Short-wavelength Features Research Articles

Simulating spatial variations of lithospheric folding in the south polar terrain of Enceladus

The South Polar Terrain (SPT) of Saturn's moon Enceladus is a young, heavily lineated region that has been shown to be actively venting cryovolcanically. A set of roughly evenly spaced, subparallel fissures, collectively known as the Tiger Stripes, cut across the SPT and is the source of the venting. Additionally, thermal observations demonstrated anomalously high heat flow coming out of the whole SPT in general, and the Tiger Stripes in particular; total heat power out of the region has been estimated to be ∼5–18 GW, more than what can be supplied by equilibrium tidal heating and suggesting temporal variability in the thermal structure of the SPT. Between the Tiger Stripes are a series of closely spaced, short wavelength (1.1 km) linear features generally following the trend of the Tiger Stripes, which has been interpreted as folding of a surface layer undergoing compression. In addition, periodic ridges and troughs (5 km wavelength) found in the zone rimming the SPT have been interpreted recently as contractional features. Here, we simulate the formation of both types in order to constrain the thermal conditions required for their formation. Reproducing the shorter wavelength features necessitates high surface temperatures (185 K) and high heat flows (400 mW m−2), results consistent with past work. The long wavelength features need lower surface temperatures (130K) and heat flows (100 mW m−2), which demonstrates a spatial variability heat of lost from the center to the periphery of the SPT.

Comparative evaluation of five global gravity models over a part of the Bay of Bengal

Several global gravity models (GGMs) are freely available in the public domain, which can be utilised to study the earth's gravity field in almost every part of the globe. The present study compared the free-air gravity anomalies calculated from the five GGMs EGM2008, EIGEN6C4, GECO, XGM2019e_2159, and SGG-UGM-2 archived by the International Centre for Global Earth Models (ICGEM) with respect to shipborne gravity in the Bay of Bengal. The average correlation coefficient and covariance are ∼ 96 % and ∼ 450mGal2. The mean difference between the shipborne and the modelled gravity is − 5 mGal. Relatively higher amplitude gravity differences observed at the continental-oceanic transition, the 85°E and Ninetyeast ridges, and the western basin are possibly due to high gradient, dominant density contrasts, and rugged topography. The average standard deviation and root-mean-square-error (RMSE) of the differences are ∼ 6.5 mGal and ∼ 7.5 mGal. A significantly lower standard deviation and RMSE found for the models generated at higher degree/order compared to lower degree/order is due to diminishing omission error of the GGMs with increasing degrees of truncation. The spectral analysis and coherence estimation of the modelled gravity demonstrate excellent correspondence for anomalies wider than ∼ 25 km. The agreement between anomaly amplitudes and shapes and calculated statistics indicates that the accuracy and resolution of the modelled gravity data are certainly good enough for regional-scale studies aiming to map Moho topography and mantle structures. However, the delineation of shorter wavelength features originating from the shallow-level basement/sedimentary might be uncertain and requires further validations. The present study confirms that all five models show promising results in terms of their accuracy and resolution. Moreover, the SGG-UGM-2 and XGM2019e_2159 models compare favourably with respect to the GECO, EIGEN6C4 and EGM2008 models in the Bay of Bengal.

Unique Molecular Features of Water-Soluble Photo-Oxidation Products among Refined Fuels, Crude Oil, and Herded Burnt Residue under High Latitude Conditions

Photo-oxidized petroleum hydrocarbons are a unique class of water-soluble bioavailable compounds that have gained emerging recognition within toxic regulatory management bodies as an urgent and priority research need in high latitudes. In order to characterize the molecular signatures of photo-oxidized petroleum, bench-scale spills were irradiated over Alaskan seawater and freshwater at 5.5 °C. “Refined fuels” included heating oil, diesel, Jet-A, kerosene, and gasoline, with the Alaska North Slope (ANS) crude reference. An additional experiment assessed the photolytic aging of ANS crude “remediated” using a recently popularized strategy of in situ burning with and without herder application. A four-component fluorescence parallel factor model revealed a unique short-wavelength feature associated with photo-oxidized refined fuel that is not associated with traditional “microbial”- or “terrestrial-like” components. In contrast, crude oil photolytically decomposes into long-wavelength humic-like components (high humification index) and oxidized aliphatics. Fourier transform ion cyclotron resonance mass spectrometry data corroborated the optical data. Overall, on a per-volume basis, the refined fuels diesel, heating oil, kerosene, and Jet-A produce a significantly higher mass of photoproducts than crude oil and carry a unique chemical signature. This warrants new considerations regarding marine biota toxicity. This study also highlights new potential for tracking photo-modified water-soluble fractions of crude and refined fuels in high latitudes with fluorescence spectroscopy.

