On the problem of determining the vertical gradients of gravity anomalies

Summary Green's theorem on harmonic functions makes it possible to determine the integral relationship between the harmonic function and its derivative with respect to the normal on a closed Lyapunov surface. The conditions of solvability are given by Fredholm's theory of integral equations. The solution for a sphere was presented by Molodenskii[3] and the general solution with the help of Molodenskii's parameter k by Ostach[4]. The present paper indicates a possibility of solving this problem with the help of a system of linear algebraic equations, a simplified modification of the Ostach-Molodenskii solution and, finally, a method, based on Eremeev's solution of the fundamental integral equation[5].     

Density modeling of the Escollos Alijos Seamount from inversion of its geoid undulation anomaly

Escollos Alijos is a large seamount located in the NE Pacific Ocean about 300 km off the Baja California Peninsula. Geochronology and geochemical analysis of volcanic rocks capping the seamount indicate recent magmatism that resulted from extensive differentiation of a mildly alkalic basalt parent magma.Escollos Alijos is located towards the eastern edge of a long-wavelength geoid undulation minimum, of up to -47 m with respect of the WGS84 ellipsoid, which extends over the northeastern Pacific Ocean. Subtracting from the geoid undulation its long-wavelength component and the undulation due to the seamount topography itself, a negative undulation anomaly persists that indicates a mass deficit at depth. Linear inversion of the undulation anomaly yields a region characterized by a negative density contrast, localized under the seamount at a depth between 9 and 13 km.The age and chemical composition of Escollos Alijos, and the inferred mass deficit suggest magma trapped between the oceanic crust and the uppermost mantle, which explains the magmatic activity in recent times.     

Location of secondary faults from cross-correlation of the second vertical derivative of gravity anomalies1

A method is described to locate secondary faults, which can be difficult to identify on the Bouguer gravity map. The method is based on cross-correlation between the theoretical anomaly due to a vertical step and the second vertical derivative of the Bouguer anomaly. Faults are located from the closed maxima and minima on the cross-correlation contour map calculated for two perpendicular directions. One-dimensional model computations show that the magnitude of the extremum of the cross-correlation is related to the depth to the top of the hanging wall and the throw of the fault. Application of the method to the Bouguer gravity map of the former mouth of the Yellow River in the Shengli Oilfield area near the Bo Hai Sea shows the effectiveness of the method.     

On some types of gravity anomalies

Summary The gravity anomaly is a matter of convention. So far, only mixed gravity anomalies have been used. However, if in the future we shall have a sufficiently accurate geoid map covering the entire Earth's surface, it might be convenient to apply another type of gravity anomaly, as suggested Pellinen[1]. The object of this paper is to analyse this question with respect to the solution of the problems of physical geodesy.     

On the gravimetric undulations of the geoid and the deflections of the vertical

Summary The author mentions the aims of the World-wide gravity project he established in the Ohio State University in Columbus, in 1950. He outlines the practical procedure of the gravimetric computations of the undulationsN and the vertical deflection components and and emphasizes that only by the global international cooperation and additional gravity observations at sea carried out during the last decade it has been possible to gather to Columbus the needed gravity material. Since there exist still large gravimetrically unsurveyed areas it is of vital significance to study what gravity anomalies are best to be used for these regions. The given figures concerning the accuracy of theN, and , estimated theoretically and obtained in practice, indicate that in the gravimetrically well surveyed parts of the world like in Europe and the United States we can get gravimetrically on basis of existing gravity material theN-values with accuracy of about 5–10 meters, and and with the accuracy of about 1. The geoid undulationsN are already computed in Columbus for more than 6000 points of the northern hemisphere. The sample maps show the interesting geoid of Europe and vicinity between the latitudes 60° and 30° and longitude 5° W and 30° E, drafted on basis of more than 1000N-values computed at the corners of 1°×1° squares. It is interesting to realize that the geoid undulations in all this area are positive, the extreme values being between 40 and 50 meters. The geophysical significance of the geoid maps of this kind is pointed out.     

SEASAT geoid anomalies and the Macquarie Ridge complex

The seismically active Macquarie Ridge complex forms the Pacific-India plate boundary between New Zealand and the Pacific-Antarctic spreading center. The Late Cenozoic deformation of New Zealand and focal mechanisms of recent large earthquakes in the Macquarie Ridge complex appear consistent with the current plate tectonic models. These models predict a combination of strike-slip and convergent motion in the northern Macquarie Ridge, and strike-slip motion in the southern part. The Hjort trench is the southernmost expression of the Macquarie Ridge complex. Regional considerations of the magnetic lineations imply that some oceanic crust may have been consumed at the Hjort trench. Although this arcuate trench seems inconsistent with the predicted strike-slip setting, a deep trough also occurs in the Romanche fracture zone.Geoid anomalies observed over spreading ridges, subduction zones, and fracture zones are different. Therefore, geoid anomalies may be diagnostic of plate boundary type. We use SEASAT data to examine the Macquarie Ridge complex and find that the geoid anomalies for the northern Hjort trench region are different from the geoid anomalies for the Romanche trough. The Hjort trench region is characterized by an oblique subduction zone geoid anomaly, e.g., the Aleutian-Komandorski region. Also, limited first-motion data for the large 1924 earthquake that occurred in the northern Hjort trench suggest a thrust focal mechanism. We conclude that subduction is occurring at the Hjort trench. The existence of active subduction in this area implies that young oceanic lithosphere can subduct beneath older oceanic lithosphere.     

