Severe Topography Research Articles

Generalizable data driven full waveform inversion for complex structures and severe topographies

Traditionally, simplification has been used in scientific modeling practices. However, recent advancements in deep learning techniques have provided a means to represent complex models. As a result, deep neural networks should be able to approximate the complex models, with a high degree of generalization. To achieve generalization, it is necessary to have a diverse range of examples in the training of the neural network, for example in data-driven FWI, training data should cover the expected subsurface models. To meet this requirement, we porposed a method to creat geologically meaningful velocity models with complex structures and severe topography. However, it is important to note that generalization comes with its own set of challenges.Because of significant variation in topography of the generated velocity models, we need to include this information as an additional input data in training of the network. Therefore, we have transformed the seismic data to a fixed datum to incorporate geometric information. Additionally, we have enhanced the network's performance by introducing a term in the network loss function. Multiple metrics have been employed to evaluate the performance of the network. The results indicate that by providing the necessary information to the network and employing computational techniques to refine the model's accuracy, deep neural networks are capable of accurately estimating velocity models in complex environments characterized by extreme topography.

Questioning the effects of raster-resampling and slope on the precision of TanDEM-X 90 m digital elevation model

Defining watersheds with enough topographical features is crucial when large infrastructure projects are concerned. German Aerospace Center (DLR) recently announced the dissemination of the 90 m variant of the original global TanDEM-X 12 m Digital elevation model (DEM). It was announced as produced with a special averaging technique, which would even surpass the precision of the 12 m DEM. This study aimed to test this claim while simultaneously testing whether resolution coarsening would deteriorate the performance of a higher precision DEM. AW3D30 was used as auxiliary data in four sites. Results confirmed that the 90 m DEM was indeed highly reliable at or below 20% slopes in two investigated dam reservoir areas with gentle terrain conditions, and overestimated in other two dam reservoirs with severe topography. The resampling approach did not necessarily worsen the elevation values aggregated into a larger raster resolution as obvious from the auxiliary data analyses.

X-ray photoelectron spectroscopy: A perspective on quantitation accuracy for composition analysis of homogeneous materials

We present a perspective on the use of XPS relative peak intensities for determining composition in homogeneous bulk materials. Nonhomogenous effects, such as composition variation with depth or severe topography effects (e.g., in nanoparticles), are not discussed. We consider only the use of conventional laboratory-based instruments with x-ray sources, Alkα or Mgkα. We address accuracy (not precision, which is much more straightforward) using relative sensitivity factors, RSFs, obtained either empirically from standards (e-RSF) or from the use of theoretical cross sections, σ, (t-RSF). Issues involved are (1) the uncertainty of background subtraction of inelastically scattered electrons, (2) the accuracy of the RSFs, and (3) the role of XPS peak satellite structure, which affects both (1) and (2) above. The XPS of materials tends to fall into two broad classes: where the signals being used for quantification are “main” peaks, which are narrower and more symmetric, followed by a relatively low background with only weak satellite structure and where the “main” peaks are broader and often asymmetric, followed by backgrounds that are higher and have a stronger satellite structure. The former generally will yield better accuracy, more easily, than the latter. The latter comprises all compounds containing elements with open valence shell electrons. These are mostly the 3d, 4d, and 5d transition metals, the lanthanides, and the actinides. Compounds involving only the first row elements, Li to F, where the 1s binding energy is used for quantitation, are those where the best accuracy is potentially achievable. We specifically address the issue of long-claimed serious discrepancies between e-RSFs and t-RSFs, which were interpreted as indicating calculated σs, used as a parameter in t-RSFs, were seriously in error. We conclude this claim to be untrue and that, if done correctly, there is no disagreement between the two approaches within the limits of accuracy claimed. Finally, we suggest protocols for rapid element composition analysis by obtaining relative XPS signal intensities using only low energy resolution.

Q-compensated reverse time migration in viscoacoustic media including surface topography

Conventional reverse time migration (RTM) may not produce high-quality images in areas with attenuation and severe topography because severe topographic surfaces have a great impact on seismic wave simulation, resulting in strong scattering and diffraction waves, and anelastic properties of the earth affect the kinematics and dynamics of seismic wave propagation. To overcome these problems, we have developed a [Formula: see text]-compensated topographic RTM method. In this method, a new viscoacoustic quasidifferential equation is introduced to simulate forward- and backward-propagated wavefields. The viscoacoustic equation has a lossy term and a dispersion term without memory variables, and it is solved by a hybrid spatial partial derivative scheme. A new stabilization operator is derived and substituted into the [Formula: see text]-compensated viscoacoustic quasidifferential equation to suppress high-frequency noise during the attenuated wavefield compensation. Numerical tests on a sag attenuating topographic model and an attenuating topographic Marmousi2 model demonstrate that our [Formula: see text]-compensated topographic RTM can produce accurate and high-quality images by correcting the anelastic amplitude loss and phase-dispersion effects. Finally, our method is tested on a field data set.

