The Theory of Multi-Earthquake Location by Least Squares and Applications to Groups of North Island, New Zealand Mantle Earthquakes

<p>Aspects of the standard least squares method of locating earthquakes and its extensions are discussed. It is shown that there is a need to carefully separate and distinguish between the statistical and deterministic properties of the least squares solution and the algorithm used to obtain it. Standard linear statistical analysis gives reasonable confidence regions for the hypocentre provided that the errors in the model travel time to pairs of stations are not correlated. The travel time residuals which result from the overdetermined system are unreliable estimates of the model errors, as are the pooled residuals from groups of events whether or not the data are homogeneous. The concepts of Absolute and Relative hypocentre determination are clarified and the Homogeneous Station method is developed and demonstrated to be a good relative location method. The application of the method to a group of North Island, New Zealand subcrustal earthquakes chosen for homogeneity revealed that the earthquakes occurred in a thin, fairly that dipping zone that could be as thin as 9 km and is not thicker than 18 km. The result is a significant refinement of previous estimates for New Zealand. The method of Joint Hypocentre Determination first described by Douglas (1967) is examined. The advantage of the method is that the error in the travel time model is estimated as well as allowing for and estimating the effect of an interaction of this error with the hypocentre parameters of the earthquakes. The application of this method to groups of, North Island, New Zealand earthquakes allows very significant improvements to the travel time model to be made and confirms the result that there is a velocity contrast for both P and S of between six and ten percent between paths in and entirely out of the downgoing Pacific plate. Estimates of the velocities in the plate are 8.6 [plus or minus] .1 km/sec. for P and 4.74 [plus or minus] km/sec. for S. In addition, station terms are calculated which describe the average departure from the new model of travel times to the stations contributing data to the study. These terms may be interpreted as arising from crustal structure local to the station which is different from that of the average crustal model used. The conclusion is reached that apart from providing better absolute hypocentre estimates, the method of Joint Hypocentre Determination can be made to yield worthwhile information about structure on the scale considered here.</p>

The Theory of Multi-Earthquake Location by Least Squares and Applications to Groups of North Island, New Zealand Mantle Earthquakes

<p>Aspects of the standard least squares method of locating earthquakes and its extensions are discussed. It is shown that there is a need to carefully separate and distinguish between the statistical and deterministic properties of the least squares solution and the algorithm used to obtain it. Standard linear statistical analysis gives reasonable confidence regions for the hypocentre provided that the errors in the model travel time to pairs of stations are not correlated. The travel time residuals which result from the overdetermined system are unreliable estimates of the model errors, as are the pooled residuals from groups of events whether or not the data are homogeneous. The concepts of Absolute and Relative hypocentre determination are clarified and the Homogeneous Station method is developed and demonstrated to be a good relative location method. The application of the method to a group of North Island, New Zealand subcrustal earthquakes chosen for homogeneity revealed that the earthquakes occurred in a thin, fairly that dipping zone that could be as thin as 9 km and is not thicker than 18 km. The result is a significant refinement of previous estimates for New Zealand. The method of Joint Hypocentre Determination first described by Douglas (1967) is examined. The advantage of the method is that the error in the travel time model is estimated as well as allowing for and estimating the effect of an interaction of this error with the hypocentre parameters of the earthquakes. The application of this method to groups of, North Island, New Zealand earthquakes allows very significant improvements to the travel time model to be made and confirms the result that there is a velocity contrast for both P and S of between six and ten percent between paths in and entirely out of the downgoing Pacific plate. Estimates of the velocities in the plate are 8.6 [plus or minus] .1 km/sec. for P and 4.74 [plus or minus] km/sec. for S. In addition, station terms are calculated which describe the average departure from the new model of travel times to the stations contributing data to the study. These terms may be interpreted as arising from crustal structure local to the station which is different from that of the average crustal model used. The conclusion is reached that apart from providing better absolute hypocentre estimates, the method of Joint Hypocentre Determination can be made to yield worthwhile information about structure on the scale considered here.</p>

Crustal structure of the Volgo-Uralian subcraton revealed by inverse and forward gravity modeling

