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Yang, D (2016)

Characterization of noise in airborne transient electromagnetic data using Benford's law

SEG Technical Program Expanded Abstracts 2016, pp. 1043-1047.

ISSN/ISBN: 1949-4645 DOI: 10.1190/segam2016-13972000.1



Abstract: Given any data set, extract the first significant digit of every number, and count how often whole numbers 1 to 9 appear as the first significant digit in the data set. Benfordís law states that the frequency distribution of first digits 1 to 9 obeys a particular probability for many naturally occurring data, especially those spanning many orders of magnitude in a log-uniform distribution. I find that airborne transient EM data obey Benfordís law, whereas a random noise with a zero-mean normal distribution does not. So the relative magnitude of such noise can be characterized by the deviation of the first-digit frequency from Benfordís law. A high noise level can result in a large Benford deviation. This approach is first demonstrated by a simple mathematical example using a synthetic data set contaminated by Gaussian noises in different strengths. Then I apply Benfordís law to three real airborne transient EM data sets, including MegaTEM (2006), HeliGEOTEM (2008), and HeliTEM (2012). The HeliTEM data set has shown to be in great conformity to Benfordís law, and it is inferred to have the lowest relative noise level of the three. Application of Ben-fordís law does not involve sophisticated statistics, data preparation and visualization, because it only counts the frequencies of the first digits. Its simplicity makes it a practically useful tool in the first-pass noise characterization of large airborne EM data sets.


Bibtex:
@inbook{doi:10.1190/segam2016-13972000.1, author = {Dikun Yang}, title = {Characterization of noise in airborne-transient electromagnetic data using Benford's law}, booktitle = {SEG Technical Program Expanded Abstracts 2016}, chapter = {}, pages = {1043-1047}, doi = {10.1190/segam2016-13972000.1}, URL = {http://library.seg.org/doi/abs/10.1190/segam2016-13972000.1}, eprint = {http://library.seg.org/doi/pdf/10.1190/segam2016-13972000.1} }


Reference Type: Conference Paper

Subject Area(s): Physics