Local Wavenumber Methods Research Articles

Local Wavenumber Method for Delamination Characterization in Composites With Sparse Representation of Lamb Waves.

This article presents a quantitative Lamb wave detection method for delamination characterization in composite laminates using local wavenumber features. In contrast to the conventional Fourier transform-based methods, the improved sparse reconstruction method is efficient and able to evaluate the spatial wavenumbers of Lamb waves with limited measurements. To improve the feasibility of the sparse reconstruction method, the analytical solution of the local wavenumbers to the compressed sensing (CS) formulation with considering structural discontinuity is firstly investigated. The estimated wavenumber values for the spatial window located on healthy and damaged regions simultaneously are governed by a nonlinear optimization function. Benefiting from revealing the evolution of local wavenumber slopes, a delamination characterization method is proposed to accurately determine the damage location and depth by wavenumber banalization. Subsequently, the performance of the proposed method on local wavenumber estimation and damage quantification is verified by the simulation data. The parameters are discussed in order to improve the algorithm stability. Finally, the experimental investigation was conducted on a quasi-isotropic carbon fiber reinforced polymer (CFRP) laminate with an induced delamination. Lamb wave was generated and scanned by the Nd:YAG laser spot with spatial intervals of 2 mm. The results verify the sparse reconstruction method for delamination characterization, which shows value of reducing labor cost and testing time.

Localization and characterization of delamination in laminates using the local wavenumber method

This paper proposes a method to effectively locate and characterize mode I delamination in carbon fiber/epoxy (CF/EP) composite laminates using the local wavenumber method of propagating guided waves in a fine grid of spatial sampling points. Mode I interlaminar fracture tests were conducted using a double cantilever beam (DCB) specimen to evaluate the developed method. Wave propagation in composite laminates with delamination at different center frequencies were investigated by two-dimensional finite element (FE) simulation. The results revealed some unique mechanisms of interaction between guided wave and delamination in detail. They demonstrated that the wave propagation velocity is transformed at the delamination, and the wave attenuation and dispersion are larger with the increase of the center frequency. The guided waves were rapidly excited at each grid point using a non-contact scanning laser Doppler vibrometer (SLDV) system and actuated by a single fixed piezoelectric (PZT) sensor in the experimental study. The spatially dependent wavenumber value of the center frequency was determined by the local Fourier domain analysis method for processing guided wave filed data. The results showed that the local wavenumber method for guided waves is capable of locating and characterizing the delamination in composite laminates.

Determination of source parameters of simple-shaped geologic subsurface structures from self-potential anomalies using enhanced local wavenumber method

Simple geometry model structures can be useful in quantitative evaluation of self-potential data. In this paper, we solve local wavenumber equation to estimate the horizontal position, the depth and the type of the causative source geometry by using a linear least-squares approximation. The advantages of the algorithm in determining the horizontal position and depth measure are its independency to shape factor of the sources and also its simple computations. The algorithm is built in Matlab environment. The validity of the algorithm is illustrated on variable noise-free and random noise included synthetic data from two-dimensional (2-D) models where the achieved parametric quantities coincide well with the actual ones. The algorithm is also utilized to real self-potential data from Ergani Copper district, Turkey. The results from the actual data application are in good agreement with the published literature for the study area. The source code of the algorithm is available from the authors on request.

Estimation of Magnetic Contact Location and Depth of Magnetic Sources in a Sedimentary Formation

Abstract The aeromagnetic data of Idogo, Southwestern Nigeria, have been used to study the lithology and to determine the magnetic source parameters within Idogo and its environs. Idogo lies between latitudes 6°30′N and 7°00′N and between longitudes 2°30′E and 3°00′E. The magnetic anomaly map, the regional geology, the analytic signal and the local wavenumber were used to identify the nature and depth of the magnetic sources in the region. Data enhancement was carried out to delineate the residual features relative to the strong regional gradients and intense anomalies due to the basin features. The estimated basement depth using the horizontal gradient method revealed depths ranging between 0.55 km and 2.49 km, while the analytic signal amplitude and local wavenumber methods estimated depth to the magnetic sources to range from 0.57 km to 4.22 km and 0.96 km to 2.43 km, respectively. Depth computations suggested the presence of both shallow and deep sources. The total magnetic intensity values ranged from 3.1 nT to 108.3 nT. The area shows magnetic closures of various sizes in different parts of the area trending West, with prominence at the centre and distributed East–West.

