Least-squares Inversion Research Articles

Least-squares decomposition with time–space constraint for denoising microseismic data

SUMMARY Microseismic data are usually of low signal-to-noise ratio (SNR), which makes it difficult to utilize the microseismic waveforms for imaging and inversion. We develop a useful denoising algorithm based on a non-stationary least-squares decomposition model to enhance the quality of microseismic signals. The microseismic signals are assumed to be represented by a superposition of several smoothly variable components. We construct a least-squares inverse problem to solve for the the smooth components. We constrain the least-squares inversion via both time and space constraints. The temporal smoothness constraint is applied to ensure the stability when calculating the non-stationary autoregression coefficients. The space-smoothness constraint is applied to extract the spatial correlation among multichannel microseismic traces. The new algorithm is validated via several synthetic and real microseismic data and are proved to be effective. Comparison with the state-of-the-art algorithms demonstrates that the proposed method is more powerful in suppressing random noise of a wide range of levels than its competing methods.

CHEMOMETRICS ASSISTED SPECTROSCOPIC METHOD DEVELOPMENT AND VALIDATION FOR SIMULTANEOUS DETERMINATION OF SOFOSBUVIR AND DACLATASVIR DIHYDROCHLORIDE IN TABLET FORMULATION

Four chemometric methods, namely Classical Least Square (CLS), Inverse Least Square (ILS), Partial Least Square (PLS) and Principal Component Regression (PCR), were developed for the simultaneous estimation of sofosbuvir and daclatasvir dihydrochloride in tablet formulation. Full factorial design was used to construct calibration set as well as validation set. Twenty five mixed solutions were prepared for calibration set and sixteen mixed solution of drugs were prepared for validation set. The absorbance of all prepared solutions was measured in the range of 230 nm to 335 nm at 16 wavelength points at an interval of 7 nm. Linearity was observed in the range of 10 – 90 µg/mL for sofosbuvir and 4 - 20 µg/mL for daclatasvir dihydrochloride. The developed chemometric methods were validated in terms of precision and accuracy as per ICH guidelines. The developed methods can be applied for the routine quantitative analysis of formulation.

QUake-MD: Open-Source Code to Quantify Uncertainties in Magnitude–Depth Estimates of Earthquakes from Macroseismic Intensities

AbstractThis article presents a tool to quantify uncertainties in magnitude–depth (M-H) estimates for earthquakes associated with macroseismic intensity data. The tool is an open-source code written in Python and is named quantifying uncertainties in earthquakes’ magnitude and depth (QUake-MD). In QUake-MD, uncertainties are propagated from the individual intensity data point (IDP) to the final magnitude (M), depth (H), epicentral intensity (I0) solution. It also accounts for epistemic uncertainties associated with the use of different intensity prediction equations (IPEs). For each IPE, QUake-MD performs a sequential least-square inversion process to estimate the central M, H value. QUake-MD then explores the uncertainties around this central M, H solution by constructing a probability density function (PDF) constrained to be consistent with the range of plausible epicentral intensity I0, a plausible depth range, and IDP uncertainties. The resulting PDFs of all IPEs provided to QUake-MD are then stacked to obtain a final PDF of possible M, H, I0 solutions representative of both data quality and IPE epistemic uncertainties. This tool is geared toward end users who would like to grasp a more complete understanding of the uncertainties associated with historical earthquake parameters beyond the classical standard deviation values proposed today in parametric earthquake catalogs. We apply QUake-MD to two events of the SisFrance macroseismic database to illustrate the challenges involved in building realistic spaces of M, H, I0 solutions reflecting the quality of the data and the epistemic uncertainties in IPEs.

Nonlinear inversion of seismic amplitude variation with offset for an effective stress parameter