Probing the source of ancient linear gravity anomalies on the Moon

A large set of linear to arcuate gravity anomalies which are not associated with any surface expressions was revealed by lunar gravity data from the GRAIL mission. The anomalies can be categorized into two types: a set of large anomalies that border the Procellarum KREEP terrane (PKT) region, and the linear gravity anomalies (LGAs) that are scattered throughout the lunar highlands. In this study, we use band-passed gravity gradient maps and localized power spectral analyses to characterize the nature of and the differences between the two types of anomalies. The results show that the PKT border anomalies are primarily long wavelength features whose power spectra are not clearly distinguishable from the background spectrum of the surrounding region, while the linear gravity anomalies are short wavelength features whose power spectra in at least one case rises significantly above the background spectrum over a wide range of degrees. This difference in gravitational signature suggests a fundamental difference in the nature of the sources of the two types of anomalies. We then used a Markov chain Monte Carlo model to test different interpretations for the most prominent LGA by comparing the observed power spectrum to modeled spectra for elliptical, triangular, and T-shaped intrusive geometries. We find multiple geometries are able to fit the power spectrum of the LGA equally well. Analogs of comparable scale to the LGAs originate from extensional stress regimes, supporting an inferred period of global expansion in the early Moon, though the cause of that expansion remains uncertain. If the depth extent of the intrusions were governed by neutral buoyancy, we find that intrusions on the nearside similar to those on the farside would have been eruptive and may have contributed to the earliest mare volcanism. The total volume of the intrusions is ~20% of the mare volume, revealing a lower magma production rate on the farside than on the nearside.

Multiscale nonlinear inversion of gravity data for depth-to-basement estimation via coupled stochastic-deterministic optimization

We have developed a multiscale approach for solving 2D and 3D nonlinear inverse problems of gravity data in estimating the basement topography. The inversion is carried out in two stages in which the long-wavelength features of the basement are first estimated from smoothed gravity data via a stochastic optimization algorithm. The solution of this stage is used as the starting model for a deterministic optimization algorithm to reconstruct the short-wavelength features from the full-spectrum gravity data. The forward problem is capable of handling lateral and vertical variations in the density of sediments. Two cases are considered regarding prior knowledge about the density: (1) The density contrast between sediments at the surface and the underlying basement and its vertical variations are a priori known, and (2) only the density contrast at the surface is known with its vertical gradient to be recovered in the inversion. In the former case, the unknowns of the problem are the depths, whereas in the latter case, they are the depths and density gradients defined individually for each prism. Therefore, the inverse problem is ill-posed and has many local minima. The stochastic optimization algorithm uses a random initial model and estimates a coarse model of the basement topography. By repeating the stochastic inversion, an ensemble of solutions is formed defining an equivalent domain in the model space supposed to be within the neighborhood of the global minimum of which several starting solutions are extracted for the secondary deterministic inversion. The presented methodology has been tested successfully in converging to the global minima in 2D and 3D cases with 50 and 2352 total number of prisms, respectively. Finally, the inversion algorithm is used to calculate the thickness of the sediments in the South Caspian Basin using the EIGEN-6c4 global gravity model.

Marine terraces of the last interglacial period along the Pacific coast of South America (1° N–40° S)