Recovery of marine gravity anomalies from ERS1, ERS2 and ENVISAT satellite altimetry data for geoid computations over Norway

Free-Air Anomalies (FAA) for the Norwegian marine area including some parts of the North Sea, the Norwegian Sea and the Barents Sea are computed from satellite altimetry data. A total of 84 cycles of ERS2 along-track data, 25 cycles of ENVISAT along-track data and high density ERS1 data during its geodetic mission are used. The new geopotential model from the Gravity Recovery and Climate Experiment (GRACE) mission, GGM02S (Tapely et al., 2005) is used to compute the long wavelength contributions of the geoid and the FAA. To correct data for mean dynamic topography, the available Levitus climatology model (Levitus and Boyer, 1994) is used. Corrected data are then used to compute along-track gradients in each cycle-pass to suppress the orbital and the atmospheric errors below the noise level of the altimeter. Resulted gradients are then stacked and the east-west and the north-south components of the deflection of verticals are computed where ascending and descending tracks meet each other. Finally, the inverse Vening-Meinesz formula is implemented on the gridded deflections to compute FAA. Results are then compared with available marine and airborne data. Standard deviations of ± 4.301 and ± 6.159 mGal in comparison with airborne and marine FAA were achieved. Thereafter, the derived anomalies are combined with marine and airborne FAA together with the land FAA to compute a fine resolution geoid for Norway and the surrounding marine areas. This geoid is evaluated over sea and land with the synthetic geoid (the geoid derived from the mean sea surface by subtracting the mean dynamic topography) and Global Positioning System (GPS)-levelling and the standard deviations of the differences are ± 20.9 and ± 12.8 cm respectively. ali.soltanpour@ntnu.no, hossein.nahavandchi@ntnu.no, kourosh.ghazavi@ntnu.no     

大地水准面异常在湖南地区的地球物理解释

以湖南地区为例,利用超高阶地球重力位模型EGM2008计算了研究区的重力大地水准面,并采用棱柱体公式和球体公式相结合的方法分别进行了完全地形改正和Airy-Heiskanen局部均衡改正,得到布格大地水准面和均衡大地水准面.对三种大地水准面进行不同波长分量的分离处理,得到包含不同深度异常信息的剩余大地水准面,并结合其他地球物理资料对研究区进行了详细的地球物理解释.结果表明,剩余重力大地水准面可以有效地反映出研究区内的深部构造特征,如深大断裂带分布、构造块体位置、上地幔密度横向分布等,但对地壳内异常结构反映不明显;研究区岩石圈密度变化相对平缓,厚度由东向西增加;根据剩余均衡大地水准面及研究区Airy局部均衡莫霍面,可以大致推测出研究区的莫霍面起伏形态以及均衡状态,可作为一种有用的参考信息.     

On the calculation of the gravity terrain corrections in Czechoslovakia

Summary A calculation of the gravity terrain corrections by computer is proposed.

---

¶rt;aam m¶rt; uuu mnauu nna unau uuum muu.

     

Full gravity gradient tensors from vertical gravity by cosine transform

We present a method to calculate the full gravity gradient tensors from pre-existing vertical gravity data using the cosine transform technique and discuss the calculated tensor accuracy when the gravity anomalies are contaminated by noise. Gravity gradient tensors computation on 2D infinite horizontal cylinder and 3D ??Y?? type dyke models show that the results computed with the DCT technique are more accurate than the FFT technique regardless if the gravity anomalies are contaminated by noise or not. The DCT precision has increased 2 to 3 times from the standard deviation. In application, the gravity gradient tensors of the Hulin basin calculated by DCT and FFT show that the two results are consistent with each other. However, the DCT results are smoother than results computed with FFT. This shows that the proposed method is less affected by noise and can better reflect the fault distribution.     

地形-均衡补偿重力、大地水准面异常频谱分析

将地形高、地球内部质量异常以及重力、大地水准面展开成球谐级数,依据岩石圈弹性挠曲均衡补偿理论建立地形—均衡补偿重力、大地水准面异常的球谐级数表达式.由此我们可以研究地形—均衡补偿重力、大地水准面异常与球谐级数阶次的关系,以及不同波长地形荷载与岩石圈挠曲补偿的关系,探讨地形—均衡补偿重力、大地水准面的频谱特性.从观测大地水准面异常和自由空气重力异常扣除地形—均衡补偿大地水准面、重力异常,可以得到均衡大地水准面异常和均衡重力异常.均衡大地水准面异常已经消除了浅层物质不均匀的影响,反映的是地球深部物质密度不均匀分布.均衡重力异常显示出中短波长特性,反映的是地壳上地幔物质分布的失衡和物质调整的动力学特征.     