Radar Forest Height Estimation in Mountainous Terrain Using Tandem-X Coherence Data

In this paper, we consider the problem of radar estimation of forest canopy height in regions with dense forests and severe topography. We combine a reference digital elevation model with multiple satellite baselines from ascending and descending orbits to develop a merging algorithm relating single pass interferometric coherence to forest canopy height. We first describe the algorithm and processing steps used for height estimation and then apply the technique to a mountainous study site in British Columbia, Canada, using data from the Tandem-X satellite pair. We devise a new masking scheme to isolate potential problem areas in sloped terrain and apply the new merging algorithm by using multiple Tandem-X tracks to overcome the gaps left due to the masking procedure. The radar height products are validated by using a network of ground forest measurement sites and supporting lidar. The regression statistics show an r2 of 0.70 and rmse of 4.1 m between the radar and the field measured heights. By examining height errors, we implement a new test for the presence of canopy extinction, or subcanopy surface scattering, and demonstrate that in the dense and mountainous forests of British Columbia, there are significant canopy extinction effects in X-band imagery.

Wafer-Level Packaging Method for RF MEMS Applications Using Pre-Patterned BCB Polymer.

A radio-frequency micro-electro-mechanical system (RF MEMS) wafer-level packaging (WLP) method using pre-patterned benzo-cyclo-butene (BCB) polymers with a high-resistivity silicon cap is proposed to achieve high bonding quality and excellent RF performance. In this process, the BCB polymer was pre-defined to form the sealing ring and bonding layer by the spin-coating and patterning of photosensitive BCB before the cavity formation. During anisotropic wet etching of the silicon wafer to generate the housing cavity, the BCB sealing ring was protected by a sputtered Cr/Au (chromium/gold) layer. The average measured thickness of the BCB layer was 5.9 μm. In contrast to the conventional methods of spin-coating BCB after fabricating cavities, the pre-patterned BCB method presented BCB bonding layers with better quality on severe topography surfaces in terms of increased uniformity of thickness and better surface flatness. The observation of the bonded layer showed that no void or gap formed on the protruding coplanar waveguide (CPW) lines. A shear strength test was experimentally implemented as a function of the BCB widths in the range of 100–400 μm. The average shear strength of the packaged device was higher than 21.58 MPa. A RF MEMS switch was successfully packaged using this process with a negligible impact on the microwave characteristics and a significant improvement in the lifetime from below 10 million to over 1 billion. The measured insertion loss of the packaged RF MEMS switch was 0.779 dB and the insertion loss deterioration caused by the package structure was less than 0.2 dB at 30 GHz.

Effect of Split Variable Rate Fertilization on Wild Blueberry Plant Growth and Berry Yield

Abstract. Traditionally, wild blueberry growers apply fertilizer uniformly without considering the substantial variation in soil characteristics, topographic features, and berry yield. Occurrence of heavy rainfall events, gentle to severe topography along with high proportion of bare spots and weed patches emphasize the need for variable rate split (VRS) fertilization. The VRS fertilization has a potential to improve fertilizer use efficiency and reduce environmental impacts. Two commercial wild blueberry fields were selected in central Nova Scotia. Fields were divided into three sections [VRS section, uniform rate split (URS) section, and uniform rate (UR) section]. Fertilization was performed by following the global positioning system (GPS) guided prescription map. Soil samples and plant growth parameters were collected during the vegetative year and berry yield samples were collected during the crop year. The experimental design used for this study was split-plot design and the analysis of all collected data were performed using SAS (SAS, 2010) at 5% level of significance. Plant density and plant height were non-significantly different under all slope zones of VRS, URS, and UR treatment sections. Plants in URS and UR sections were taller than VRS sections in low lying areas. Although there were non-significant differences for berry yield in all slope zones of VRS, URS, and UR fertilizer treatments, the mean berry yield was higher in VRS section as compared to the other sections. Significant correlations were observed between soil properties and plant growth parameters under all treatment sections. The VRS fertilization saved 39% and 42% fertilizer in Cooper (field-1) and North River (field-2) fields, respectively. Based on the results of this study, it can be concluded that the VRS fertilization in wild blueberry fields could reduce fertilizer usage without affecting the crop productivity.

