Using Benford’s law on the seismic reflectivity analysis

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, …) occur more frequently than those with higher first digits (…, 8, 9). A data set from earth’s geomagnetic field, the estimated time in years between reversals of earth’s geomagnetic field, the seismic P-wave speed of earth’s mantle below the southwest Pacific, and other geophysical data obey the BL. Although there are other statistical methods for analyzing a data set, we test, for the first time, the analysis of the seismic reflectivity through the Benford distribution point of view. We applied the BL on real reflectivity data from two wells from the Penobscot field and another two from the Viking Graben field. In both data sets, the reflectivity was in conformity with the BL. Moreover, after analyzing the effect of sonic and density logs despiking on Benford’s distribution through the BL, we found an optimum coefficient for the despiking process, which was a common procedure used to edit the well-log data before its use on reservoir studies.

Collaborational Metastructuralism: Advances in Organizational Theory and Administration

“…El estudio concluye que hay evidencia de la necesidad de un mejor control del gasto público mediante el uso de tarjetas corporativas (2018, pp. 54-78) En la aplicación sismica podemos encontrar a, de Macedo, de Figueiredo (2018).…”

Using residual heat maps to visualise Benford’s multi-digit law

“…Note that we can cancel the 1 ln (10) terms from all terms in the bracket with the 1 ln (10) in λ c which gives the desired form.…”

“…Numerous data sets that arise in different scientific disciplines have been found-to differing quantitative extents-to conform with Benford's law. The physics phenomena include alpha decay [5]; astrophysics [6]; atomic line strengths [7]; biophysics [8]; extra-solar planets [9]; geophysics [10]; particle physics [11]; quantum critical phenomena [12]; spectroscopy [13] and end-of-chapter exercises in physics textbooks [14]. An extensive database of articles, books and other resources related to Benford's law can be found at [15].…”