Fast local wavenumber (FLW) method for the inversion of magnetic source parameters

The current local wavenumber methods for the interpretation of magnetic anomalies compute the locations of geological bodies by solving complex matrices. Presently, such methods require to know the structural index, which is a parameter that represents the source type. The structural index is hard to know in real data; consequently, the precision of current methods is low. We present the fast local wavenumber (FLW) method, and define the squared sum of the horizontal and vertical local wavenumbers as the cumulative local wavenumber. The FLW method is the linear combination of the umulative local wavenumberand other wavenumbers, and is used to compute the locations and structural index of the source without a priori information and matrix solution. We apply the FLW method to synthetic magnetic anomalies, and the results suggest that the FLW method is insensitive to background and oblique magnetization. Next, we apply the FLW method to real magnetic data to obtain the location and structural index of the source.

Basement structure of the United Arab Emirates derived from an analysis of regional gravity and aeromagnetic database

Gravity and aeromagnetic data covering the whole territory of the United Arab Emirates (UAE) have been used to evaluate both shallow and deep geological structures, in particular the depth to basement since it is not imaged by seismic data anywhere within the UAE. Thus, the aim has been to map the basement so that its structure can help to assess its control on the distribution of hydrocarbons within the UAE. Power spectrum analysis reveals gravity and magnetic signatures to have some similarities, in having two main density/susceptibility interfaces widely separated in depth such that regional-residual anomaly separation could effectively be undertaken. The upper density/susceptibility interface occurs at a depth of about 1.0km while the deeper interface varies in depth throughout the UAE. For gravity, this deeper interface is assumed to be due to the combined effect of lateral changes in density structures within the sediments and in depth of basement while for magnetics it is assumed the sediments have negligible susceptibility and the anomalies unrelated to the volcanic/magmatic bodies result from only changes in depth to basement. The power spectrum analysis over the suspect volcanic/magmatic bodies indicates they occur at ~5km depth. The finite tilt-depth and finite local wavenumber methods were used to estimate depth to source and only depths that agree to within 10% of each other were used to generate the depth to basement map. This depth to basement map, to the west of the UAE-Oman Mountains, varies in depth from 5km to in excess of 15km depth and is able to structurally account for the location of the shear structures, seen in the residual magnetic data, and the location of the volcanic/magmatic centres relative to a set of elongate N-S to NE-SW trending basement highs. The majority of oilfields in the UAE are located within these basement highs. Therefore, the hydrocarbon distribution in the UAE basin appears to be controlled by the location of the basement ridges.

The amplitude and phase of the derivatives of the magnetic anomalies of thin dykes and contacts

If the horizontal and vertical derivatives of the total field magnetic anomalies of thin dykes and contacts (and the magnetic anomaly from a thin dyke) are put into an amplitude-phase form, then this can aid in their interpretation. First, it allows derivatives of fractional order to be calculated analytically; second, estimates of the source dip can be made; and finally, the relationships between local wavenumber and source-distance semi-automatic interpretation methods are clarified. The approach is demonstrated on synthetic data and aeromagnetic data from South Africa.

Estimation of depth to top of magnetic sources using the local-wavenumber approach in an area of shallow Moho and Curie depth — The Red Sea

The local-wavenumber method estimates the depth to a magnetic source based on the spectral content of a single anomaly assuming that the base of the magnetic body is at infinite depth. However, the “infinite-depth” assumption can lead to significant underestimation of the depth to the top of magnetic bodies, especially in areas where the depth to the bottom of the magnetic layer is not large compared to the depth to the top, as would occur in high heat-flow regions and thinned continental margins. Such underestimation of depths has been demonstrated in model studies and using real data with seismic and well control. We evaluated a modification to the local-wavenumber approach to estimate the depth to the top of magnetic sources assuming that the depth to the bottom of the magnetic sources is controlled by the Curie temperature or crustal thickness. We applied this new method to a simple model of a continental margin and to magnetic survey data over the central Red Sea where the Curie isotherm is shallow. The effective structural index of this finite depth extent model is found to increase continuously from the continent to the ocean as the depth to the magnetic basement increases and the depth to the bottom of the magnetic layer decreases. We have also discovered in this study that the local-wavenumber maxima correlate well with major seafloor spreading magnetic reversal epochs in the central Red Sea segment.

Improving the local wavenumber method by automatic DEXP transformation

In this paper we present a new method for source parameter estimation, based on the local wavenumber function. We make use of the stable properties of the Depth from EXtreme Points (DEXP) method, in which the depth to the source is determined at the extreme points of the field scaled with a power-law of the altitude. Thus the method results particularly suited to deal with local wavenumber of high-order, as it is able to overcome its known instability caused by the use of high-order derivatives. The DEXP transformation enjoys a relevant feature when applied to the local wavenumber function: the scaling-law is in fact independent of the structural index. So, differently from the DEXP transformation applied directly to potential fields, the Local Wavenumber DEXP transformation is fully automatic and may be implemented as a very fast imaging method, mapping every kind of source at the correct depth. Also the simultaneous presence of sources with different homogeneity degree can be easily and correctly treated. The method was applied to synthetic and real examples from Bulgaria and Italy and the results agree well with known information about the causative sources.