Plume-induced geoid anomalies from 2D axi-symmetric temperature- and pressure-dependent mantle convection models

A collection of numerical simulations of 2D axi-symmetric thermal convection is presented here. The aim is to investigate the shape of geoid anomalies and dynamic topography above a plume. The simulation is based on the Boussinesq approximation and infinite Prandtl number and is carried out in the spherical shell with strongly temperature- and depth-dependent Arrhenius-type viscosity. According to the Arrhenius law, plume models with purely depth-dependent rheology are unphysical and should be taken with care. The strongly coupled temperature- and depth-dependent viscosity enables us to better understand the plume's behavior inside the Earth.The topography and geoid anomalies produced from plumes are sensitive to rheology of the mantle and rheology of the plume; both have effects on shape and amplitude of the geoid anomalies. We determined different categories of the geoid which are related to various rheology. Depth-dependent viscosity models show a geoid with a negative sign above the plume, and temperature-dependent viscosity models depict a bell-shaped geoid. We identified different behaviors in the combined model with temperature- and pressure-dependent viscosity.     

On the calculation of magnetic anomalies of irregular two-dimensional bodies

Summary An easy method of calculating the magnetic anomalies of two-dimensional irregular bodies is presented. The body under consideration is replaced by a set of line doublets with a pole strength equal to the intensity of magnetisation and parallel to its direction. The magnetic effects of some of the equally spaced doublets are obtained, added and multiplied by the distance between them to yield the magnetic anomaly. The expressions involved here are simpler than those existing in geophysical literature.     

On the interpretation of vertical gravity gradients produced by magmatic intrusions

A method for the computation and interpretation of gravity and height changes and vertical gravity gradients produced by magmatic intrusions in a layered elastic–gravitational medium is presented. The methodology assumes a planar medium geometry, which consists of welded layers overlying a half-space. The medium is elastic and gravitating. The intrusion is treated as a point source and can be located at any depth inside the medium. The theoretical elastic–gravitational model allows the computation of the so-called geometric and orthometric vertical displacements as well as gravity changes of different types. The corresponding vertical gravity gradients can also be computed. We present several examples of theoretical computations and study different types of these geometric and orthometric gravity gradients and the information we can get from the application of the methodology described. The results presented show that the use of these gradients is a useful tool to obtain information on the dynamics of the injection processes, including the detection of new magma recharge. We show that using the elastic–gravitational deformation model we can explain non-linear gravity–height relationships that appear in volcanic areas. We also present the application of the methodology to Mayon volcano, Philippines, delineating the intrusion of new magma, consistent with the produced eruptions after the observation period.     

Surface deformation, gravity and the geoid from a three-dimensional convection model at low Rayleigh numbers

The two-dimensional surface deformation, gravity field and geoid are calculated from the temperature fields of a number of numerical models of constant viscosity three-dimensional convective flows, heated from within and from below, using the appropriate Green's functions. The admittance is positive, with positive gravity anomalies above hot rising regions, except for large aspect ratio circulations with undeformable lower boundaries. The surface deformation and the geoid are insensitive to the short wavelength features of the temperature variation. The gravity field is less smooth, though still does not clearly indicate the narrowness of the upwelling and downwelling regions at large Rayleigh numbers. When the lower boundary of the convecting region is deformable, the gravity field is dominated by lateral temperature variations within the upper thermal boundary layer, even when their contribution to the overall circulation is small. The variation of surface deformation with Rayleigh number agrees well with that expected from simple boundary layer arguments when the circulation is driven by heating from below, but less well when the heating is internal. These results suggest that the convective upwelling beneath regions showing positive geoid and residual depth anomalies is more localized than the horizontal extent of these features would suggest.     

A new technique of interpreting gravity and vertical magnetic anomalies due to infinite horizontal cylindrical ore bodies

Summary A novel method of interpreting gravity and magnetic anomalies is presented here. Two diagrams of master curves, one for gravity and the other for vertical magnetic interpretation are presented. They are useful in calculating the depth of burial and the radius of infinite horizontal cylindrical bodies irrespective of density contrast or strength and direction of magnetisation. This method also enables us to infer the direction of magnetisation, resultant intensity of magnetisation and from them the susceptibility contrast; and density contrast. ThoughHenderson [8]²) reported the applicability of continuations and derivatives in the interpretation of magnetic anomalies for the first time, the authors have treated them in a more exhaustive manner in the present paper to obtain valuable relationships.     

Long-wavelength gravity anomalies and intraplate seismicity

Anomalously high mid-plate and Mid-Oceanic Ridge seismicity apparently characterizes the flanks of the regional free-air gravity and topographic high roughly centered on the postulated Iceland hot spot; anomalously high mid-plate seismicity also occurs around the deep free-air gravity low centered just south of India. Although the correlation between gravity and seismicity is still somewhat inconclusive, it seems to suggest active asthenosphere flow associated with the regional gravity anomalies. Added to other stresses in the plate, the stress transmitted to the plate by this flow would encourage its fracture.