Effective stress estimates play important roles in reservoir characterization, for instance, in guiding the selection of fracturing areas in unconventional reservoirs. Based on Gassmann’s fluid substitution model, we have set up a workflow for nonlinear inversion of seismic data for dry rock moduli, fluid factors, and a stress-sensitive parameter. We first make an approximation within the fluid substitution equation, replacing the porosity term with a stress-sensitive parameter. We then derive a linearized reflection coefficient as a function of a stress-parameter reflectivity and reexpress it in terms of elastic impedance (EI). An amplitude-variation-with-offset (AVO) inversion workflow is set up, in which the seismic data are transformed to EI, after stacking within five incidence angle ranges; these are then inverted to determine the stress-sensitive parameter. The two-step process involves two inversions with significantly different properties. The first is a model-based least-squares inversion to estimate EI; the second is a more complex nonlinear inversion of the EI for a set of unknowns including the stress-sensitive parameter. Motivated by an interest in hybridizing AVO and full-waveform inversion (FWI), we set the latter step up to resemble some features of a published AVO-FWI formulation. The approach is subjected to synthetic validation, which permits us to analyze the response and test the stability of the workflow. We finally apply the workflow to real data acquired over a gas-bearing reservoir, which reveals that the approach generates potential indicators of fluid presence and stress prediction.

Using the Schlumberger configuration resistivity geoelectric method to analyze the characteristics of slip surface at Solok

Landslides are the frequent disaster in the wavy topography zone, such as Sungai Lasi Solok. Landslide disaster was difficult to predict. Based on these conditions, we need to do the research. The aims of the research were to find out the characteristic of landslide slip surface at Sungai Lasi Solok base on Geoelectric Data. Data were collected by Automatic Resistivity Multi-electrode using Resistivity Geoelectric Method with Schlumberger configuration. The interpretation of the Geoelectric data was used Two Dimensions Least-Square Inversion Method. Characteristics of the landslide such as were estimated by Trigonometry theory in order to get both the angle and the depth of landslide slip surface. The results of the research are both the angle and the depth of the slip surface is 40 degrees and 14 meters.

A Multi-Observation Least-Squares Inversion for GNSS-Acoustic Seafloor Positioning

Monitoring deformation on the seafloor is a major challenge for modern geodesy and a key to better understanding tectonic processes and assess related hazards. The extension of the geodetic networks offshore can be achieved by combining satellite positioning (GNSS) of a surface platform with acoustic ranging to seafloor transponders. This approach is called GNSS-Acoustic (GNSS-A). The scope of this work is to provide a tool to identify and quantify key points in the error budget of such experiment. For this purpose, we present a least-squares inversion method to determine the absolute position of a seafloor transponder array. Assuming the surface platform is accurately positioned by GNSS, the main observables are the two-way travel time in water between the transponders on the seafloor and the surface platform acoustic head. To better constrain transponder positions, we also consider the baseline lengths and the relative depth-differences between different pairs of them. We illustrate the usefulness of our forward modeling approach and least-square inversion by simulating different experimental protocols (i.e., platform trajectories, with or without information on the distance and depth between transponders). We find that the overall accuracy of a GNSS-A experiment is significantly improved with additional information about the relative depths of the instruments. Baseline lengths also improve the accuracy, but only when combined with depth differences. The codes in Python3 used in this article are freely available online.

Matrix-fluid-fracture decoupled-based elastic impedance variation with angle and azimuth inversion for fluid modulus and fracture weaknesses

The ratio of normal-to-shear fracture compliances, approximate to the product of two ratios of shear-to-compressional (S-to-P) wave velocity and normal-to-tangential fracture weakness, has been treated as an indicator of fluid content for an oil-bearing reservoir with aligned fractures. However, this indicator depends on both fluid saturation and fracturing strength of rocks, while the effective fluid bulk modulus as a sensitive indicator decouples the double effects of rock porosity and pore fluid. Moreover, an incorrect value of S- and P-wave velocity ratio may have a significant effect on the estimation of normal-to-shear fracture compliances. Based on the anisotropic poroelasticity amplitude variation with offset and azimuth (AVOAz) theory, we use the Born formalism and a first-order perturbation assumption to derive a matrix-fluid-fracture decoupled-based linearized PP-wave reflection coefficient in an oil-bearing fractured porous medium. Our derived formula reveals that the combined effects of background matrix, pore fluids and fracture strength on seismic amplitudes are separated, more applicable to implement the fluid identification and fracture detection in a liquid-filled porous reservoir with aligned fractures. Following a Bayesian framework, we develop a Bayesian inversion method to reasonably obtain the fluid modulus and saturated fracture weaknesses. The implementation methodology includes two steps: a model-based least-squares inversion for azimuthal elastic impedances and an iterative Bayesian seismic inversion for model parameters. Tests on synthetic data corrupted with moderate random noise indicate that these model parameters can be estimated reasonably and accurately when the oil-saturated rock is permeated with a single fracture system. Test on a real data set validates that the reliable estimates of fluid and fracture parameters can be used to realize the fluid identification and fracture detection in an oil-bearing fractured porous reservoir in a more direct manner than previous approach.