Alternative local wavenumber methods to estimate magnetic source parameters

Three alternative local wavenumber methods are proposed to estimate the depth and the nature (structural index) of the 2D magnetic source simultaneously using various combinations of different forms of the local wavenumbers to compute the source parameters without any prior information about the source. A clustering method is also provided to get more accurate results. The proposed local wavenumber methods are demonstrated on synthetic noise-free and noise-corrupted magnetic data, and they successfully estimate the location parameters and structural index of the causative sources. The actual application of the proposed methods is demonstrated on a magnetic anomaly from southern Illinois.

Depth Estimation and Source Location of Magnetic Anomalies from a Basement Complex Formation, Using Local Wavenumber Method

Source locations and depths to magnetic contacts were estimated from the total intensity magnetic field of an area of 3,025.25 square kilometres on geographical latitude

Magnetic gradient techniques on digitized aeromagnetic data of Ibadan area, south-western Nigeria

AbstractLocations and depths to magnetic contacts were estimated from the total intensity magnetic field using the Horizontal Gradient Magnitude (HGM), Analytic Signal Amplitude (ASA) and Local Wavenumber (LWN) methods. Aeromagnetic data from the Ibadan area, in south-western Nigeria, were analyzed to estimate depths to magnetic sources as well as source locations. The minimum/maximum depth limits of the HGM and LWN are relatively close and comparable, while shallow source depths limits are greater than expected in the ASA method when compared with the HGM and LWN functions.

Improved Local Wavenumber Methods in the Interpretation of Potential Field Data

We present two new potential-inversion methods for estimating the depth and the nature (structural index) of the source, which use various combinations of different forms of local wavenumbers and the information about the horizontal location to estimate individually the depth and the nature of a magnetic source. The improved local wavenumber methods only use the horizontal offset and vertical offset of local wavenumbers to estimate the depth and the structural index of the source, so they yield more stable results compared with the results obtained by current methods that require the derivatives of local wavenumbers. Tests conducted with synthetic noise-free and noise-corrupted magnetic data show that the proposed methods can successfully estimate the depth and the nature of the geologic body. However, our methods are sensitive to high-wavenumber noise present in the data, and we reduced the noise effect by upward continuing the noise-corrupted magnetic data. The practical application of the new methods is tested on a real magnetic anomaly over a dike whose source parameters are known and the inversion results are consistent with the true values.

Interpretation of Potential Field Tensor Data Using the Tensor Local Wavenumber Method and Comparison with the Conventional Local Wavenumber Method

AbstractMeasurements of potential field tensors (PFT) have been widely used in geophysical exploration because of the advantages of big capacity, high‐precision, and low noise. In this paper, we suggest using tensor local wavenumber (TLW) to interpret potential field tensor data. We firstly define the tensor local wavenumber, and then derive the inversion formula based on the tensor local wavenumber. The TLW method does not require any prior information about the nature of the source to estimate location parameters, and then the nature of the source can be obtained by the source location parameters. The effectiveness of the TLW method is demonstrated using theoretical potential field data, and we compare it with the conventional local wavenumber (CLW) method. Our work shows that the inversion results of the TLW method are more accurate. Especially in the case that observational points are distributed unreasonably, the TLW method still can yield accurate results. At last, we applied the TLW method to a gravity data example in Texas, USA, and inversion results are consistent with previous work.

A Study on the Effect of Depressed Topography on Rayleigh Surface Wave

AbstractIn the paper using local discrete wave‐number method we study the effect of topography on Rayleigh surface waves due to an explosive source near surface. Firstly we analyze the propagation character of Rayleigh surface wave in the course of passing topography, compare the changes on its energy and frequency before and after passing topography. Then, we discuss the relation between the changes and topographical steepness. It can be seen that the Rayleigh wave produces new scattering body wave during passing the topography with reduction of energy and loss of high frequency. Moreover, the steeper the topography is, the more energy of frequency is lost.