Abstract. Tectonically active coasts are dynamic environments characterized by the presence of multiple marine terraces formed by the combined effects of wave erosion, tectonic uplift, and sea-level oscillations at glacial-cycle timescales. Well-preserved erosional terraces from the last interglacial sea-level highstand are ideal marker horizons for reconstructing past sea-level positions and calculating vertical displacement rates. We carried out an almost continuous mapping of the last interglacial marine terrace along ∼ 5000 km of the western coast of South America between 1∘ N and 40∘ S. We used quantitatively replicable approaches constrained by published terrace-age estimates to ultimately compare elevations and patterns of uplifted terraces with tectonic and climatic parameters in order to evaluate the controlling mechanisms for the formation and preservation of marine terraces and crustal deformation. Uncertainties were estimated on the basis of measurement errors and the distance from referencing points. Overall, our results indicate a median elevation of 30.1 m, which would imply a median uplift rate of 0.22 m kyr−1 averaged over the past ∼ 125 kyr. The patterns of terrace elevation and uplift rate display high-amplitude (∼ 100–200 m) and long-wavelength (∼ 102 km) structures at the Manta Peninsula (Ecuador), the San Juan de Marcona area (central Peru), and the Arauco Peninsula (south-central Chile). Medium-wavelength structures occur at the Mejillones Peninsula and Topocalma in Chile, while short-wavelength (< 10 km) features are for instance located near Los Vilos, Valparaíso, and Carranza, Chile. We interpret the long-wavelength deformation to be controlled by deep-seated processes at the plate interface such as the subduction of major bathymetric anomalies like the Nazca and Carnegie ridges. In contrast, short-wavelength deformation may be primarily controlled by sources in the upper plate such as crustal faulting, which, however, may also be associated with the subduction of topographically less pronounced bathymetric anomalies. Latitudinal differences in climate additionally control the formation and preservation of marine terraces. Based on our synopsis we propose that increasing wave height and tidal range result in enhanced erosion and morphologically well-defined marine terraces in south-central Chile. Our study emphasizes the importance of using systematic measurements and uniform, quantitative methodologies to characterize and correctly interpret marine terraces at regional scales, especially if they are used to unravel the tectonic and climatic forcing mechanisms of their formation. This database is an integral part of the World Atlas of Last Interglacial Shorelines (WALIS), published online at https://doi.org/10.5281/zenodo.4309748 (Freisleben et al., 2020).

Acoustic full-waveform inversion to match far-offset reflections with pseudo-horizontal particle acceleration data

In the early stage of acoustic full-waveform inversion (AFWI), it is important to exploit the long-wavelength features of the gradient and suppress its short-wavelength features to update the background velocity. However, due to strong near-offset PP reflections and multiples within the pressure data, conventional AFWI sometimes primarily reconstructs the short-wavelength features of a given model and fails to converge on a reliable subsurface P-wave velocity model. Therefore, this study, we propose the usage of pseudo-horizontal particle acceleration (pseudo-ax) data for AFWI, rather than the original pressure data. Because the amplitudes of PP reflections are implicitly weighted according to the reflection angle in pseudo-ax data, the near-offset PP reflections and multiples of the pseudo-ax data are much weaker than those of the pressure data. As a result, AFWI using pseudo-ax data focuses on reconstructing the longer-wavelength features of a given model in the early iterations, and then gradually reconstructs short-wavelength features as the inversion process continues. Using synthetic and real data examples for the Volve oilfield in the North Sea, we examined the effects and feasibility of this strategy. In the synthetic data example, the proposed strategy rapidly reduced far-offset data misfits related to long-wavelength feature updates and achieved smaller model misfits than the conventional strategy. The real data example showed that the velocity model reconstructed using the proposed strategy flattened some of the reflectors at the angle-domain common-image gathers (ADCIGs) better than the velocity model obtained using the conventional strategy. These findings demonstrate that our strategy converges closer to the real P-wave velocity model than the conventional strategy by building a hierarchical velocity model from long- to short-wavelength structures.

Present-day crustal deformation revealed active tectonics in Yogyakarta, Indonesia inferred from GPS observations

We investigated the active crustal structure in Yogyakarta, Indonesia, using new and denser Global Positioning System (GPS) data. Deformation rate estimated from five years (2013–2018) of observations on 22 campaign might record broad deformation after the 2006 Mw7.8 Java tsunami earthquake and postseismic transient due to the 2006 Mw6.3 Yogyakarta earthquake. We conducted a decomposition method to obtain a short wavelength feature by removing those postseismic deformations from the observation data. The short wavelength pattern revealed active tectonics indicating a combination of E–W dip-slip motion and N–S left-lateral structure. A large maximum shear strain rate (>0.1 microstrain/yr) was estimated along the Opak fault while a large dilatation rate (<-0.1 microstrain/yr) was estimated around the Bantul Graben. The analysis result indicates important implications for crustal dynamics and assessing future seismic hazards potential in the Yogyakarta region.