Effect of Split Fertilization on Subsurface Water Quality in Wild Blueberry Fields

Abstract. The majority of wild blueberry ( Ait.) fields are situated in acidic soils, having poor water holding capacities, weed patches, gentle to severe topography, and substantial proportion of bare spots, which emphasize the need for variable rate split (VRS) fertilization. Two commercial wild blueberry sites were selected in Nova Scotia, Canada to evaluate the impact of VRS fertilization on subsurface water contamination. The sites were divided into three sections [VRS section, uniform rate split (URS) section, and uniform rate (UR) section]. Prescription maps were generated with ArcGIS 10.1 software based on slope variation for VRS fertilization. Fertilization was performed based on the prescription maps using variable rate (VR) spreader. Fifty-four lysimeters were installed in VRS, URS, and UR treatment sections to collect subsurface water samples. Subsurface water samples were collected after every heavy rainfall event (>15 mm), and were analyzed for nitrate nitrogen (NO 3 - -N) and ammonium nitrogen (NH 4 + -N) concentrations. Leaf samples were collected from each fertilizer treatment and analyzed for macro and micro nutrients. Results suggested that the VRS treatment significantly decreased (p 3 - -N and NH 4 + -N concentrations in subsurface water samples when compared to URS and UR treatments. Overall for the Cooper site, mean NO 3 - -N leaching under the VRS treatment section were 45% and 47% lower as compared to the URS and UR treatment sections, respectively. However, mean values of NH 4 + -N concentration under the VRS treatment section of the North River site were 38% and 45% lower as compared to the URS and UR treatment sections, respectively. Results revealed that the VRS treatment did not have any negative effect on leaf nutrient concentrations. The VRS fertilization saved almost 40% in this study. Results demonstrated that the VRS fertilization in wild blueberry fields can increase fertilizer use efficiency and reduce water contamination via subsurface leaching.

Effect of Split Variable Rate Fertilizationon Ammonia Volatilization in Wild Blueberry Cropping System

<abstract><title><italic>Abstract. </italic></title> Currently, fertilizer is applied uniformly in wild blueberry (Vaccinium angustifolium. Ait) fields, once in a two year production cycle, without considering substantial variation in soil/plant characteristics, topographic features, and fruit yield. The heavy rainfall, gentle to severe topography with high proportion of bare spots, and weed patches in wild blueberry fields emphasizes the need for variable rate split (VRS) fertilization to avoid environmental contamination. Two commercial wild blueberry fields were selected in central Nova Scotia to examine the impact of VRS fertilization on ammonia volatilization losses. Management zones (MZs) were delineated based on slope variation within the selected fields (steep slope (Zone-1), moderate slope (Zone-2), and low slope areas (Zone-3)). The fields were divided into two sections (VRS section and uniform rate (UR) section). Global positioning system (GPS) guided prescription maps based on slope variation were generated in ArcGIS 10 software to apply fertilizer in both fields. In VRS section, fertilizer was applied three times with commercial variable rate (VR) fertilizer spreader in Zone-1, Zone-2, and Zone-3 with fertilization rates of 66, 50, 33, and kg ha^-1, respectively. Single uniform grower’s fertilizer rate (200 kg ha^-1) was applied in UR sections of the selected fields for comparison. The ammonia volatilization trials were established under VRS and UR fertilized sections of the selected fields immediately following the fertilization. The ammonia volatilization samples were collected after each fertilization in VRS sections and once in UR sections. The samples were analyzed for ammonium nitrogen (NH₄⁺-N) concentrations. Leaf samples were collected in third week of July at tip-dieback stage and analyzed for leaf nutrient concentrations. The results of repeated measure analysis of variance showed ammonia volatilization losses were significantly (p < 0.05) lower in VRS sections as compared to uniformly fertilized sections of the selected fields. Secondly, the study found that the leaf nutrient concentrations were not reduced using VRS fertilization. Results of this study also indicated that the VRS fertilization improved the nitrogen use efficiency and reduced the ammonia volatilization in wild blueberry fields.

