approaches), offer attractive alternatives. In this context, the global and mostly homogeneous data available free of charge from the dedicated satellite gravity missions GRACE (Tapley et al. 2004) and GOCE (Drinkwater et al. 2003; Floberghagen et al. 2011) are of particular interest.
Different attempts to estimate a global crustal model have appeared during the years with different and often unclear accuracies. A pioneer model, named CRUST5.1, was determined at a resolution of 5° × 5° by Mooney et al. (1998) based on seismic refraction data, succeeded by CRUST2.0 (Bassin 2000), which was compiled with a resolution of 2° × 2°. Another model was created by Zhou et al. (2006)-based constraining Rayleigh and Love wave data in the crust and upper mantel, while Meier et al. (2007) directly used surface wave data in their global MD model. Today, CRUST1.0 (Laske et al. 2013) is the most frequently cited and applied model, compiled from active seismic source and receiver function data. A recent global model of Szwillus et al. (2019), here named CRUST19, uses geostatistical Kriging technique (closely related with the method of collocation) for interpolation of discrete crustal depths derived from seismic data to a global model.
The isostatic compensation of the gravity field originates with Airy (1855) and Pratt (1855, 1859) [local isostatic compensation] and Vening Meinesz (1931) [regional compensation] and, finally, Moritz (1990, Section 8.3.2) [global compensation], whose technique was solved to 2nd order by Sjöberg (2009) under the name Vening Meinesz-Moritz (VMM) method. The gravimetric-isostatic compensation is dependent on both variables MD and Moho Density Contrast (MDC), but the methods above are only solved for the MD by assuming a fixed MDC. Sjöberg and Bagherbandi (2011) modified the method to solve for the MDC alone or in combination with the MD using both seismic and gravity data. Later, Tenzer and Bagherbandi (2012) demonstrated that replacing the gravity anomaly by gravity disturbance improves the VMM solution, and Sjöberg (2013) confirmed that the gravity anomaly and kernel function of the original VMM solution are inconsistent, so that either the gravity anomaly should be replaced by the gravity disturbance, or the kernel function needs a slight change.
The uncertainties in the gravimetric-isostatic MD models are typically attributed to stochastic and systematic errors (NIEs) in the global gravity, topographic and ice and sediment model data sets, but also to systematic biases (so-called Non-Isostatic Effects; NIEs) due to unmodeled mantle (and crustal) density structures and geophysical processes. As the observed gravity data include signals generated by sources in the Earth’s interior that may cause significant biases in the computational results, such NIEs must be reduced below noise level. The method used here to remove those effects was introduced by Bagherbandi and Sjöberg (2012).
Errors in the seismic crustal models arise from several factors such as the used 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 (Christensen and Mooney 1995; Chulick et al. 2013). A major problem in validating the accuracies in available seismic crustal models of MD and MDC is that their qualities, which vary from place to place, are typically not specified. The uncertainties are different in various seismic methods and can differ even for the same method in different surveys. The largest uncertainties of the MDs are strongly attributed to inaccuracies of crustal models currently available (Grad and Tiira 2012). Čadek and Martinec (1991) estimated MD uncertainties in their global Moho model of the order 20% (5 km) for the oceanic crust and of the order 10% (3 km) for the continental crust. The results of more recent seismic and gravity studies, however, demonstrate that these error estimates are too optimistic. Grad et al. (2009), for example, revealed that the uncertainties in the estimated MDs based on the seismic data under the European continent are about 10 km with an average error of more than 4 km. Much larger Moho uncertainties are expected over large portions of the world, particularly at sea, where the seismic data are sparse.
In the present article, some new features are used to determine a global MD model called MOHV21 from five available models, namely (a) as the standard errors (STEs) of the models and correlations among them are frequently missing, these statistics are estimated (cf. Sjöberg and Abrehdary 2021) as a preparation to (b) a proper adjustment of the individual models in a weighted least squares approach, c) including modeling the STEs of MOHV21. The following MD models are used in the merging process: MDN07 (Meier et al. 2007), CRUST1.0 (Laske et al. 2013), GEMMA1.0 (Reguzzoni and Sampietro 2015), KTH15C (Abrehdary et al. 2017) and CRUST19 (Szwillus et al. 2019). The new model is determined at a resolution of 1° × 1°.
Admittedly, as the input data were not specified for continental and oceanic crusts, we could not with reasonable efforts specify the resulting MDs accordingly, but we use the terms land and ocean region MDs.