Locating geologic contacts with magnitude transforms of magnetic data

Locating geologic contacts by mapping lateral magnetization changes provides a variety of useful geologic information. Magnetic contacts will often correspond to lithologic boundaries, while the shapes and textures of contact maps can also indicate rock type and the style of deformation present. Well-established methods for contact mapping are the horizontal gradient magnitude of the pseudogravity (PSG-hgm) and the total field (TF-hgm). More recent mappers include the analytic signal (AS), the 3-D local wavenumber (LW) and the horizontal gradient magnitude of the tilt (TI-hgm). PSG-hgm and TF-hgm generally produce coherent contact trends but the locations are dependent on the contact dip and its magnetization direction. The AS, LW and TI-hgm methods produce contact locations that are independent of dip and magnetization. Magnitude transforms of the anomalous magnetic field offer an alternative approach to contact mapping since only the field components or the field component derivatives are used, in contrast with other methods that require total field derivatives, possibly up to second order. The magnitude transforms are also dip- and magnetization-independent. Contact maps determined for the magnitude transforms are compared with those from the PSG-hgm and TF-hgm methods for a recently-flown survey over a poorly-exposed Precambrian Shield area in Manitoba, Canada. The T transform map (magnitude of the anomalous magnetic field) is similar to that from PSG-hgm. The other magnitude transforms perform less well because of sensitivity to noise and gridding artefacts, resulting in less coherent trends. None of the transforms are able to resolve the same detail that TF-hgm does. Contact maps from magnitude transforms are therefore only to be preferred over PSG-hgm and TF-hgm maps in areas of high remanent magnetization and gently dipping geology.

A Study on Frequency Responses of Topography with Different Scales Due to Incident SH Wave

AbstractTopography is a main factor affecting ground motion. Theoretical investigations proved that it affects the arrival time, propagation energy, and waveform. Moreover, topography is also an important source to produce coda wave. It has been showed that the influence of complex topography on seismic waves not only depends on the spectral nature of seismic source, but also depends on the character of topographical scales. In this article, we simulated frequency responses of topography with multiple spatial scales due to incident SH wave by using local discrete wave‐number method, and found a resonance‐like relationship between the scales of topography and the frequency of incident wave. Such relationship underlies the explanation for the phenomena that frequency responses of topography depend on both topographical scale and frequency of incident wave. It is also useful in constructing the models for synthesizing seismograms. For example, we can ignore those spatial components of structural model whose contribution to the total seismic response is too small to be accounted, to achieve maximum computation efficiency.

Interpretation of magnetic data using an enhanced local wavenumber (ELW) method

This paper presents an enhancement of the local-wavenumber method (named ELW for “enhanced local wavenumber”) for interpretation of profile magnetic data. This method uses the traditional and phase-rotated local wavenumbers to produce a linear equation as a function of the model parameters. The equation can be solved to determine the horizontal location and depth of a 2D magnetic body without specifying a priori information about the nature of the sources. Using the obtained source-location parameters, the nature of the source can then be inferred. The method was tested using theoretical simulations with random noise over a dike body. It was able to provide both the location and an index characterizing the nature of the source body. The practical utility of the method is demonstrated using field examples over dikelike bodies from Canada and Egypt.

Interpretation of the aeromagnetic map of Eastern Hoggar (Algeria) using the Euler deconvolution, analytic signal and local wavenumber methods

The interpretation of regional aeromagnetic data is very useful for structural interpretations. In this study, we have used three techniques to locate geological contacts and major faults, namely: the Euler deconvolution, the analytic signal and the local wavenumber methods. These three techniques have been tested on synthetic models for accuracy and sensitivity, to determine the best parameters that yield a realistic interpretation. The results obtained from each method on synthetic data, with or without random noise, are compared and discussed here. The three methods were applied to the interpretation of aeromagnetic data from Eastern Hoggar (Algeria). This interpretation led to the establishment of a structural map of the Eastern Hoggar with the eastern boundary of the Issalane terrane suggested to be the suture zone between the central Hoggar and the Saharan metacraton.

Detection of Cavities and Tunnels from Gravity Data using a Neural Network

High-resolution aeromagnetic surveys were acquired for the Albuquerque basin in the central Rio Grande rift, a basin filled with poorly consolidated sediments. The surveys proved successful in efficiently and economically mapping previously unknown hydrogeologic features of the shallow subsurface. This success suggests that aeromagnetic methods may be useful in hydrogeologic studies of other sediment-filled basins.The aeromagnetic surveys were used primarily to delineate buried igneous rocks and to locate faults within the basin fill, both important for understanding the subsurface hydrogeology. Buried igneous rocks were recognized from their high-frequency, high-amplitude magnetic responses and characteristic map patterns. The horizontal-gradient and local wavenumber methods were used to obtain estimates of their source depths.The aeromagnetic surveys were also successfully used to locate faults within the basin fill. Magnetic signatures associated with faults are produced by the juxtaposition of sediments having differing magnetic properties rather than the products of secondary processes. Expression of faults is abundant throughout the basin, revealing patterns that cannot be mapped at the surface due to widespread cover.A fault signature recognized in the high-resolution data that has multiple inflection points is best explained by a fault with a thin magnetic layer on the upthrown block and thick magnetic layer on the downthrown block, called the thin-thick layers model. Geologically, this signature indicates erosion of the upthrown block or a growth-faulting scenario: fault-controlled sedimentation for faults that offset sediments, and successive accumulation of basalt on the downthrown block for faults that offset volcanic rocks.