Introducing Novel Correction Methods to Calculate Sedimentary Basin Overpressure and Its Application in Predicting Pressure Value and Origin

Abstract

Overpressure is an important phenomenon observed in sedimentary basins. To enhance the precision of identifying the origin of overpressure and predicting it accurately, this paper presents four practical methods for analyzing formation overpressure, taking into account various factors, such as burial history, rock properties, mechanical models and data quality. By illustrating the application examples in typical basins, this paper demonstrates the practicality and potential of each model. Based on the analysis of organic matter content and denudation, our understanding of the origin of overpressure in the first member of the Cretaceous Qingshankou Formation in Songliao Basin has been revised. A novel model based on the static equilibrium equation was established, which not only demonstrates theoretical rationality but also exhibits practical advantages in the Junggar Basin and Southeast Hainan Basin. The incorporation of lateral loading in the correction model and the utilization of colored inversion in seismic velocity processing model have significantly enhanced pressure prediction accuracy in Junggar Basin and Southeast Hainan Basin, respectively. In conclusion, these correction models demonstrate a high level of reliability and possess significant potential for widespread adoption.

1. Introduction

The distribution of subsurface fluids is closely related to overpressure, which exists in most sedimentary basins [1]. Therefore, it is necessary to accurately predict the distribution of underground pressure for proper and systematic exploration and development of hydrocarbon resources [2,3,4]. With the recent advances in seismic and logging technologies as well as developments in the geophysics discipline, several predictive models for overpressure origin identification and quantification methods have been developed over the years. To identify the origin of overpressure, many methods have been developed based on the abnormal response of a series of geophysical parameters at the location of overpressure. Zhao et al. (2017) categorized these methods into six types [5]: the well logging curve combination analysis method [6,7,8], loading–unloading curve method [8], sonic velocity and density cross plot method [9,10,11], porosity comparison method [7,12,13], calculation result analysis method [14] and comprehensive analysis method [5,15]. In addition, several methods have been developed to quantitatively predict the amount of overpressure [16], such as the equivalent depth method [17], Eaton method [18], Bowers method [19,20], Fillippone method [21] and Liu method [22]. These models are divided into two categories: the first group relies on the empirical relationship between sonic velocity and pressure, and the second group includes the relationship between actual sonic velocity and the normal compaction trend (NCT).

Combining these methods could result in good accuracy when it comes to the determination of the origin as well as the magnitude of the formation overpressure [15,23,24,25,26]. However, the quality of the input data and complexity of the geological setting can lead to abnormal results. For instance, some overpressure analysis methods rely on the NCTs, requiring that correct compaction trends be established. In these cases, the complex burial processes greatly affect the results. In addition, some common overpressure analysis methods depend on sonic velocity. As the response characteristics of sonic velocity are not controlled by a single factor [27,28,29], it is necessary to eliminate other factors that have a significant influence on it. Moreover, the quality of geophysical data, especially seismic data, often does not meet the requirements of overpressure analysis methods [30]; therefore, it is necessary to combine logging data for systematic error correction. Furthermore, most overpressure analysis methods are based on the Terzaghi model [16,31], but whether a model that was originally applied in soil mechanics can be incorporated into deep geologic bodies has yet to be further studied.

In this paper, four common and practical correction methods were introduced to identify the origin and quantify formation overpressure based on a series of parameters including burial process, rock properties, mechanical model and data quality. These methods were applied for several fields in China. Finally, some suggestions for how to improve the predictive performance of these correction models are provided.

2. Research Methods

2.1. Basic Concepts and Overpressure Analysis Methods

In this section, the concept of “formation overpressure” and methods to calculate it are described.

2.1.1. Effective Stress and Static Equilibrium Equation

The term “effective stress” was originally used in soil mechanics to denote the contact stress (or support stress) between soil particles. Terzaghi (1923) proposed the concept of effective stress based on research on the mechanical characteristics of water-saturated soil [31], assuming that the effective stress (σ_e) is equal to the difference between the overburden pressure (S) and the pore pressure (P_f):

$${\sigma }_e=S-P_f$$

(1)

Due to the excessive number of symbols, it is noted that all symbols are explicated in the appendix located at the end of this paper.