Separation and Recovery of Geophysical Signals Based on the Kalman Filter with GRACE Gravity Data

Monthly gravitational field solutions as spherical harmonic coefficients produced by the GRACE satellite mission require post-processing to reduce the effects of shortwave-length noises and north–south stripe errors. However, the spatial smoothing and de-striping filter commonly used in the post-processing step will either reduce spatial resolution or remove short-wavelength features of geophysical signals, mainly at high latitudes. Here, by using prior covariance information that reflects the spatial and temporal features of the geophysical signals and the correlated errors derived from the synthetic model, together with the covariance matrix of the formal errors for the monthly gravity spherical harmonic coefficients, we apply the Kalman filter to separate the geophysical signal from GRACE Level-2 data and simultaneously to estimate the correlated errors. By increasing the number of observations, the iterative process is applied to update the state vector and covariance in the Kalman filter because the prior information is not accurate. Due to the inevitable truncation error, multiple gridded-gain factors method considering different temporal frequencies has been developed to recover the geophysical signal. The results show that the Kalman filter can reduce the high-frequency noises and correlated errors remarkably. When compared with the commonly used filter, no spatial filter (such as Gaussian filter) is used in the Kalman filter. Therefore, the estimated signal preserves its natural resolution, and more detailed information is retained. It shows good consistency when compared with mascon solutions in both secular trend and annual amplitude.

The Influence of Vertical Advection Discretization in the WRF-ARW Model on Capping Inversion Representation in Warm-Season, Thunderstorm-Supporting Environments

Abstract Previous studies have suggested that the Advanced Research version of the Weather Research and Forecasting (WRF-ARW) Model is unable, in its default configuration, to adequately resolve the capping inversions that are commonly found in the warm-season, thunderstorm-supporting environments of the central United States. Since capping inversions typically form in environments of synoptic-scale subsidence, this study tests the hypothesis that this degradation results, in part, from implicit numerical damping of shorter-wavelength features associated with the model-default third-order-accurate vertical advection finite-differencing scheme. To aid in testing this hypothesis, two short-range, deterministic, convection-allowing model forecasts, one using the default third-order-accurate vertical advection finite-differencing scheme and another using a fourth-order-accurate differencing scheme (which lacks implicit damping but is numerically dispersive), are conducted for 25 days during the 2017 NOAA Hazardous Weather Testbed Spring Forecasting Experiment. Model-derived vertical profiles at lead times of 11 and 23 h are validated against available rawinsonde observations released in regions located in the Storm Prediction Center’s 0600 UTC day 1 convection outlook’s “general thunderstorm” forecast area. The fourth-order-accurate vertical advection finite-differencing scheme is shown to not result in statistically significant improvements to model-forecast capping inversions or, more generally, the vertical thermodynamic profile in the lower troposphere. Instead, the fourth-order-accurate differencing scheme primarily impacts the representation of longer-wavelength features already reasonably well resolved by the model. The analysis does, however, provide quantitative evidence over a large sample that, on average, the WRF-ARW model forecasts capping inversions that are too weak, with negative buoyancy spread out over too deep of a vertical layer, compared to observations.

Full model wavenumber inversion: Identifying sources of information for the elusive middle model wavenumbers

We recognized over the years that our conventional surface seismic recording can effectively identify two main features of the earth: its seismic propagation attributes and those attributes resulting in echoes or reflections. Thus, the resulting expression of the earth is dominated by the generally smooth (long-wavelength) features that control wave propagation, which we use to invert for the short-wavelength features causing reflections in a process we refer to as migration velocity analysis and imaging, respectively. The features of the earth that fall in between these two model scales — the middle wavenumbers — have been elusive, which is a dilemma for full-waveform inversion because we need to build the full velocity model (a broad band of model wavenumbers). We analyze the middle model wavenumber gap, but we focus more here on potential sources of information for such middle model wavenumbers. Such sources include regularization, objective function enhancements, and multiscattered energy. Regularization, provided by a total variation (TV) constraint admits middle and high model wavenumber components into the model to enforce the model’s compliance with such a constraint. As opposed to minimizing the TV, such a constraint merely reduces the model space, and thus, these injected middle model wavenumbers are as good as the projected data information to the reduced model space. Such data information includes large offsets, but also multiscattered energy, in which the energy through wavepath and scattering updates can admit more of the elusive middle-wavenumber information that comes from the data. The combination of the right level of allowable model variations with the added data information from large offsets and multiscattering can help in filling the elusive middle model wavenumber gap and admit plausible models.

Directional tilt derivatives to enhance structural trends in aeromagnetic grids

The tilt derivative remains one of the most simple and useful image enhancement methods that can be applied to gridded potential field data. Since it acts as a type of automatic gain control it is particularly useful for revealing low-amplitude short-wavelength features in data. This derivative has now been modified to improve its ability to enhance linear trends with specific spatial orientations. When calculated for a range of directions it may be possible to detect subtle lineations that are not so evident in the original non-directional version of the tilt derivative.