Volgo-Uralia is a Neoarchean easternmost part of the East European craton. Recent seismic studies of the Volgo-Uralian region provided new insights into the crustal structure of this area. In this study, we combine satellite gravity and seismic data in a common workflow to perform a complex study of Volgo-Uralian crustal structure which is useful for further basin analysis of the area. In this light, a new crustal model of the Volgo-Uralian subcraton is presented from a step-wise approach: (1) inverse gravity modeling followed by (2) 3D forward gravity modeling. First, inversion of satellite gravity gradient data was applied to determine the Moho depth for the area. Density contrasts between crust and mantle were varied laterally according to the tectonic units present in the region, and the model is constrained by the available active seismic data. The Moho discontinuity obtained from the gravity inversion was consequently modified and complemented in order to define a complete 3D crustal model by adding information on the sedimentary cover, upper crust, lower crust, and lithospheric mantle layers in the process of forward gravity modeling where both seismic and gravity constraints were respected. The obtained model shows crustal thickness variations from 32 to more than 55 km in certain areas. The thinnest crust with a thickness below 40 km is found beneath the Pericaspian basin, which is covered by a thick sedimentary layer. The thickest crust is located underneath the Ural Mountains as well as in the center of the Volga-Uralian subcraton. In both areas the crustal thickness exceeds 50 km. At the same time, initial forward gravity modeling has shown a gravity misfit of ca. 95 mGal between the measured Bouguer gravity anomaly and the forward calculated gravity field in the central area of the Volga-Uralian subcraton. This misfit was interpreted and modeled as a high-density lower crust which possibly represents underplated material. Our preferred crustal model of the Volga-Uralian subcraton respects the gravity and seismic constraints and reflects the main geological features of the region with Moho thickening in the cratons and under the Ural Mountains and thinning along the Paleoproterozoic rifts, Pericaspian sedimentary basin, and Pre-Urals foredeep.

Forward Modelling of Bouguer Anomalies along a transect of the Southern Apennines and the Tyrrhenian back-arc basin.

&lt;p&gt;Abstract&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;In the present study, starting from original measurement stations, we created the Bouguer anomaly map of Southern Italy with a reduction density of 2670 kg m&lt;sup&gt;-3&lt;/sup&gt;. We perform a regional gravity modelling at crustal scale along the trace of the CROP-04 (on-shore) and MB6 (off-shore) deep seismic reflection profiles crossing the Southern Apennines and the Southern Tyrrhenian Sea. Along the 320 km-long modelled profile, we investigate crustal-scale sources for the observed gravity anomalies.&amp;#160;&lt;/p&gt;&lt;p&gt;After a compelling review of the published Moho geometries in the area, that were retrieved from either active or passive seismic methods, we test them in the observed gravity field through forward modeling of the Bouguer gravity anomalies. The comparison between the different Moho interpretations shows that the steepness of the subducting slab, the position of the step between the western (Tyrrhenian) and the eastern (Adriatic) Moho and Moho depth represent the main features influencing the observed Bouguer anomalies at crustal scale.&lt;/p&gt;&lt;p&gt;Finally, we provide a best-fitting model across both onshore and offshore areas. In the proposed best-fitting model, the wide wavelength and strong regional Bouguer anomalies correlate with the geometry of the Moho discontinuity and deep tectonic structures. On the other hand, the small-amplitude oscillations of the gravity anomalies were attributed to the low-density values of the Pliocene-Quaternary deposits both on- (e.g. the Bradanic trough) and off-shore (e.g. recent deposits in the Tyrrhenian sea bottom). Gravity minima correspond to the crustal doubling underneath the Southern Apennines where the Tyrrhenian Moho (~27 km depth) overlies the deeper Adriatic Moho (~50 km depth). The positive trend of the observed anomaly toward NE is related to the shallowing of the Adriatic Moho to depths of ~28 km in the Adriatic. Similarly, towards SW, the observed anomaly follows a positive trend towards the maxima located in the Central Tyrrhenian Sea. We model this trend as representative of crustal thinning and shallowing to values of ~12 km depth of the Tyrrhenian Moho. We also model a crustal transition from geometries and density values typical of a continental crust in the Adriatic domain towards a more oceanic structure and composition in the Tyrrhenian domain. This crustal model locates the westward flexure of the Adriatic Moho, mimicking the subduction of the Adriatic lithosphere beneath the Peri-Tyrrhenian block and locates step between the western (Tyrrhenian) and the eastern (Adriatic) Moho beneath the Apennines range.&lt;/p&gt;&lt;p&gt;The resulted gravity forward model provide contributions to the tectonic settings understanding of the area by providing a robust crustal model ranging from the Tyrrhenian Sea to the Apulian foreland.&lt;/p&gt;&lt;p&gt;&amp;#160;Finally, we believe that the proposed model can serve as a starting point for future studies investigating the upper crustal geometries in the area and addressing open questions about its relations with seismicity distribution.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;

