arxiv: 2604.23616 · v1 · submitted 2026-04-26 · ⚛️ physics.geo-ph · math.DS

Recognition: unknown

Studying the seismic activity of the earthquake in India using fractal analysis

Santanu Nandi

Pith reviewed 2026-05-08 04:59 UTC · model grok-4.3

classification ⚛️ physics.geo-ph math.DS

keywords fractal analysisseismic activityearthquake magnitudesIndiafractal spectrumprobability estimationepicenters

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The pith

Fractal analysis of Indian seismic data from 2016-2023 yields a model for estimating probabilities of future earthquakes by magnitude.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies fractal statistics to records of earthquake magnitudes and epicenters across India over roughly seven years. It examines the data at multiple scales to extract a fractal spectrum that captures repeating patterns in how quakes occur. From this spectrum the authors derive probabilities for events of different sizes in the future. A reader might care because earthquakes cause sudden damage and any quantitative handle on their likelihood could inform planning, even when the method rests on past behavior. The work treats the fractal description as a direct tool for turning observed self-similarity into forward risk numbers.

Core claim

The study performs fractal analysis on seismic activity data for India from 4 October 2016 to 31 May 2023, studying both magnitudes and epicenters at varying scales. This produces a fractal spectrum that reveals patterns within the catalogue. The same spectrum is then used inside a fractal model to assign probabilities to future earthquakes according to their magnitudes.

What carries the argument

The fractal spectrum derived from multi-scale statistics on magnitudes and epicenters, which supplies the numerical basis for assigning probabilities to future events.

If this is right

Probabilities for earthquakes of specific magnitudes can be read directly from the fractal spectrum of the historical catalogue.
Self-similar patterns appear in both magnitude and location data when examined across different scales.
The fractal model supplies a quantitative link between past observations and estimated future occurrence rates.
Seismic activity in the studied interval can be summarised by a single spectrum that organises risk estimates.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same fractal-spectrum approach could be tested on catalogues from other tectonically active regions to see whether comparable probability estimates emerge.
Updated spectra calculated from post-2023 data would allow direct comparison against the original probabilities to check stationarity.
The method might be combined with conventional seismic-hazard maps that already incorporate fault geometry and recurrence intervals.

Load-bearing premise

The fractal spectrum calculated from the 2016-2023 catalogue stays unchanged and can be applied directly to forecast probabilities without shifts in the underlying tectonic drivers.

What would settle it

A sequence of new earthquakes after May 2023 whose magnitude distribution deviates markedly from the probabilities given by the 2016-2023 fractal spectrum would show that the extrapolation does not hold.

read the original abstract

Natural disaster strikes at any given moment from seemingly out of nowhere Akin to earthquake that strongly affects human with different magnitudes through the course of time. The main aim of this study is the fractal analysis of seismic activity data of India in the interval from 04-10-2016 to 31-05-2023. This includes analyzing the earthquake magnitudes and their epicenters using fractal statistics, which were studied at different scales to identify patterns in the data through the use of the fractal spectrum. The probabilities of future earthquakes with different magnitudes were estimated using the fractal model.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This is a routine regional application of fractal analysis to Indian seismic data from 2016-2023 that fits a spectrum to the catalog and treats the fit as a probability forecast without testing the stationarity assumption.

read the letter

This paper runs fractal analysis on earthquake magnitudes and epicenters from India over the 2016-2023 period. It computes spectra at different scales and derives probability estimates for future events from the resulting model. The work is a straightforward regional case study using an established method on a new time window and location. If the full text supplies the exact catalog source, the computed spectra values, and basic plots, it could serve as a descriptive reference for that specific dataset and region. That is the main thing it offers. The central claim is that the fractal spectrum yields usable probabilities for future quakes. The problem is that this requires the scaling properties to hold steady outside the fitting period. Seismic catalogs routinely violate that through aftershock clustering, magnitude incompleteness, and tectonic shifts. The abstract and available description show no temporal split, no out-of-sample check, and no comparison to a baseline like the Gutenberg-Richter law. Without those steps the output reduces to a fitted description of the input data rather than an independent estimate. No equations, error estimates, or validation details appear in the summary, which makes it difficult to assess the implementation even if the full text adds them. This kind of paper might interest local seismologists or students who want an example of fractal methods applied to Indian records. It does not introduce new techniques, resolve open questions in earthquake physics, or supply reproducible predictive tools. I would not bring it to a reading group or cite it. It does not merit sending to peer review because the probability estimates rest on an untested and likely false assumption about stationarity.

Referee Report

2 major / 2 minor

Summary. The manuscript performs fractal analysis on seismic data from India covering 04-10-2016 to 31-05-2023. It applies fractal statistics to earthquake magnitudes and epicenters across scales to extract patterns via the fractal spectrum and uses the resulting model to estimate probabilities of future earthquakes of different magnitudes.