Plasmonic Features in the Absorption Spectrum of a Monodisperse Ensemble of Gold Nanoislands on Sapphire

Plasmonic features in the absorption spectrum of a monodisperse ensemble of gold nanoislands on a sapphire substrate are considered. An explanation of the long-wavelength and UV bands in the absorption spectrum of the sample is proposed. The long-wavelength feature is interpreted as a consequence of surface plasmon polariton excitation under coherent scattering from a regular lattice of gold particles on sapphire, and the short-wavelength feature is considered to be a plasmon resonance, localized on individual gold nanoparticles.

Spatial Scales in Topography and Strain Rate Magnitude in the Western United States

AbstractSpatial spectral analyses of topography and strain rate magnitude across the western United States reveal the presence of at least two separable spectral peaks, representative of characteristic length scales, one short (~10–50 km) and one long (~150–250 km). Less spectral power at intermediate wavelengths aside from that expected for a red, or power law, spectrum occurs in either data set. These results quantify previous qualitative observations that the topography of western North America contains both short and long characteristic wavelength features. Comparing the spectral results to simplified bounding solutions for elastic, viscous, and layered models under tension shows that multiple spectral peaks of comparable power can be reproduced only by mechanical models with more than one layer. Therefore, the simplest model of lithospheric architecture capable of generating the observed dominant characteristic length scales is an elastoplastic lid over a viscous layer.

Lineament Mapping over Sir Creek Offshore and its Surroundings using High Resolution EGM2008 Gravity Data: An Integrated Derivative Approach

ABSTRACT The present study deals with the delineation of lineaments over Sir Creek offshore and its surroundings from EGM2008 gravity data using various derivative techniques owing to their cost-effectiveness in prospective hydrocarbon exploration. Initially, 2-D and 3-D synthetic models have been generated with vertical prismatic objects at different depths. The effectiveness of total horizontal derivative (THD) technique has been established by comparing with E-W and N-S Horizontal derivatives and First Vertical derivative techniques. The residuals of Bouguer gravity data have been estimated with different cut-off wavelengths. Further, the residual anomaly map has been enhanced by the derivative techniques for the delineation of the structural features. Possible depths of the delineated lineaments have been estimated using Euler deconvolution of the Bouguer gravity data, which indicates maximum clustering over the delineated lineaments. It is observed that most of the lineaments are in the depth range of 1.0 km to 5.5km, which correlate well with the previous seismic studies. The present study reveals that the major lineament trends in the N-S, E-W and NNW-SSE directions followed by NE-SW, NW-SE and ENE-WSW directions. These major lineament trends are due to the tectonic activities occurred during Precambrian and Cretaceous period. Different small circular features, rectangular features and shorter wavelength features have also been identified, which could be the key parameter for mapping potential location for hydrocarbon exploration.

Short-wavelength out-of-band EUV emission from Sn laser-produced plasma

We present the results of spectroscopic measurements in the extreme ultraviolet regime (7–17 nm) of molten tin microdroplets illuminated by a high-intensity 3 J, 60 ns Nd:YAG laser pulse. The strong 13.5 nm emission from this laser-produced plasma (LPP) is of relevance for next-generation nanolithography machines. Here, we focus on the shorter wavelength features between 7 and 12 nm which have so far remained poorly investigated despite their diagnostic relevance. Using flexible atomic code calculations and local thermodynamic equilibrium arguments, we show that the line features in this region of the spectrum can be explained by transitions from high-lying configurations within the Sn–Sn ions. The dominant transitions for all ions but Sn are found to be electric-dipole transitions towards the n = 4 ground state from the core-excited configuration in which a 4p electron is promoted to the 5s subshell. Our results resolve some long-standing spectroscopic issues and provide reliable charge state identification for Sn LPP, which could be employed as a useful tool for diagnostic purposes.

Gravity Gridding in South Australia

Creating an image of the acceleration due to gravity over a large area (in this case a large portion of South Australia) is not a trivial process. This paper examines some of the issues involved with creating such an image, and presents some examples. Treating the state gravity as a single dataset highlights outliers and results in ‘dimples’. These are short wavelength features around single points. Treating the data as a compilation of grids and then levelling the grids results in linear artefacts where the survey boundaries meet. Two new approaches have been implemented, involving removing selected data points (based on proximity to adjacent points) and implementing variable density gridding techniques. The resulting grids still have artefacts (notable when viewing a first vertical derivative of the grid), but are smoother and more geologically plausible.

