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Benford's law

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Journal Article
Journal: Interpretation
Published: 17 July 2018
Interpretation (2018) 6 (3): T689–T697.
...Isadora A. S. de Macedo; Jose Jadsom S. de Figueiredo Abstract Benford’s law (BL) is a mathematical theory of leading digits. This law predicts that the distribution of first digits of real-world observations is not uniform and follows a trend in which measurements with a lower first digit (1, 2...
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Journal Article
Published: 26 November 2014
Seismological Research Letters (2015) 86 (1): 192–201.
...J. Díaz; J. Gallart; M. Ruiz Benford’s law (BL), also known as the first‐digit law, is an intriguing pattern in data sets, first discovered more than a century ago then forgotten and rediscovered in the twentieth century. This law establishes that the frequency of occurrence of the first digit...
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Journal Article
Journal: Geology
Published: 01 April 2012
Geology (2012) 40 (4): 327–330.
...A. Geyer; J. Martí Abstract Benford's law predicts that the distribution of first digits of real-world observations is not uniform, but instead the lower digits (1, 2, and 3) occur more frequently than the higher ones (… , 8, 9). It has been shown that the use of Benford's law may help...
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Identification of teleseismic and local events using Benford’s law (BL). (Left) The vertical seismic components are overlaid by the Benford’s law estimator (BLe) values. Solid‐ and dashed‐line boxes, respectively, show examples of time windows with and without positive detections. (Right) BL predictions for the distributions of first digits (gray bars) and the results for time windows on the seismic waveform with or without detections (black and white circles, respectively). (a) Two teleseismic events with epicenters in northern Chile. The seismic trace is unfiltered, and the time‐window length used for the analysis is 1 hr. (b) A local swarm near Lourdes (southern France), at about 50 km of the recording site. The trace is band‐pass filtered between 5 and 40 Hz. The amplitudes have been clipped to show minor events. The time window used in this case is 60 s.
Published: 26 November 2014
Figure 1. Identification of teleseismic and local events using Benford’s law (BL). (Left) The vertical seismic components are overlaid by the Benford’s law estimator (BL e ) values. Solid‐ and dashed‐line boxes, respectively, show examples of time windows with and without positive detections
Image
First-digit frequencies according to Benford's law prediction (Equation 1) compared to (A) the data set of areas in square kilometers for the 346 collapse calderas in the Collapse Caldera Database (CCDB) (http://www.gvb-csic.es/CCDB.htm) with the area recorded, and (B) the data set of ages in years for the 213 collapse calderas in the CCDB with the age recorded, and the same data set without the North American calderas that occurred between 23 and 42 Ma (modified set).
Published: 01 April 2012
Figure 1. First-digit frequencies according to Benford's law prediction (Equation 1 ) compared to (A) the data set of areas in square kilometers for the 346 collapse calderas in the Collapse Caldera Database (CCDB) ( http://www.gvb-csic.es/CCDB.htm ) with the area recorded, and (B) the data set
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First-digit frequencies according to Benford's law prediction (Equation 1) compared to the data set of duration of volcanic eruptions in days, which occurred during the period 1900–2009, extracted from the Smithsonian Institution's Global Volcanism Program volcanic eruptions catalogue (http://www.volcano.si.edu).
Published: 01 April 2012
Figure 2. First-digit frequencies according to Benford's law prediction (Equation 1 ) compared to the data set of duration of volcanic eruptions in days, which occurred during the period 1900–2009, extracted from the Smithsonian Institution's Global Volcanism Program volcanic eruptions catalogue
Book Chapter

Author(s)
Joe Dellinger
Series: Society of Exploration Geophysicists Distinguished Instructor Series
Published: 24 September 2024
DOI: 10.1190/1.9781560804000.ch10
EISBN: 9781560804000
... look? This being 2024, of course machine learning has been proposed as a solution ( Vinayak et al., 2022 ). Are there any traditional techniques for detecting problems with data that might work? Benford's lawBenford's law” is an old-school statistical technique for catching fraudulent data...
Journal Article
Journal: Lithosphere
Publisher: GSW
Published: 01 April 2017
Lithosphere (2017) 9 (2): 223–234.
..., pitches steeply downdip to the east. Removal of the effects of tilting due to Miocene and Holocene Basin and Range extension yields a subvertical foliation and lineation ( Tikoff et al., 2001 ). The WISZ extends from the Owyhee Mountains south of Boise ( Benford et al., 2010 ) to north of Riggins...
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First thumbnail for: Kinematic and vorticity analyses of the western Id...
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Journal Article
Journal: Geology
Published: 01 July 2016
Geology (2016) 44 (7): 563–566.