Assessment of different topographic correction methods in ALOS AVNIR-2 data over a forest area

Because the removal of topographic effects is one the most important pre-processing steps when extracting information from satellite images in digital Earth applications, the problem of differential terrain illumination on satellite imagery has been investigated for at least 20 years. As there is no superior topographic correction method applicable to all areas and all images, a comparison of topographic normalization methods in different regions and images is necessary. In this study, common topographic correction methods were applied on an ALOS AVNIR-2 image of a rugged forest area, and the results were evaluated through different criteria. The results show that the simple correction methods [Cosine, Sun-Canopy-sensor (SCS), and Minnaert correction] are inefficient in exceptionally rough forests. Among the improved correction methods (SCS+C, modified Minnaert, and pixel-based Minnaert), the best result was achieved using a pixel-based Minnaert approach in which a separate correction factor in various slope angles is used. Thus, this method should be considered for topographic correction, especially in forests with severe topography.

Influence of river channel geometry in stream flow modelling and guidelines for field investigation

Fully physics-based, process-level, distributed fluid flow and reactive transport hydrological models are rarely used in practice until recent years. These models are useful tools to help understand the fundamental physical, chemical, and biological processes that take place in nature. In this study, sensitivity analyses based on a mountain area river basin modelling study are performed to investigate the effect of river channel geometric characteristics on downstream water flow. Numerical experiments show that reduction in the river channel geometric measurement interval may not significantly affect the downstream water stage simulation as long as measurement accuracy at special nodes is guaranteed. The special upstream nodes include but are not limited to 1) nodes located close to the observation station, 2) nodes near the borders of different land covers with considerable riverbed roughness changes, 3) nodes at entering points of tributaries causing discharge jump and 4) nodes with a narrow cross-section width that may control the flow conditions. This information provides guidelines for field investigation to efficiently obtain necessary geometric data for physics-based hydrological modelling. It is especially useful in alpine areas such as the Tibetan Plateau where field investigation capability is limited under severe topography and climate condition. Copyright © 2013 John Wiley & Sons, Ltd.

Impact of Variable Rate Fertilization on Subsurface Water Contamination in Wild Blueberry Cropping System

Abstract. Wild blueberry fields have gentle to severe topography with high proportion of bare spots, and weed patches emphasizing the need for variable rate (VR) fertilization. To evaluate the impact of VR fertilization on subsurface water contamination, two wild blueberry fields were selected in Nova Scotia, Canada. The field boundaries, weeds and bare spots were mapped using real-time kinematics global positioning system. The variation in slope was mapped and management zones i.e. steep slope (Zone-1), moderate slope (Zone-2) and low lying areas (Zone-3) were delineated. Both fields were divided into two halves (VR and uniform). The GPS-guided prescription maps were generated in ArcGIS 9.3 for VR treatment sections. Three fertilization rates 200, 150, and 100 kg ha -1 were applied in Zone-1, Zone-2 and Zone-3, respectively, with a VR fertilizer spreader. The bare spots/weeds were classified as a separate class in the prescription maps and no fertilizer was applied in those areas. For comparison, the uniform fertilizer rate of 200 kg ha -1 used by growers was applied in uniform treatment sections of the selected fields. Subsurface water samples were collected after every heavy rainfall (>20 mm) from 36 suction lysimeters placed in each field with 18 lysimeters in each treatment. The subsurface water samples were analyzed for nitrate nitrogen (NO 3 — N), and ammonium nitrogen (NH 4 + -N) concentrations under VR and uniform fertilization. Leaf samples were collected from both VR and uniform treatments and were analyzed for leaf nutrient concentrations. The results of this study suggested significantly lower NO 3 — N and NH 4 + -N loading from subsurface water samples leaving the root zone in moderate and low lying areas for VR treatment as compared to uniform treatment. The nitrogen, phosphorus, and potassium nutrient levels in leaves were found to be higher than the recommended ranges for uniform treatment as compare to VR treatment suggesting the excess uptake by plants in uniform treatment which may result in more vegetative growth and lower yield. The results indicated that VR fertilization based slope can increase input use efficiency, farm profitability and reduce subsurface water contamination.