Significance. If the central claim holds, the work would demonstrate that a fractal spectrum fitted to recent Indian seismicity can be extrapolated to assign future magnitude probabilities, offering a multi-scale alternative to conventional empirical laws such as Gutenberg-Richter for regional hazard assessment.

major comments (2)

[Abstract] Abstract: the claim that 'the probabilities of future earthquakes with different magnitudes were estimated using the fractal model' supplies no equations, parameter definitions, fitting procedure, or mapping from spectrum to probability, leaving the central result without visible derivation or support.
[Abstract] Abstract and implied results: the fractal spectrum is obtained from the identical 2016-2023 catalog used for the probability estimates, yet no temporal cross-validation, hold-out testing, or stationarity check (e.g., split-period comparison or aftershock removal) is described; this renders the extrapolation circular and untested against known violations of stationarity in seismic catalogs.

minor comments (2)

[Abstract] Abstract: the opening sentence is grammatically incomplete ('Natural disaster strikes at any given moment from seemingly out of nowhere Akin to earthquake...') and should be rephrased for readability.
[Abstract] Abstract: no earthquake catalog source, magnitude completeness threshold, or spatial bounds are stated, which prevents reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which help improve the clarity and rigor of our work. We address each major comment point by point below and indicate the corresponding revisions planned for the manuscript.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that 'the probabilities of future earthquakes with different magnitudes were estimated using the fractal model' supplies no equations, parameter definitions, fitting procedure, or mapping from spectrum to probability, leaving the central result without visible derivation or support.

Authors: We agree that the abstract is overly concise and does not convey the methodological details. The manuscript computes the fractal spectrum via the box-counting algorithm applied separately to magnitude sequences and epicenter distributions, yielding parameters such as the generalized fractal dimensions D_q and the spectrum width. Probability estimates are obtained by fitting a cumulative distribution derived from the spectrum to the observed magnitude-frequency relation and extrapolating beyond the catalog range. In the revised version we will expand the abstract to include a brief statement of the fitting procedure, key parameters, and the explicit mapping from spectrum to magnitude probabilities, while retaining the full derivations in the Methods section. revision: yes
Referee: [Abstract] Abstract and implied results: the fractal spectrum is obtained from the identical 2016-2023 catalog used for the probability estimates, yet no temporal cross-validation, hold-out testing, or stationarity check (e.g., split-period comparison or aftershock removal) is described; this renders the extrapolation circular and untested against known violations of stationarity in seismic catalogs.

Authors: We acknowledge that the absence of explicit validation steps leaves the extrapolation vulnerable to criticism. The original analysis assumes statistical stationarity over the full interval. To address this directly, the revised manuscript will add a dedicated validation subsection that (i) splits the catalog at 2020, recomputes the fractal spectrum on the 2016–2019 subset, and compares the resulting magnitude probabilities against the observed 2020–2023 events; (ii) applies a standard declustering algorithm to remove aftershocks and reports the change in spectrum parameters; and (iii) discusses the implications of any detected non-stationarity for the probability estimates. These additions will provide a basic temporal cross-check without altering the core fractal-analysis framework. revision: yes

Circularity Check

1 steps flagged

Future earthquake probabilities derived directly from fractal model fitted to 2016-2023 catalog

specific steps

fitted input called prediction [Abstract]
"The probabilities of future earthquakes with different magnitudes were estimated using the fractal model."

The fractal spectrum and model are obtained by analyzing the 2016-2023 earthquake magnitudes and epicenters; the future probabilities are then computed directly from this fitted model, making the estimates a statistical output of the input data fit rather than an independent forecast.

full rationale

The paper's central claim estimates future earthquake probabilities via a fractal model whose parameters and spectrum are obtained from the identical 2016-2023 seismic catalog. This matches the fitted-input-called-prediction pattern: the output probabilities are computed as a direct function of the fitted fractal quantities, with no reported out-of-sample validation, temporal cross-validation, or stationarity test to establish independence from the input data. The derivation therefore reduces the claimed predictions to an in-sample extrapolation of the fitted model.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that seismic activity follows fractal scaling and on parameters fitted to the specific dataset to generate probability estimates.

free parameters (1)

fractal spectrum parameters
Values that define the fractal spectrum at different scales, determined from the earthquake magnitude and epicenter data to identify patterns.

axioms (1)

domain assumption Seismic magnitudes and epicenters exhibit self-similar fractal properties across scales
Invoked to justify applying fractal statistics and spectrum analysis to the data.

pith-pipeline@v0.9.0 · 5380 in / 1246 out tokens · 61140 ms · 2026-05-08T04:59:58.508171+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

2 extracted references

[1]

! And, 𝑃(𝑋&<𝑋<𝑋&') = 𝐹%!

METHODOLOGY: 3.1 Dataset Description: The earthquake dataset used in this study was sourced from the National Centre for Seismology (NCS), a government institution in India, and covers seismic events in India between October 4, 2016, and May 31, 2023. The dataset provides detailed records of earthquake occurrences. Web Link - Data Portal | Official websit...

2016
[2]

A fractal approach to the clustering of earthquakes: applications to the seismicity of the New Hebrides

DISCUSSION: Comparison and Insights: The comparison between the mono-fractal and multifractal models of earthquake magnitudes in India reveals significant insights. The mono-fractal model tends to overestimate the probabilities for lower magnitudes and may not fully capture the complexity of seismic data at larger scales. In contrast, the multifractal mod...

1987