Characterization of geological boundaries using 1‐D wavelet transform on gravity data: Theory and application to the Himalayas

Abstract

We investigate the use of the continuous wavelet transform for gravity inversion. The wavelet transform operator has recently been introduced in the domain of potential fields both as a filtering and a source-analysis tool. Here we develop an inverse scheme in the wavelet domain, designed to recover the geometric characteristics of density heterogeneities described by simple-shaped sources. The 1-D analyzing wavelet we use associates the upward continuation operator and linear combinations of derivatives of any order. In the gravity case, we first demonstrate how to localize causative sources using simple geometric constructions. Both the upper part of the source and the whole source can be studied when considering low or high altitudes, respectively. The homogeneity degree of the source is deduced without prior information and allows us to infer its shape. Introducing complex wavelets, we derive analytically the scaling behavior of the wavelet coefficients for the dyke and the step sources. The modulus term is used in an inversion procedure to recover the thickness of the source. The phase term provides its dip. This analysis is performed on gravity data we measured along a profile across the Himalayas in Nepal. Good agreement of our results with well-documented thrusting structures demonstrates the applicability of the method to real data. Also, deeper, less constrained structures are characterized.

Identification of sources of potential fields with the continuous wavelet transform: Two‐dimensional wavelets and multipolar approximations

“…They demonstrated, in the case of total field magnetic anomaly profiles, some useful relations between parameters of the wavelet coefficients and the apparent inclination of magnetization, in addition to depth, vertical extent, and dip angle of the sources. Martelet et al [2001] have applied similar relations to the case of gravity profiles.…”

“…However, such a 3-D geometrical procedure needs sophisticated graphical implementations to be useful in a computer-aided interpretation program. As shown in previous papers [Moreau et al, 1999;Sailhac et al, 2000;Martelet et al, 2001], we instead prefer to invert equation (16) along each line defined in the modulus maxima by using a series of linear regressions in log-log plots, and by testing for a range of trial depths z 0 . In practice, this is done by plotting log( W a j j/a g ) versus log(a + z 0 ) and by searching the z 0 .…”

“…[15] Like in profile analysis [Moreau et al, 1999;Sailhac et al, 2000;Martelet et al, 2001], let us now consider the modulus maxima of wavelet coefficients (also called ridges or skeleton). They are determined using classical procedures of local maxima detection and have the useful property of being located nearby above the sources and having good signal to noise ratios.…”

Gravity Data Decomposition Based on Spectral Analysis and Halo Wavelet Transform, Case Study at Bird’s Head Peninsula, West Papua

“…The decomposition process of gravity data in China using DWT gave feasible results according to observed geology and field data [5]. In addition, the wavelet transform can also be used for various other purposes, such as removing noise from gravity data [6], finding the boundaries of anomaly sources [7], and for gravity data inversion [8].…”

Application of artificial intelligence for Euler solutions clustering

“…Typically, several indices are used, and the one that provides the best fit to known superficial geological structure, seismic data, boreholes, etc., or the one having good clustering properties is accepted. [On a possibility to estimate structural index, see Slack et al (1967), Steenland (1968), Barbosa et al (1999), and Martelet et al (2001)]. …”