Effective stress is a fundamental principle that distinguishes the soil mechanics from other mechanics. Generally, soil is a three-phase system. Water-saturated soil, however, is a two-phase system. After application of the external load, the stress in soil is shared by the soil skeleton as well as the fluid contained in the soil, but only the effective stress transmitted by the soil particles can deform the soil and have shear strength. However, pore pressure transferred by the water and gas contained in the pores does not contribute to the strength and deformation of the soil.

Terzaghi and Peck (1948) explained the compression and drainage processes of water-saturated soil through an experimental study focusing on compaction and consolidation of water-saturated soil [32].

In the closed system shown in Figure 1, when load (S) is applied to the top plate, if water is not drained from the container, the height of the spring remains unchanged. In this stage (Figure 1a), all the load (S) is supported by water pressure (P_f):

$$\left\{\begin{array}{c}S=P_f\\ \alpha =1\end{array}\right.$$

(2)

At the optimum equilibrium condition when load (S) is completely supported by the skeleton (i.e., grains in the reality or spring in the schematic shown in Figure 1), the value of α is 0. However, in the actual process of compaction balance, the effect of load (S) is gradually supported by the skeleton and intergranular water (hydrostatic), and the value of α eventually becomes equal to the vertical pressure gradient, that is, 0.465 (which is equivalent to the vertical pressure gradient in the Gulf of Mexico, approximately 0.465 psi/feet):

$$\left\{\begin{array}{c}S={\sigma }_e+P_f\\ \alpha =0.465\end{array}\right.$$

(3)

When the mass reaches the state of mechanical equilibrium, the relationship among the total stress, fluid pressure and effective stress in Equation (3) is referred to as the “static equilibrium equation”. Most pressure prediction models and origin analysis methods are based on this equation [16].

2.1.2. Methods for Identification of the Overpressure Origin

In the early days, the disequilibrium compaction theory dominated the research on overpressure analysis. With the development of the theory of “loading-unloading”, it was gradually recognized that the contribution of disequilibrium compaction to overpressure is limited. In order to facilitate identification of the overpressure origin, Bowers (2002) summarized the bulk density as the bulk property (BP), and the sonic velocity as the transport property (TP) [8]. According to this study, when the porosity is kept constant and the pore structure is altered, the BPs become unchanged or change minimally while TPs change significantly. Using an experimental approach, Bowers and Katsube (2001) determined that BPs are affected by both the pore and throat, but TPs are mainly affected by the throat [34]. Since the disequilibrium compaction only pauses or slows down the compaction process, its effects on BPs and TPs are consistent because it has little effect on the pore structure. For the overpressure caused by fluid expansion (i.e., hydrocarbon generation), the pressure is generated internally, and its influence on throats and pore redistribution is more obvious; therefore, TPs respond strongly while BPs do not respond at all or respond weakly.

Under the influence of the “loading-unloading” theory, a series of practical methods for overpressure origin analysis have been produced. In this paper, we discuss only three methods: the loading–unloading curve method (LUCM), sonic velocity and density cross plot method (SDCPM), and porosity comparison method (PCM). The LUCM was proposed by Bowers (1995) [19]. In this method, the loading–unloading curve is established according to the relationship between porosity and vertical effective stress. This method has been extensively applied and is widely accepted in the literature. The SDCPM is an improved version of the LUCM, mainly aiming at obtaining the measured pressure. The PCM aims to compare the porosity of the overpressure interval with that of the normal pressure at the same depth to determine the overpressure origin. Zhao et al. (2017) provided a summary comparing various methods to determine overpressure origin and proposed an analysis diagram and table [5] (Figure 2 and

Table 1. Determining overpressure origin using different analysis methods.

	Analysis Method	LUCM	SDCPM	PCM
Overpressure Origin
Disequilibrium Compaction		Abnormal pressure points on the loading curve.	Abnormal pressure points on the loading curve.	The actual porosity is abnormally high. The porosity values calculated by sonic velocity, Neutron and density all show high anomalies.
Fluid Expansion/Pressure Transfer		The effective stress is greatly reduced. The change in sonic velocity is relatively small. Density is not sensitive to unloading.	The sonic velocity decreases with the increase in overpressure. The density stays the same or changes insignificantly.	The actual porosity does not deviate from the NCT. The porosity calculated according to density is almost normal. The porosity calculated according to sonic velocity shows a high anomaly.
Clay Mineral Conversion		Strength of rock particle skeleton becomes weak and the compressibility increases. Load transfer from matrix to fluid. The speed of sound waves slows down. Density may increase. Effective stress is reduced.	The density increases with overpressure. The sonic velocity is not reduced or is reduced slightly.	There are porosity anomalies, but the deviation from the NCT is small.
Tectonic Compression		Tectonic compression is not easy to find without fluid discharge. When some of the fluids are discharged, the overpressure interval is characterized by abnormally low porosity, abnormally low sonic velocity and constant vertical effective stress.	Sonic velocity and density are distributed along the NCT.	Porosity changes along the NCT.