Improved depth conversion with FWI – a case study

In the study region, notoriously heterogeneous shallow carbonates, here between depths of approximately 1.5- 2.5 km, give rise to short-wavelength velocity variations in the overburden, which can cause severe depth undulations at the reservoir level (~3 km depth subsea). As the reservoirs are relatively thin (~30 m), stacked, fluvial-deltaic channel sands with sharp meanders and lateral truncations, even a localised 1% velocity error can produce a 30 m depth error at 3 km, which is not acceptable for development well planning. The resolution of traveltime-tomography is limited and may not resolve overburden variability in a manner suitable for depth conversion in a development setting. Geostatistical scaling using the available well control is one option to further improve depth conversion reliability. This workflow utilizes time-depth data at well locations along with geophysically constrained statistics to derive a stable, geologically plausible background trend that accounts for the majority of depth error. The result is a regionally consistent model that ties the available well control and provides more reliable depth conversion away from wells. The background trend provided by the well-based velocity calibration is however a long-wavelength solution and is unlikely to be able to correct for the short-wavelength depth errors which can arise at depth. FWI on the other hand provides a resolution of less than half a seismic wavelength to capture thin and localized subsurface features. With short-wavelength features accurately resolved, well control can then be used to correct for any residual long-wavelength errors and ensure more reliable depth conversion away from the wells. In this study, reflection tomography and 3D TTI (tilted transverse isotropy) FWI velocity models were geostatistically calibrated to wells and compared for depth conversion accuracy. Using the calibrated reflection tomography model, early appraisal wells were still more than 50 m off prognosis at the top reservoir level. These appraisal wells were just a few hundred metres away from the exploration wells used for control. 3D TTI FWI was then run using the reflection tomography model as input. The same geostatistical calibration to wells was applied to the FWI output and ultimately provided a model with depth conversion accuracy to within 15 m at the reservoir level.

A novel method of micro-Doppler parameter extraction for human monitoring terahertz radar network

Human target characteristic parameter extraction is an important approach of behavior monitoring. The extraction of the characteristic can be applied in various backgrounds, such as sanatorium and hospital. Therefore, this technology is widely studied. Towards extracting physiological characteristic parameters and motion characteristic features of human target, a novel human parameter extraction algorithm is proposed in this paper which has high detection accuracy. The high accuracy detection is achieved by combining the time-frequency analysis and image processing algorithm. Besides that, the utilization of short wavelength and evident micro-motion features inherent with terahertz radar also contributes the improvement of detection accuracy. Simulations test the effectiveness of proposed the algorithm, and illustrate its performance of high extraction precision and insensitivity to noise. For comparison, the simulations are also performed in X-band radar. Via the thorough simulations, we can clearly find the advantage of our proposed algorithm in human target characteristic parameter extraction.

Application of Hyperbolic S-transform in Environmental Gravity Investigation

In this paper, a new method is developed based on downward continuation with a varying shape window of hyperbolic S-transforms to estimate the depth of subsurface structures from gravity data. To increase the sensitivity of the algorithm to better define the top surface of a buried structure (i.e., enhanced resolution of short wavelength features), the Fourier transform operator in the downward continuation equation is replaced by a hyperbolic S-transform window with critical shape parameters. The hyperbolic S-transform allows us to focus on the high wavenumber features in the gravity data. Using the downward continuation equation, the greater the continuation level, the more unstable the values of the continued gravity data will be because of the exponentially increasing effects of continuation level within the formula. One of the objectives of our method is to employ a new formula for depth estimation based on a variant version of downward continuation, where the exponential operator is replaced by a logarithmic operator. Because the logarithm has a slow increase initially (gravity anomalies are usually located at the early portion of the position–wavenumber space), a result is the gradual increase in depth values, which avoids large and unrealistic variations in the calculated depths. Unlike the Fourier transform, the S-transform provides depth values dependent on both position and wavenumber. This allows us to average different calculated depths at each station to obtain a value for the depth in each position. The estimated depth values for gravity sources are referenced to the x-axis, because the S-transform provides the localized Fourier spectrum of data. The depth values must be averaged to decrease spatial shifting of locally obtained depths. Moreover, the averaging neutralizes the repetitive depth information that occurs through S-transforms of the original gravity data, rather than the S-transform of the analytic signal of gravity data. Analysis of synthetic and field gravity data illustrates the usefulness of the hyperbolic S-transform for estimating depth values of geologic structures.