A Comparative Study of Inversion Optimization Algorithms for Underground Metal Target Detection

Underground metal target detection refers to estimating the properties of underground metal targets based on a set of observed data. Electromagnetic induction (EMI) method and the least-squares inversion provide the data acquisition method and the parameter estimation method for the detection, respectively. As an important part of least-squares inversion, optimization algorithms directly affect the efficiency of the least-squares inversion. To improve the efficiency of underground metal target detection, it is necessary to compare the performance of different optimization algorithms. In this paper, we analyzed the characteristic of the complex EMI forward model using sensitivity analysis and inverse sensitivity analysis at first. Then, the EMI forward model and least squares were used to build the objective function. The estimation error, run time and number of iterations of six numerical optimization algorithms were compared under different signal-to-noise ratios (SNRs) and under different data acquisition spacing. The algorithms include gradient descent, steepest descent, Newton's method, Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, conjugate gradient method and Levenberg-Marquardt (LM) algorithm. A simulation platform was established to generate observed data and compare the optimization algorithms. The results of algorithm comparison showed that the BFGS, conjugate gradient and LM algorithm can efficiently and accurately estimate the properties of underground metal targets and the LM algorithm has the shortest run time and the least number of iterations. Finally, we carefully analyzed the time consumption of each optimization algorithm. The results show that the calculation of the gradient and step length selection greatly affect the efficiency of the optimization algorithms.

Monitoring of velocity changes based on seismic ambient noise: A brief review and perspective

Over the past two decades, the development of the ambient noise cross-correlation technology has spawned the exploration of underground structures. In addition, ambient noise-based monitoring has emerged because of the feasibility of reconstructing the continuous Green’s functions. Investigating the physical properties of a subsurface medium by tracking changes in seismic wave velocity that do not depend on the occurrence of earthquakes or the continuity of artificial sources dramatically increases the possibility of researching the evolution of crustal deformation. In this article, we outline some state-of-the-art techniques for noise-based monitoring, including moving-window cross-spectral analysis, the stretching method, dynamic time wrapping, wavelet cross-spectrum analysis, and a combination of these measurement methods, with either a Bayesian least-squares inversion or the Bayesian Markov chain Monte Carlo method. We briefly state the principles underlying the different methods and their pros and cons. By elaborating on some typical noise-based monitoring applications, we show how this technique can be widely applied in different scenarios and adapted to multiples scales. We list classical applications, such as following earthquake-related co- and postseismic velocity changes, forecasting volcanic eruptions, and tracking external environmental forcing-generated transient changes. By monitoring cases having different targets at different scales, we point out the applicability of this technology for disaster prediction and early warning of small-scale reservoirs, landslides, and so forth. Finally, we conclude with some possible developments of noise-based monitoring at present and summarize some prospective research directions. To improve the temporal and spatial resolution of passive-source noise monitoring, we propose integrating different methods and seismic sources. Further interdisciplinary collaboration is indispensable for comprehensively interpreting the observed changes.

Gaussian process models—II. Lessons for discrete inversion

Summary By starting from a general framework for probabilistic continuous inversion (developed in Part I) and introducing discrete basis functions, we obtain the well-known algorithms for probabilistic least-squares inversion set out by Tarantola & Valette (1982). In doing so, we establish a direct equivalence between the spatial covariance function that must be specified in continuous inversion, and the combination of basis functions and prior covariance matrix that must be chosen for discretised inversion. We show that the common choice of Tikhonov regularisation ($\mathbf {C_m^{-1}} = \sigma ^2\mathbf {I}$) arises from a delta-function spatial covariance, and that this lies behind many of the artefacts commonly associated with discretised inversion. We show that other choices of spatial covariance function can be used to generate regularisation matrices yielding substantially better results, and permitting localisation of features even if global basis functions are employed. We are also able to offer a straightforward explanation for the spectral leakage problem identified by Trampert & Snieder (1996).