).

2.1.3. Methods to Quantify Overpressure

At present, there are various methods that can be used to predict pore pressure using logging data. In this paper, we discuss two methods, namely the equivalent depth method and the Eaton method. To review details of method derivation/development, the readers are encouraged to review the corresponding papers of Magara (1975) [17] and Eaton (1975) [18]. The common prerequisite to applying either of these two methods is to obtain a reasonable NCT. Under normal compaction, shale porosity decreases exponentially with increasing burial depth. In consolidated strata with uniform distribution of small pores, there is a direct linear relationship between porosity and sonic time difference. Therefore, the sonic time difference and depth are linearly related in the semi-logarithmic coordinate system according to the following formula:

$$ln\Delta t=-C·H+ln\Delta t_0$$

(4)

(1)

Equivalent depth method

The essence of the “equivalent depth method” is the corresponding depth associated with a certain porosity in the NCT. According to Equation (4), the equivalent depth corresponding to a certain sonic time difference (Δt) can be expressed as

$$H_e=-\frac{1}{C}ln\left(\frac{\Delta t}{\Delta t_0}\right)$$

(5)

The effective stress is the same at a certain porosity value. The effective stress corresponding to the sonic time difference (Δt) can be expressed as

$${\sigma }_e=\left({\rho }_r-{\rho }_w\right)g{H}_e=-\frac{1}{C}\left({\rho }_r-{\rho }_w\right)gln\left(\frac{\Delta t}{\Delta t_0}\right)$$

(6)

The equivalent depth method is based on the irreversibility of mudstone compaction; therefore, the model representing the pressure can be expressed as

$$P_f=S-{\sigma }_e={\rho }_{r}gH+\frac{1}{C}\left({\rho }_r-{\rho }_w\right)gln\left(\frac{\Delta t}{\Delta t_0}\right)$$

(7)

(2)

Eaton method

The equivalent depth method is limited in that it can only calculate the overpressure caused by disequilibrium compaction. The equivalent depth method tends to underestimate the pressure due to the low response of some geophysical parameters. The Eaton method makes up for this defect by introducing the exponent n according to the following equation:

$$\left\{\begin{array}{c}{P}_f=P_{ov}-\left(P_{ov}-P_w\right){\left(\frac{\mathsf{\Delta }{t}_n}{\mathsf{\Delta }t}\right)}^n\hfill \\ \mathsf{\Delta }{t}_n=\Delta t_0{e}^{-C·H}\hfill \end{array}\right.$$

(8)

The origin of overpressure can be determined based on the approximate value of exponent n. for instance, the overpressure caused by uneven compaction is obtained at an approximate value of n = 3. An n value of 6.5 indicates that the overpressure is caused by fluid expansion or pressure transfer.

2.2. Correction Methods and Their Principles

2.2.1. Correction for Burial Processes

The burial process has a direct impact on overpressure calculation when a normal compaction trend model is used. Denudation occurs in many areas. The equivalent depth or Eaton methods should be used with caution when the thickness of the newly deposited strata is less than the thickness to be denuded. Due to denudation, the present porosity at one point on the NCT is a result of normal compaction at a greater depth. If it is directly used for calculation without correction, the equivalent effective stress value will be lower than the actual value, which leads to pore pressure overestimation. In order to eliminate this uncertainty, the current NCT should be uniformly moved upward by a total amount of denudation to obtain the NCT at the maximum burial depth (Figure 3). Note that the total denudation, in this case, is the difference between the maximum depth and the present depth, and not the sum of all the denudation. The specific steps to be followed in this case are as follows:

(1)

Determine the current NCT, based on the longitudinal distribution characteristics of the sonic time difference for mudstone in the normal compaction interval;

(2)

Calculate the denudation thickness using the sonic time difference method [35];

(3)

Obtain the historical maximum burial depth of point A in Figure 3a, using denudation thickness calculation;

(4)

Calculate ΔH, which is the difference between the maximum and present burial depths;

(5)

Move the NCT down by ΔH, and obtain the new NCT based on which the porosity values at each depth correspond one-to-one to the effective stress values at each depth in Figure 3c.