SUEX Laminates for Fan-In, Fan-Out and eWLB Development

The focus of this presentation is on the use of SUEX epoxy Thick Dry Film Sheets (TDFS) as a photoimagable dielectric layer in fan-in, fan-out and e-WLP applications. The sheets can be laminated over severe topography from under 2 μm to over 200 μm in height yielding void free coatings with 100% planarization over the entire substrate. The TDFS are available in a range of thicknesses and wafer or panel sizes. This new material is prepared under a highly controlled solvent-less process, which provides uniform coatings between two throw-away layers of protective polyester film. SUEX sheets of 100 μm thickness have been vacuum laminated in an isothermal process at 60–80°C over 180 μm high, 2mm X 2mm device chips mounted onto a silicon carrier wafer. Process optimization studies were run to determine the desired chamber vacuum, chuck temperature, lamination pressure and lamination time for optimal performance. The entire lamination process has a cycle time of about 10min. Using a vacuum laminator we have been able to obtain totally void-free coatings over 2 to 5 μm high bonding pads and buss lines at the silicon surface with a resist thickness of 205 μm over the trench and 25 μm thickness over the back of the chip with 100% planarization over the surface interface. Exposures on a contact aligner have yielded nominal 50 μm diameter via holes through the resist film to the contact pads at the bottom of the trench. Excellent adhesion to all surfaces on both the carrier wafer and the device chip has been obtained without any delamination or crack formation. Additional work to be presented will demonstrate the filling of the vias with electroplated copper to form interconnects the interconnects to for connection to bonding pads on the fan-out package surface.

Efficient simultaneous wave-equation statics and trace regularization by series approximation

To address the problems of irregular trace spacing and statics correction, simultaneous regularization and wave-equation statics (WE statics) are implemented by least-squares inversion. In general, inversion is found to be intractable in three dimensions, so series approximation is made to reduce significantly the number of required integrals. The resulting operator is suitable for direct inversion or for use with gradient methods. Real and synthetic data are used to determine the viability of the inversion. For synthetic data, even for severe velocity variation and topography, inversion converges to an acceptable solution, and aliasing is reduced significantly. Similarly, for real data, inversion is found to return an antialiased, regularized result with WE statics applied.

An Automated Cost-effective System for Real-time Slope Mapping in Commercial Wild Blueberry Fields

The development of site-specific agriculture has increased the need for knowledge regarding within-field variability in factors such as soil/plant characteristics and topography that influence wild blueberry (Vaccinium angustifolium) production. Surface soil properties are the first type of information most frequently used by blueberry producers in developing management plans. Topographic features are not yet routinely used to guide within-field management. The majority of blueberry fields in eastern Canada have gentle to severe topography. An automated slope measurement and mapping system (SMMS) consisting of low-cost accelerometers used as tilt sensors, differential global positioning system (DGPS), and laptop and custom software was developed. The SMMS was mounted on an all-terrain vehicle for real-time slope measurement and mapping. Six commercial wild blueberry fields were surveyed in central Nova Scotia to evaluate the performance of SMMS. The automatically sensed slopes (SS) were also compared with manually measured slopes (MS) at 20 randomly selected points in each field to examine the accuracy of SMMS. The SMMS measured slope reliably in the selected fields with root mean square error ranging from 0.12 to 0.56 degrees and correlations of SS with MS of R2 = 0.95 to 0.99. The selected fields had substantial variation in slope (ranging from 0.8 to 31.0 degrees). Therefore, the use of low-cost and reliable accelerometers with a DGPS is a better option than expensive real-time kinematic DGPS for developing cost-effective SMMS to quantify and map slopes (real-time) for planning site-specific management practices in commercial fields. The SS maps or real-time SMMS could also be used to adjust vehicle speed at particularly steep slopes.

Detecting Bare Spots in Wild Blueberry Fields Using Digital Color Photography

Wild blueberry fields are developed from native stands on deforested land by removing competing vegetation. The majority of fields are situated in naturally acidic and non-fertile soils that have high proportions of bare spots, weed patches, and gentle to severe topography. Producers presently apply agrochemicals uniformly without considering bare spots. The unnecessary or over-application of agrochemicals in bare spots may increase cost of production and environmental pollution. An automated cost-effective machine vision system using digital color photography was developed and tested to detect and map bare spots for site-specific application of agrochemicals within wild blueberry fields. The experiment was conducted at a 4-ha wild blueberry field in central Nova Scotia. The machine vision system consisting of a digital color camera, differential global positioning system, and notebook computer was mounted on a specialized farm vehicle. Custom software for grabbing and processing color images was developed in Delphi 5.0 and C++ programming languages. The images taken by the digital camera were stored in the notebook computer automatically and then processed in red, green, and blue (RGB), and hue, saturation, and value (HSV) color spaces to detect bare spots in real-time within blueberry fields. The best results were achieved in hue image color space with 99% accuracy and a processing speed of 661 ms per image. The results indicated that bare spots could be identified and mapped with this cost-effective digital photography technique in wild blueberry fields. This information is useful for site-specific application, and has the potential to reduce agrochemical usage and associated environmental impacts in the wild blueberry production system.