2D least-squares elastic reverse time migration of multicomponent seismic data

Elastic reverse time migration (ERTM) is a state-of-the-art imaging technique used for determining complicated subsurface structures. However, the migrated images often suffer from low spatial resolution, low signal-to-noise ratio (S/N), and unbalanced amplitudes because the theoretical hypothesis of ERTM cannot be satisfied in practice. Although elastic least-squares reverse time migration (ELSRTM) has been proposed to address the issues of ERTM, the resulting images are generally represented by parameter perturbations such as P- and S-velocity perturbations, which have the different physical meanings from the ERTM images. To produce improved ERTM images, we used a least-squares RTM method for elastic data in isotropic media by applying least-squares inversion to ERTM. In the least-squares ERTM method, the forward operator generates multicomponent seismic data from the migrated images by applying elastic wavefield decomposition, scalar wavefield extrapolation, and wavefield recomposition operators. Additionally, the adjoint operator generates PP and PS images using ERTM, at which point the wavefield decomposition operator and scalar imaging condition are applied in the imaging process. Compared to conventional ERTM, our least-squares ERTM method enables us to produce improved ERTM images with higher resolution, more balanced amplitudes, and fewer artifacts. Several synthetic and field data examples were used to validate the effectiveness of the proposed least-squares ERTM method.

Nonlinear creep model and parameter identification of mudstone based on a modified fractional viscous body

To study the evident nonlinear creep characteristics of mudstone, the creep process of rock is regarded as the superposition of linear and nonlinear creep processes. Using an element combination model for reference, we introduce the mechanical element (FC) with a fractional derivative based on fractional calculus theory. Compared with the Newtonian element, the FC can react more effectively to the nonlinear gradual process of rheological problems. The variable viscosity coefficient FC element with fractional calculus is connected to both Kelvin and spring elements in series instead of a Newton body element. In addition, considering the effects of load level and time damage variables, a five-element nonlinear creep damage model is proposed that can simulate the entire process of mudstone creep, particularly the accelerated creep phase of mudstone, and both constitutive and creep equations of the model can be derived. Based on the creep model’s use of multiple parameters under graded loading, this study employs a modified particle swarm optimization algorithm with a genetic crossover factor and least-square method joint inversion algorithm. Using creep experimental data of mudstone, this study identifies the parameters for the proposed five-element fractional creep damage model and derives reasonable parameter values. A parameter sensitivity analysis of the constitutive model is also conducted. The results show that the size of the stress loading level $$ \sigma $$ determines the length of the stable creep phase of the mudstone and the time to enter the accelerated creep phase. The derivative order $$ \gamma $$ becomes a direct influence factor on the rock creep rate.

Characterization of acoustic attenuation in a coral reef environment

Coral reefs are complicated and understudied acoustic propagation environments. In addition to geometric spreading, there are propagation losses due to bottom attenuation, volumetric scattering, and boundary scattering from bathymetric variability and sea surface roughness. On a Hawaiian coral reef, a field test was performed in shallow water during which low-level tones were projected from an underwater speaker and received by a single hydrophone at various ranges up to 500 m from the source. Acoustic data gathered during the field test were analyzed to characterize the sound propagation environment. Conventional geometric spreading assumptions were challenged for the sloping bathymetry characteristic of the Hawaiian coral reef environment. Geoacoustic parameters of the coral reef environment were extracted from transmission loss measurements using a nonlinear least-squares inversion. Losses were estimated for frequencies of 500 Hz, 2 kHz, 5 kHz, 10 kHz, and 15 kHz.Coral reefs are complicated and understudied acoustic propagation environments. In addition to geometric spreading, there are propagation losses due to bottom attenuation, volumetric scattering, and boundary scattering from bathymetric variability and sea surface roughness. On a Hawaiian coral reef, a field test was performed in shallow water during which low-level tones were projected from an underwater speaker and received by a single hydrophone at various ranges up to 500 m from the source. Acoustic data gathered during the field test were analyzed to characterize the sound propagation environment. Conventional geometric spreading assumptions were challenged for the sloping bathymetry characteristic of the Hawaiian coral reef environment. Geoacoustic parameters of the coral reef environment were extracted from transmission loss measurements using a nonlinear least-squares inversion. Losses were estimated for frequencies of 500 Hz, 2 kHz, 5 kHz, 10 kHz, and 15 kHz.