2.2.2. Correction for Rock Skeleton Composition

Although the “loading-unloading” theory has been recognized and used by a large number of scholars, obvious anomalies of sonic velocity and density can often be found in the normal pressure interval or the overpressure interval where the pressure is not parallel with the overpressure. Without direct pressure measurement, this phenomenon can be easily interpreted as disequilibrium compaction. However, the abnormality of these geophysical parameters may not be caused by overpressure in most cases. The rock skeleton and pore fluid properties are important causes of these abnormalities.

Taking an organic-rich dark mudstone as an example, it differs from normal mudstone in that the skeleton contains a lot of low-density organic matter. Compared with the normal mudstone interval, the sonic velocity and the bulk density of the source rock interval are smaller. Since pore pressure mainly affects porosity and pore structure, the correction method used to eliminate such effects in the overpressure analysis is mainly aimed at porosity calculation. Specific steps for the overpressure correction are as follows:

(1)

Model simplification from trigram to binary

Organic-rich dark mudstone is mainly composed of pore fluid, solid organic matter and non-organic mudstone (Figure 4). It can be simply divided into two parts: the solid skeleton and the pore fluid. Then, the density and sonic time difference for the solid skeleton can be written as

$${\rho }_{fm}=\left(1-{\varphi }_{TOC}\right){\rho }_{ma}+{\varphi }_{TOC}{\rho }_{om}$$

(9)

$$\mathsf{\Delta }{t}_{fm}=\left(1-{\varphi }_{TOC}\right)\mathsf{\Delta }{t}_{ma}+{\varphi }_{TOC}\mathsf{\Delta }{t}_{om}$$

(10)

(2)

Calculation and conversion of organic matter content

Organic carbon content (w_TOC) is an important index for the evaluation of the abundance of organic matter in source rocks and also a key parameter in the calculation of organic-rich mudstone porosity. Generally, w_TOC can be obtained via laboratory analysis and logging parameter calculation. The former is more accurate and reliable, but the cost is high and the samples are scarce. Although the accuracy of the latter method is relatively poor, the w_TOC value can be obtained at any depth when the logging data are abundant. In this paper, we mainly use the ΔlogR method [36,37,38] to calculate w_TOC.

It should be pointed out that the solid organic matter content in Equations (9) and (10) is volume fraction, and the w_TOC value measured in the laboratory is mass fraction. The following conversion could be used:

$${\varphi }_{TOC}=\frac{{\rho }_{fm}}{{\rho }_{om}}k{w}_{TOC}$$

(11)

(3)

Porosity calculation

In this paper, the following formula is used to calculate the density porosity (i.e., the porosity calculated by the density parameter):

$${\varphi }_{den}=\frac{{\rho }_{ma}-{\rho }_b}{{\rho }_{ma}-{\rho }_f}$$

(12)

According to the Wyllie equation [39] corrected by Raymer et al. (1980) [40], the sonic porosity (i.e., the porosity calculated according to the sonic time difference or the sonic velocity) can be obtained using the following equation:

$${\varphi }_{sonic}=\frac{(1/C_P) \left(\mathsf{\Delta }t-\mathsf{\Delta }{t}_{ma}\right)}{\mathsf{\Delta }{t}_f-\mathsf{\Delta }{t}_{ma}}$$

(13)

By replacing ρ_ma and Δt_ma in Equations (11) and (12) with ρ_fm and Δt_fm in Equations (9) and (10), the formulae used to calculate the porosity of organic-rich mudstone are expressed below:

$${\varphi }_{den}^{\prime }=\frac{\left(1-{\varphi }_{TOC}\right){\rho }_{ma}+{\varphi }_{TOC}{\rho }_{om}-{\rho }_b}{\left(1-{\varphi }_{TOC}\right){\rho }_{ma}+{\varphi }_{TOC}{\rho }_{om}-{\rho }_f}$$

(14)

$${\varphi }_{sonic}^{\prime }=\frac{(1/C_P)\left[\Delta t-\left(1-{\varphi }_{TOC}\right)\mathsf{\Delta }{t}_{ma}-{\varphi }_{TOC}\mathsf{\Delta }{t}_{om}\right]}{\mathsf{\Delta }{t}_f-\left(1-{\varphi }_{TOC}\right)\mathsf{\Delta }{t}_{ma}-{\varphi }_{TOC}\mathsf{\Delta }{t}_{om}}$$

