1 Introduction

    In Central and Eastern Unites states, the New Madrid area becomes the most seismically active region due to the area covered by Tertiary and Cretaceous sedimentary rocks with unconsolidated Quaternary sediments \cite{Braile_1986,Braile_1982}. So, the potential-field geophysics has played a major role in interpreting the geologic framework of the Mississippi Embayment region. Potential- field studies have revealed the ancient rift system and buried plutons as a major factor of the distribution of seismicity \cite{Csontos_2008}. One of the few studies in the Mississippi Embayment area has focused on the detailed gravity and ground-magnetic data that collected over the Reelfoot scrap to investigate the small- amplitude, short-wavelength anomalies that caused by shallow sources \cite{langenheim1995}.
    Several detailed gravity profiles in the Reelfoot graben reveal unexpected local variation in gravity values and distinguish small-amplitude anomalies characterized by sudden changes in gradient \cite{langenheim1995}. They suggest these anomalies may be caused by either shallow igneous intrusions (where the anomalies correlate with small gravity anomalies) or post-unconformity faulting. They have filtered the gravity data to improve short-wavelength features reveal the locations of density contrasts that correspond to observed subsurface faults cutting the Cretaceous unconformity \cite{Braile_1986,langenheim1995}.
    There were several plutons discovered using both gravity and magnetic surveys; Bloomfield, Paragould, Malden, and Covington are few of them located in the North Mississippi Embayment and surrounding regions \cite{langenheim1995}. The Covington Pluton is one of the most pronounced plutonic masses seen in potential studies in the New Madrid seismic region which located at 35035’N and 89035’W (fig.1)\cite{Ravat_1987}. Based on the location of hypocenters and earthquake focal mechanisms, there is no evidence that stress concentration correlated with the mass excess of the pluton is the cause of seismicity near the pluton. The seismicity is probably along zones of weakness independent of the pluton \cite{langenheim1995}. The Covington pluton is widespread more than 50 km wide, slightly blocky high on the unfiltered gravity. On the filtered gravity maps, this broad high part divided into two to three isolated anomalies; the central high most closely follows the gravity anomaly of the Covington pluton, a tiny anomaly extended in both east-west and northeast-southwest directions \cite{Ravat_1987,langenheim1995}
    One such anomaly has been drilled: a well near the Covington pluton in southwestern Tennessee confronted nepheline syenite directly beneath Upper Cretaceous sedimentary rocks. The age of the pluton has claimed as post-Ordovician and pre-Late Cretaceous and depth estimated as shallower as 2 to 4km deep along with a width of 40 to 50 km \cite{langenheim1995}. Due to the presence of the pluton in such shallow depth, there is a mass excess in the Covington area that gives a positive gravity anomaly. This study is mainly focused on determining the accurate source depth and the density contrast of the Covington pluton region using Bouguer gravity anomaly data. To estimate accurate parameters, three Nonlinear inversion methods; Newton’s method, Monte Carlo method, and Simulated Annealing method has used with the support of a forward model and other required geological parameters.