... frequency of earthquakes and decreasing sedimentation rate. This increase in stability is nonlinear (power law with b < 0.5), accelerating with decreasing interseismic sediment accumulation. The correlation is interpreted as evidence for sediment densification and associated shear strength gain induced...
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Journal Article
Published: 06 December 2016
Bulletin of the Seismological Society of America (2017) 107 (1): 229–239.
.... Geographic features: (a) Cayman Islands, (b) Virgin Islands, (c) Hispaniola, (d) Cuba, (e) Jamaica, and (f) Puerto Rico. (A) North American plate and (B) Caribbean plate. Modified from Benford et al. (2012) . The Gonave microplate is bounded by the Cayman spreading center to the west, the Oriente...
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Journal Article
Journal: Lithosphere
Publisher: GSW
Published: 01 April 2017
Lithosphere (2017) 9 (2): 157–183.
... shear zone deformation. This change in orientation is consistent with fabrics to the north being oriented ∼000° ( Manduca et al., 1993 ; Giorgis et al., 2008 ) and fabrics to the south being oriented ∼020° ( Benford et al., 2010 ). We also provide the first quantitative constraints on deformation...
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First thumbnail for: Timing and deformation conditions of the western I...
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Journal Article
Journal: Lithosphere
Publisher: GSW
Published: 01 December 2010
Lithosphere (2010) 2 (6): 418–422.
...-rich host rocks (based on a power-law exponent of 3.0 for this dislocation creep process). Detailed mapping also indicates that inclusion of up to 15% orthopyroxene in the olivine-rich host rocks does not affect their viscosity, constraining the rheological behavior of two-phase, mantle material...
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Journal Article
Journal: Geology
Published: 01 October 2015
Geology (2015) 43 (10): 891–894.
... flow law, , where is strain rate, A is a material constant, σ is differential stress, n is the stress exponent, d is the recrystallized grain size, m is the grain-size exponent, is water fugacity, Q is activation energy, P is pressure, V is activation volume, R is the molar...
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Journal Article
Journal: Geology
Published: 27 March 2020
Geology (2020) 48 (6): 569–573.
.... , 1982 , Microfabric studies as indicators of deformation mechanisms and flow laws operative in mountain building , in Hsü , K.J. , ed., Mountain Building Processes: London , Academic Press , p. 95 – 110 . Taylor , W.R. , 1998 , An experimental test of some geothermometer...
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Journal Article
Published: 16 December 2022
Bulletin of the Seismological Society of America (2023) 113 (1): 99–114.
... of the sequence with Båth’s law and the lower‐than‐expected mainshock energy release estimate have been credited for the atypical seismic sequence ( ten Brink et al. , 2022 ). The USGS focal mechanism has fault parameters 268, 43°, −58° for nodal plane 1 (henceforth named MNP1), and 47°, 54°, −116...
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First thumbnail for: Estimating Coseismic Deformation of Southwestern P...
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Journal Article
Published: 13 December 2022
Bulletin of the Seismological Society of America (2023) 113 (1): 115–130.
... dominated by strike‐slip motion, whereas transpressional deformation with significant plate boundary‐perpendicular shortening is observed around the EPGFZ in southern Haiti ( Calais et al. , 2010 ; Benford et al. , 2012 ). Between these two fault zones, there is a series of fold‐and‐thrust belts named...
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Journal Article
Journal: Lithosphere
Publisher: GSW
Published: 01 April 2017
Lithosphere (2017) 9 (2): 184–204.
... data (CPO, intragranular misorientation axes, CVA analyses) are consistent with dominantly simple shear deformation ( Lister and Hobbs, 1980 ; Law et al., 1984 ; Law, 2010 ), and when rotated into geographical space indicate reverse, top-to-the-southwest shearing on the Ahsahka shear zone...
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Journal Article
Journal: Geosphere
Published: 01 November 2023
Geosphere (2023) 19 (6): 1539–1564.
... (the “border zone” suite of Gaschnig et al., 2010 ). The western Idaho shear zone continues south into the Owyhee Mountains in southwestern Idaho. Relative to the McCall segment, the shear zone in the northern Owyhee segment is wider, less well developed, and contains an 020-oriented foliation ( Benford...
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First thumbnail for: Two phases of Cretaceous dextral shearing recorded...
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Journal Article
Journal: Geosphere
Published: 20 July 2023
Geosphere (2023) 19 (4): 1128–1156.
... in converting mapped GIRs and unranked fault linework to fault linework with confidence rankings. Here, we discuss the rupture-to-fault separation distance based on our pre-rupture fault maps and compare these results to those of Petersen et al. (2011) and the State of California’s Alquist Priolo law...
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