(15)

(4)

Corrected geophysical parameters

After step (3), satisfactory results for the overpressure origin can be obtained using the PCM. For the LUCM and SDCPM to be applicable, Equations (12)–(15) should be combined to convert the sonic time difference and density under the assumption that there is no influence of the organic matter:

$${{\rho }^{\prime }}_b={\rho }_{ma}-({\rho }_{ma}-{\rho }_f){\varphi }_{den}^{\prime }$$

(16)

$$\mathsf{\Delta }{t}^{\prime }=\mathsf{\Delta }{t}_{ma}+C_P(\mathsf{\Delta }{t}_f-\Delta t_{ma}){\varphi }_{sonic}^{\prime }$$

(17)

2.2.3. Modification of the Static Equilibrium Equation

Microscopically, the total weight per unit area of a rock column is equal to the total stress of the rock column, which is borne by the rock skeleton particles and the pore fluids:

$$F_t=F_P+F_R$$

(18)

Note that “stress” is the amount of force on the object per unit area. The total stress in the Terzaghi model is equal to the sum of the effective stress and the fluid pressure, which obviously ignores the effect of the force area. Corresponding to the experiment described in Figure 1, the effect of the number of springs on the stress relationship is ignored. As shown in Figure 5, when the rock is in static equilibrium, the force relation should satisfy Equation (18). The pressure relationship is related to the area under stress. The pore pressure in the unit rock only acts on the area corresponding to the porosity, while the stress associated with the rock skeleton particles acts on the area beyond the porosity. When the rock is in a force equilibrium state, the skeleton particle stress (σ_g), pore fluid pressure (P_f) and total overburden pressure (P_ov) are related according to the following formula:

$$P_{ov}= (1-\varphi ){\sigma }_g+\varphi P_f$$

(19)

In this paper, Equation (19) is referred to as the modified rock static equilibrium equation (MRSEE), which establishes the relationship between the overburden pressure, particle stress and pore pressure per unit area. The area can be measured by porosity, and the pore pressure can be expressed as

$$P_f=\frac{P_{ov}-(1-\varphi ){\sigma }_g}{\varphi }$$

(20)

This model is more realistic in terms of reflecting the stress associated with the underground rock, and also introduces a new parameter, “particle stress”. Different scholars have introduced different methods to obtain particle stress in pressure prediction. In this paper, various methods used to calculate particle stress are introduced, focusing on the two practical cases of the Junggar and Southeast Hainan Basins.

2.2.4. Seismic Velocity Processing and Correction for Systematic Errors

In practice, the pressure prediction based on the logging parameters often cannot meet the demand for engineering purposes. It is more desirable to be in a position to accurately predict the pressure state before commencing the drilling operation. Therefore, the application of the seismic velocity volume is of great importance. Unfortunately, pressure prediction based on seismic data is often less accurate, which is mainly due to three factors. Firstly, the accuracy of seismic data is much lower than that of logging data, which will inevitably lead to the introduction of systematic errors in pressure prediction. Secondly, the current pressure prediction methods with reliable prediction performance generally need to obtain accurate NCTs. However, it is almost impossible to calculate the NCT of every coordinate in 3D seismic pressure prediction; therefore, conventional seismic pressure prediction methods are mostly based on the empirical formula with low accuracy. Third, it is difficult to accurately identify the overpressure origin using sonic velocity alone. Therefore, in some intervals with complex origins, the seismic pressure prediction methods are often not useful.

The calculation error caused by multiple origins can only be compensated for using geological analysis and experience. This method has strong subjectivity, and is affected by the degree of data perfection; therefore, the prediction reliability is not great and it is difficult to generalize. The correction methods for such cases are briefly described in the application examples and are not provided in this section.

To solve the problem of seismic data quality, Guo et al. (2012) proposed a complete set of seismic velocity processing methods [41]. Seismic data have a certain frequency range, mainly containing intermediate frequency information but missing low-frequency information. To extract formation velocity using the seismic data, it is necessary to compensate for the low-frequency velocity component and solve the problem of velocity component superposition at different frequencies. A low-frequency velocity model was established using seismic velocity spectrum data, and the relative velocity was extracted from the seismic data using the colored inversion method [42]. The superposition of these two velocity components can be used to produce high-quality absolute seismic velocity.