200-kg large explosive detonation facing 50-km thick crust beneath west Qinling, northeastern Tibetan plateau

It is difficult to acquire deep seismic reflection profiles on land using the standard oil-industry acquisition parameters. This is especially true over much of Tibetan plateau not only because of severe topography and rapid variation of both velocity and thickness of near-surface layer, but also strong attenuation of seismic wave through the thickest crust of the Earth. Large explosive sources had been successfully detonated in US, but its application in Tibetan plateau rarely has an example of good quality. Presented herein is the data of a 200-kg single shot we recorded in west Qinling, northeastern Tibetan plateau. The shot gather data with phenomenal signal-to-noise ratios illustrate the energy of the PmP phase. Although the observations are only limited to the northeastern Tibetan plateau and thus cannot comprise an exhaustive study, they nevertheless suggest that large explosions may be a useful exploration tool in Tibetan Plateau where standard seismic sources and profiling methods fail to produce adequate data of low crust.

Multivariate image analysis strategies for ToF‐SIMS images with topography

AbstractDespite the benefits of multivariate analysis methods, many challenges remain with their robust applications to real‐life samples relevant to industry. Here, we use hair fibres pre‐treated with a multi‐component formulation to investigate different multivariate analysis strategies for complex time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) images obtained in practical analysis. This is challenging because of extreme topography, a large number of unknown chemical components and detector saturation. We compare results from principal component analysis (PCA) and multivariate curve resolution (MCR) with no scaling, Poisson scaling and binomial scaling. Because of severe topography, scaling methods are modified to operate in the spectral domain only. We propose the use of a maximum ion intensity spectrum to highlight localised chemical features and diagnose detector saturation. Dead time correction with suitable data scaling is demonstrated to be essential for the detection of small, localised chemical variations. While PCA results are difficult to interpret, MCR results resemble secondary ion mass spectrometry (SIMS) spectra and distributions directly. MCR is also superior to manual analysis for the detection of an important interaction between multiple ingredients. However, unlike PCA, the scores and loadings obtained on different MCR factors are correlated. The consequence of this for the optimal resolution of independent chemical features is discussed in detail. Binomial scaling is identified as the most appropriate data scaling method for this image due to detector saturation. This study provides a robust analysis strategy for complex ToF‐SIMS images, essential for increasingly complex multi‐organic surfaces and biomaterials. © Crown copyright 2009. Reproduced with the permission of HerMajesty's Stationery Office. Published by John Wiley &amp; Sons, Ltd.

Continuous Access to Competing Stimulation as Intervention for Self-Injurious Skin Picking in a Child with Autism

Children with autism frequently display self-injurious behavior (SIB), but skin picking—a less severe topography of SIB—has not been the focus of much clinical research. The present study evaluated a home-based intervention that was implemented with a 9-year-old girl who had autism and picked her fingers with resulting tissue damage. The intervention allowed the girl to hold and manipulate preferred objects during play and leisure activities. Evaluated in an ABAB reversal design, intervention essentially eliminated skin picking. Clinical and research implications are discussed.

2.5-D/3-D resistivity modelling in anisotropic media using Gaussian quadrature grids

SUMMARY We present a new numerical scheme for 2.5-D/3-D direct current resistivity modelling in heterogeneous, anisotropic media. This method, named the ‘Gaussian quadrature grid’ (GQG) method, cooperatively combines the solution of the Variational Principle of the partial differential equation, Gaussian quadrature abscissae and local cardinal functions so that it has the main advantages of the spectral element method. The formulation shows that the GQG method is a modification of the spectral element method but does not employ the constant elements or require the mesh generator to match the Earth's surface. This makes it much easier to deal with geological models having a 2-D/3-D complex topography than using traditional numerical methods. The GQG technique can achieve a similar convergence rate to the spectral element method. We show it transforms the 2.5-D/3-D resistivity modelling problem into a sparse and symmetric linear equation system that can be solved by an iterative or matrix inversion method. Comparison with analytic solutions for homogeneous isotropic and anisotropic models shows that the error depends on the Gaussian quadrature order (abscissa number) and the subdomain size. The higher the order or the smaller the subdomain size that is employed, the more accurate are the results obtained. Several other synthetic examples, both homogeneous and inhomogeneous, incorporating sloping, undulating and severe topography, are presented and found to yield results comparable to finite element solutions involving a dense mesh.