A physically constrained inversion for high-resolution passive microwave retrieval of soil moisture and vegetation water content in L-band

Remote sensing of soil moisture and vegetation water content from space often requires inversion of a zeroth-order approximation of the forward radiative transfer equation in L-band, known as the τ-ω model. This paper shows that the least-squares inversion of the model is not strictly convex and the widely used unconstrained damped least-squares (DLS) can lead to biased retrievals, due to preferential descending paths. In particular, the numerical experiments show that for sparse (dense) vegetation with a low (high) opacity, the DLS tends to overestimate (underestimate) the soil moisture and vegetation water content when the soil is dry (wet). A new Constrained Multi-Channel Algorithm (CMCA) is proposed that confines the retrievals with a priori information about the soil type and vegetation density and accounts for slow temporal changes of the vegetation water content through a smoothing-norm regularization. It is demonstrated that depending on the resolution of the constraints, the algorithm can lead to high-resolution soil moisture retrievals beyond the radiometric spatial resolution. Controlled numerical experiments are conducted and the results are validated against ground-based gauge observations using the passive microwave observations by the Soil Moisture Active Passive (SMAP) Satellite.

Nonlinear inversion for magnetotelluric sounding based on deep belief network

To improve magnetotelluric (MT) nonlinear inversion accuracy and stabilitythis work introduces the deep belief network (DBN) algorithm. Firstlya network frame is set up for training in different 2D MT models. The network inputs are the apparent resistivities of known modelsand the outputs are the model parameters. The optimal network structure is achieved by determining the numbers of hidden layers and network nodes. Secondlythe learning process of the DBN is implemented to obtain the optimal solution of network connection weights for known geoelectric models. Finallythe trained DBN is verified through inversion testsin which the network inputs are the apparent resistivities of unknown modelsand the outputs are the corresponding model parameters. The experiment results show that the DBN can make full use of the global searching capability of the restricted Boltzmann machine (RBM) unsupervised learning and the local optimization of the back propagation (BP) neural network supervised learning. Comparing to the traditional neural network inversionthe calculation accuracy and stability of the DBN for MT data inversion are improved significantly. And the tests on synthetic data reveal that this method can be applied to MT data inversion and achieve good results compared with the least-square regularization inversion.

Full-waveform inversion of salt models using shape optimization and simulated annealing

A good starting model is imperative in full-waveform inversion (FWI) because it solves a least-squares inversion problem using a local gradient-based optimization method. A suboptimal starting model can result in cycle skipping leading to poor convergence and incorrect estimation of subsurface properties. This problem is especially crucial for salt models because the strong velocity contrasts create substantial time shifts in the modeled seismogram. Incorrect estimation of salt bodies leads to velocity inaccuracies in the sediments because the least-squares gradient aims to reduce traveltime differences without considering the sharp velocity jump between sediments and salt. We have developed a technique to estimate velocity models containing salt bodies using a combination of global and local optimization techniques. To stabilize the global optimization algorithm and keep it computationally tractable, we reduce the number of model parameters by using sparse parameterization formulations. The sparse formulation represents sediments using a set of interfaces and velocities across them, whereas a set of ellipses represents the salt body. We use very fast simulated annealing (VFSA) to minimize the misfit between the observed and synthetic data and estimate an optimal model in the sparsely parameterized space. The VFSA inverted model is then used as a starting model in FWI in which the sediments and salt body are updated in the least-squares sense. We partition model updates into sediment and salt updates in which the sediments are updated like conventional FWI, whereas the shape of the salt is updated by taking the zero crossing of an evolving level set surface. Our algorithm is tested on two 2D synthetic salt models, namely, the Sigsbee 2A model and a modified SEG Advanced Modeling Program (SEAM) Phase I model while fixing the top of the salt. We determine the efficiency of the VFSA inversion and imaging improvements from the level set FWI approach and evaluate a few sources of uncertainty in the estimation of salt shapes.