For seismic data processing, it is necessary to correct the systematic errors of the extracted low-frequency velocity as well as the synthesized absolute velocity. Logging data are generally considered reliable. Therefore, error analysis is carried out considering the sonic logging velocity as the standard. The sonic logging velocity contains the middle- and high-frequency velocity information, which is missing from the low-frequency velocity model. It is necessary to filter the sonic logging velocity to ensure that it is compared to the low-frequency velocity in a uniform frequency range. Similarly, the frequency ranges of absolute seismic velocity and sonic logging velocity are inconsistent, so it is necessary to filter the sonic logging velocity to extract a high-frequency velocity component.

After comparing it with the sonic logging velocity, the error table can be made, and the average systematic error can be calculated. A correction factor is taken with a similar value to that of the average error but with the opposite sign. After adding the corresponding correction factor to the calculated value, the corrected result excluding the systematic error is obtained. The average systematic error with the opposite sign can then be taken as a secondary correction factor. The data corrected for the systematic error can then be obtained by adding the corresponding correction factor to the calculated results.

3. Application Examples

3.1. Origin Analysis and Prediction of Overpressure in Songliao Basin

The first member of Cretaceous Qingshankou Formation (K₂qn₁) in Songliao Basin is an important source rock in this area, and overpressure is commonly developed in K₂qn₁.

Xu et al. (2019) pointed out that a large amount of solid organic matter in K₂qn₁ has a certain effect on the sonic time difference [43]. They also corrected the effect of solid organic matter in the skeleton by applying the method described in Section 2.2.2 of this paper.

Before correction, the density porosity and sonic porosity of K₂qn₁ deviated significantly from the NCT, and the deviation amplitude of the sonic porosity was much larger than that of the density porosity (Figure 6a). When discussing the origin of overpressure in the Baram Basin, Tingay (2009) pointed out that this phenomenon reflected the existence of overpressure caused by disequilibrium compaction [12]. In the sonic velocity–density cross plot, the uncorrected intersection points are close to the NCT (Figure 6b), which also shows the characteristics of overpressure caused by disequilibrium compaction.

After correction, the density porosity is distributed along the NCT. Although the sonic porosity is lower than that before correction, it still behaves as an anomaly (Figure 6a). It is generally believed that this phenomenon is caused by the vertical pressure transfer or the fluid expansion, which is quite different from the uncorrected understanding. In the sonic velocity–density cross plot, the corrected point deviates from the NCT, with the characteristics of unchanged density and a rapid reduction in sonic velocity (Figure 6b), representing the overpressure caused by the vertical pressure transfer or the fluid expansion.

Interestingly, the pressure calculation results obtained by Xiang et al. (2006) using the equivalent depth method and the uncorrected sonic time difference were in good agreement with the measured pressure [44]. It is well established that the equivalent depth method can only calculate the overpressure caused by disequilibrium compaction, which contradicts the results of the origin analysis after the skeleton correction. It should be noted that this phenomenon occurs due to the lack of analysis of the burial processes. Taking the P532 well as an example, it suffered from strong denudation during the tectonic inversion movement at the end of the Late Cretaceous. Therefore, more attention should be paid to the influence of denudation amount when using the equivalent depth method or the Eaton method. The NCT was corrected here using the method described in Section 2.2.1 (Figure 7). The mud density of K₂qn₁ in the P532 well was changed to 1.45 g/cm³, and the corresponding pressure was 18.92 MPa. After the skeleton correction, the sonic time difference was 318 μm/s. Using n = 6.5 as the Eaton exponent, the pressure was predicted to be 18.89 MpPa, and the prediction error was only 0.03 MPa.

3.2. Overpressure Prediction in the Southern Junggar Basin

Abnormal high pressure has been generally developed in the southern Junggar Basin. In addition to the pressure transfer or fluid expansion, lateral tectonic extrusion is also an important origin of overpressure in this area [45]. Conventional pressure prediction methods only consider the relationship between the vertical stress and strain, but it is difficult to estimate the pressure caused by lateral loading.

Based on the MRSEE, Han et al. (2022) applied Equation (20) to predict the pressure [46]. Han et al. (2022) adopted the idea of “equivalent depth” for the particles stress (σ_g) and assumed that the porosity and σ_g were in one-to-one correspondence [46]. The relative error of pressure prediction results based on the MRSEE was significantly smaller than that calculated using the traditional equilibrium depth method (

Table 2. Comparison of calculated pore pressure results and associated errors [46].