Inverse and forward gravity modeling for revealing the crustal structure of Volga-Uralian subcraton

&lt;p&gt;A new crustal model of the Volga-Uralian subcraton was built. The compilation of the model was subdivided in two steps: (1) inverse gravity modeling followed by (2) thorough forward gravity modeling.&lt;/p&gt;&lt;p&gt;For inverse gravity modeling GOCE gravity gradients were used. The effect of the Earth sphericity was taken into account by using tesseroids. Density contrasts between crust and mantle were varied laterally according to the tectonic units present in the region.&amp;#160; The model is constrained by the available seismic data including receiver function studies, and deep reflection and refraction profiles.&lt;/p&gt;&lt;p&gt;The Moho discontinuity obtained during the gravity inversion was consequently modified, and complemented by the sedimentary cover, upper crust, lower crust, and lithospheric mantle layers in the process of forward gravity modeling. Obtained model showed crustal thickness variation from 34 to more than 55 km in some areas. The thinnest crust with the thickness below 40 km appeared on the Pericaspian basin with the thickest sedimentary column. A relatively thin crust was found along the central Russia rift system, while the thickest crust is located underneath Ural Mountains as well as in the center of the Volga-Uralian subcraton. In both areas the crustal thickness exceeds 50 km. At the same time, the gravity misfit of ca. 95 mGal between the measured Bouguer gravity anomaly and forward calculated gravity field was revealed in the central area of the Volga-Uralian subcraton. This misfit was interpreted and modeled as high-density lower crust which can possibly represent an underplated material.&lt;/p&gt;&lt;p&gt;In the end, the new crustal model of Volga-Uralian subcraton respects the gravity and seismic constraints, and reflects the main geological features of the region. This model will be used for further geothermal analysis of the area.&lt;/p&gt;

A New Moho Depth Model for Fennoscandia with Special Correction for the Glacial Isostatic Effect

In this study, we present a new Moho depth model in Fennoscandia and its surroundings. The model is tailored from data sets of XGM2019e gravitationl field, Earth2014 topography and seismic crustal model CRUST1.0 using the Vening Meinesz-Moritz model based on isostatic theory to a resolution of 1° × 1°. To that end, the refined Bouguer gravity disturbance is determined by reducing the observed field for gravity effect of topography, density heterogeneities related to bathymetry, ice, sediments, and other crustal components. Moreover, stripping of non-isostatic effects of gravity signals from mass anomalies below the crust due to crustal thickening/thinning, thermal expansion of the mantle, Delayed Glacial Isostatic Adjustment (DGIA), i.e., the effect of future GIA, and plate flexure has also been performed. As Fennoscandia is a key area for GIA research, we particularly investigate the DGIA effect on the gravity disturbance and gravimetric Moho depth determination in this area. One may ask whether the DGIA effect is sufficiently well removed in the application of the general non-isostatic effects in such an area, and to answer this question, the Moho depth is determined both with and without specific removal of the DGIA effect prior to non-isostatic effect and Moho depth determinations. The numerical results yield that the RMS difference of the Moho depth from our model HVMD19 vs. the seismic CRUST19 and GRAD09 models are 3.8/4.2 km and 3.7/4.0 km when the above strategy for removing the DGIA effect is/is not applied, respectively, and the mean value differences are 1.2/1.4 km and 0.98/1.4 km, respectively. Hence, our study shows that the specific correction for the DGIA effect on gravity disturbance is slightly significant, resulting in individual changes in the gravimetric Moho depth up to − 1.3 km towards the seismic results. On the other hand, our study shows large discrepancies between gravimetric and seismic Moho models along the Norwegian coastline, which might be due to uncompensated non-isostatic effects caused by tectonic motions.