3-D attenuation tomography from microseismicity in a mine

SUMMARYWe perform 3-D attenuation tomography using microseismic data recorded during an underground mine development. The whole path attenuation parameter t* is obtained by least-squares inversion of P-wave amplitude spectra of the events recorded by 7 monitoring wells each containing 4 3C geophones. The corner frequencies obtained during P-wave spectral inversion of the 488 identified events range from 140 to 220 Hz which are typical for microseismic events with a negative moment magnitude of around –1. The quality factor Q obtained from tomographic inversion varies between 9 and 72 with the event cluster location characterized by a low Q value of 10. Two high Q regions of 30–72 are located at depths of 0.45 and 0.5 km, one between 0–0.15 km east and 0.3–0.5 km north which correlate with the high-grade ore deposit, and another centred around 0.45 km east and 0.25 km north. The high (-low) Q values, in general, correlates with the high (-low) velocities present in the velocity tomography model. A joint interpretation of seismic attenuation and velocity models reveals the heterogeneity present in the mine which aids in delineating the ore body using seismic waves in addition to other measurements such as gravity inversion and direct sampling from drillholes.

A perturbed ghost model for estimating air-gun array signatures

Source designature for seismic data acquired using an air-gun array aims to remove the effects of pulse asymmetry, bubble oscillation, array directivity, and ghosting at the sea surface. For the process to be successful, we require an accurate representation of the source signature in the far field over the full data bandwidth. The well-established approach to this problem is to derive signatures from hydrophone data recorded in the near field of the source array. We perform a least-squares inversion of the near-field data, using a representation of the physics of propagation within the vicinity of the array, according to the measured geometry and incorporating bubble motion and source ghost formation. While ghost formation is typically treated using a simple linear model of propagation and reflection at the sea surface, observations suggest that this may be too simplistic. For example, ghost amplitudes are often found to be lower than expected, and features indicative of acoustically induced cavitation are observed. Hence there is interest in developing approaches that allow us to solve for the ghost directly using additional measurements made in the near field. We present an approach that builds on the standard method of inverting for notional sources and that seeks to take account of nonlinear perturbations to the downgoing wavefield, including attenuation of the ghost. Perturbation of the ghost is described using a series of virtual notional sources situated in the water column between the guns and the sea surface. This is found to provide a more accurate treatment of the ghost and does not require optimization of model parameters as is often necessary in practice with the standard approach. It is also found that the inversion is more stable than an alternative parameter-free approach that solves directly for real and mirror virtual notional sources. The improved performance and stability are demonstrated with a field data example.

Noise Reduction for Transient Electromagnetic with High Cultural Noise: Case Study in Cisarua, Bandung Barat Regency

Transient Electromagnetic data acquisition was conducted in Cisarua, Bandung Barat Regency. Data are acquired using grounded dipole transmitter 500 meter spaced, with 13 A of current injected. TEM period are 40 s with 102 measurement period in total. Magnetic impedance sensor as receiver measured vertical magnetic field, located 400 meter from transmitter center point. The measurement area was located in a residential area and very close to man-made electromagnetic noise sources including power lines, radio and cellular transmitters. Periodic noise recorded along with transient signal was very strong, where the amplitude of 50 Hz noise is higher than the transient signal even at early time. This poses a challenge where a technique that capable of reducing noise and reconstructing the transient data are needed, so the data can further be processed in inversion program to create subsurface model. First technique used was statistical selection which is simple but proven effective in reducing noise in this condition without distorting the data. Data processing then continued by applying digital notch filter. After the transient signal are obtained, smoothness constrained least-square inversion are used to get the subsurface resistivity model, which shows 2 low resistivity zone. The shallower zone was supported by Electrical Resistivity Tomography data, and interpreted as shallow unconfined aquifer. The deeper zone was taught to be old volcanic products saturated with water associated with fault in the eastern area.

Effect of Unemployment Rate on Growth Rate of Gross Domestic Product of Jordan

This study explains the effect of unemployment rate on growth rate of GDP of Jordan by depending on yearly data for the period (2009 – 2016) as unemployment rate is independent variable, and growth rate of GDP (Avariable of economic growth) as a dependent variable. This study focuses on explaining the literature both in theoretical and empirical ways of the effect of unemployment rate on growth rate of GDP, and analyzing the effect of unemployment rate on growth rate of GDP of Jordan by depending on yearly data for the period (2009 – 2016) by using the technique of ordinary least squares in version of E-views. This paper found that there are insignificant impacts of unemployment percentage to total labor force, unemployment of males percentage to male labor force, unemployment of females percentage to female labor force on growth rate of GDP of Jordan by relying on yearly data for the period 2009 to 2016 at level of significance 5%. This paper recommends testing the impacts of other obstacles in Jordan on growth rate on GDP, in order to know the variables that effect growth rate of GDP in Jordan.