Wells	Measured Pressure MPa	Modified Rock Static Equilibrium Equation		Traditional Equilibrium Depth Method
		Calculated Pressure (MPa)	Relative Error (%)	Calculated Pressure (MPa)	Relative Error (%)
Y1	113.53	69.90	38.43	63.80	43.80
	87.83	70.97	19.19	72.43	17.53
	101.50	73.27	27.82	70.13	30.91
	97.45	66.58	31.68	59.83	38.61
Z1	62.05	62.30	0.40	67.74	9.17
	60.57	57.97	4.29	53.57	11.56
Zh1	42.732	44.263	3.58	40.73	4.69

).

Han et al. (2022) divided the origin of Jurassic overpressure in the southern Junggar Basin into vertical and lateral origins (Figure 8a), and pointed out that the portion of overpressure calculated according to logging or seismic sonic velocity could only reflect the increment caused by the vertical origins [46]. According to the calculated and measured pressure data (Figure 8b–e), the additional ground stress of the lateral origin near the Jurassic top in multiple wells was extracted. The lateral pressure increment (P_L) was determined according to the following formula:

$$\left\{\begin{array}{c}{P}_f=P_w+P_V+P_L \hfill \\ \Delta P=P_f-P_w\hfill \\ P_L=\Delta P-P_V\hfill \end{array}\right.$$

(21)

As demonstrated in Figure 8f, the tectonic compression near the Y-marked wells has the greatest influence on the pressure, which gradually weakens to the north. This phenomenon accords with the general understanding that the basin has been under the compression of Tianshan Mountains on the south side for a long time. The final predicted pore pressure near the Jurassic top can be obtained by adding the amount of P_L to the calculated pressure in Figure 8f. This result can accurately evaluate the distribution characteristics of reservoir pressure (Figure 8g).

3.3. Overpressure Prediction in Southeast Hainan Basin

The ultimate goal of pressure analysis is to achieve accurate pre-drilling pressure predictions. Guo (2012) and Wang (2014) performed seismic prediction of the overpressure in the Southeast Hainan Basin using MRSEE [47,48]. Since it is difficult to establish NCTs when using seismic data for pressure prediction, it is necessary to bypass this stage and directly determine the relationship between the sonic velocity and pressure.

According to the elastic mechanics, the relationship between strain and stress can be expressed as

$$K=\frac{{\sigma }_g}{{\theta }_t}$$

(22)

Since rocks are mainly subjected to vertical compression, the strain (θ_t) per unit volume can be expressed as

$${\theta }_t=\frac{\mathsf{\Delta }V}{V}=\frac{dxdydz-dxdy\left(1-{\epsilon }_z\right)dz}{dxdydz}={\epsilon }_z=\frac{\mathsf{\Delta }H}{H}$$

(23)

From Equations (22) and (23):

$$K=\frac{{\sigma }_g}{\mathsf{\Delta }H/\mathsf{\Delta }H}$$

(24)

The relationship between P-wave velocity and the Lamé constant can be expressed as

$$v_P=\sqrt{\frac{\lambda +2\mu }{\rho }}$$

(25)

The relationship between the bulk modulus and Lamé constant can be expressed as

$$K=\lambda +\frac{2}{3}\mu$$

(26)

From Equations (25) and (26):

$$v_P=\sqrt{\frac{K+\frac{4}{3}\mu }{\rho }}$$

(27)

By substituting Equations (26) and (27) into Equation (24):

$${\sigma }_g=(\rho v_p^2-\frac{4}{3}\mu )\frac{\mathsf{\Delta }H}{H}=\rho v_p^2(1-\frac{\frac{4}{3}\mu }{\lambda +2\mu })\frac{\mathsf{\Delta }H}{H}$$

(28)

The relationship between Poisson’s ratio and Lamé constant is:

$$\upsilon =\frac{\lambda }{2(\lambda +\mu )}$$

(29)

By substituting Equation (29) into Equation (28), the final formula to calculate particle stress is obtained:

$${\sigma }_g=\frac{1+\upsilon }{3-3\upsilon }\rho v_p^2\frac{\mathsf{\Delta }H}{H}$$

(30)

From Equation (30), the particle stress is a function of Poisson’s ratio, P-wave velocity and compression per unit thickness. In a certain destination layer, when the thickness is not very large, Poisson’s ratio and compression per unit thickness can be regarded as constants; then, the relationship between the particle stress and square of the P-wave velocity is simplified in the form of a linear relationship:

$${\sigma }_g=AB\rho v_p^2$$

(31)

where $\mathrm{A}=\frac{1+\upsilon }{3-3\upsilon }$, $\mathrm{B}=\frac{\mathsf{\Delta }H}{H}$.

The relationship between the sonic velocity and porosity can be determined according to the porosity–time mean equation:

$$\frac{1}{v}=\frac{\varphi }{v_f}+\frac{1-\varphi }{v_r}$$

(32)

By substituting Equations (31) and (32) into Equation (20), the pressure term can be calculated using the following equation:

$$P_f=\frac{v_P\left(v_r-v_f\right)}{v_f\left(v_r-v_P\right)}\left[{{\displaystyle \int }}_0^H{\rho }_{b}ghdh-(1-\frac{v_f\left(v_r-v_P\right)}{v_P\left(v_r-v_f\right)}AB\rho v_p^2\right]$$

(33)

Equation (33) is a complex functional relationship between the P-wave velocity, porosity and overburden pressure. In the calculation process, some important parameters need to be determined, such as formation sonic velocity, skeleton sonic velocity, pore fluid sonic velocity, formation density, formation Poisson’s ratio and formation compression per unit thickness. The quality of formation sonic velocity obtained from the seismic data largely determines the accuracy of pressure prediction.

As mentioned above, the absolute velocity can be obtained with high accuracy by synthesizing low-frequency and relative velocities. Firstly, the frequency spectrum characteristics of the low-frequency velocity and relative velocity should be determined. Four typical wells, Q1, Q2, Q3 and Q4, were selected for seismic velocity spectrum analysis. The results show that the dominant frequency of the Southeast Hainan Basin is about 20 Hz. The relative velocity energy, which is greater than 80 Hz, decreases sharply, and the energy decays to almost zero at frequencies greater than 120 Hz. In Figure 9a, the corresponding energy value at the frequency cut-off point is about 10% of the greatest energy value, and the frequency value is 6.12 Hz. Therefore, 6.12 Hz can be taken as the critical frequency value of the relative and low-frequency velocity components. After 0~6.12 Hz filtering of logging sonic velocity, the average relative error of the low-frequency velocity model is determined to be 3.7% (Figure 9b–e). After 0~120Hz filtering of logging acoustic velocity, the average relative error of absolute seismic velocity can be determined as 6.92% (Figure 9f–i). According to Equation (33) and the seismic velocity after processing, seismic pressure prediction can be finally realized (Figure 10). By comparing the predicted pressure results with the measured values, the average relative error of the seismic pressure prediction is found to be only 7.43%.

4. Discussion

The four correction methods mentioned in this paper are very practical for pressure analysis of sedimentary basins. These methods are useful in improving the accuracy of subsurface fluid assessment based on geophysical data. Below is a brief discussion on each of these methods.

In the correction method based on the burial process, the objective is to obtain the true effective stress required to maintain the current porosity by shifting the NCT. The advantage of this correction method is that it avoids overestimating the formation pressure. Because of the need to restore the amount of denudation, the correction method and its accuracy of denudation restoration are very important. When applying seismic data to predict pressure, it is often difficult to realize the correction associated with each seismic track; therefore, this method is relatively difficult to apply.

In the correction method developed based on the rock skeleton composition, the aim is to normalize the rock skeleton components with different geophysical responses. When applying geophysical means for pressure analysis, this method can eliminate all the interference factors other than pressure, which is often of great significance for the overpressure origin analysis. The skeleton composition calculation is one of the important factors affecting this method’s accuracy. In this paper, we corrected the pressure calculations of the organic-rich mudstone, which required the application of the ΔlogR method to predict w_TOC. There were still some differences between the predicted and measured w_TOC values. Therefore, the accuracy of component content prediction determines the correctness of the normal method. This idea can also be applied for the analysis of other particle compositions that have important effects on the rock geophysical responses. Although this method is of great significance in overpressure origin analysis, it is difficult to implement for various field-scale case studies due to the numerous factors that need to be considered.

The processing of seismic sonic velocity is the basis of 3D pre-drilling pressure prediction. The aim of this method is to obtain data consistent with the logging sonic velocity through various means. The method introduced in this paper involves obtaining the relative velocity by using colored inversion and low-frequency velocity through filtering, and finally high-accuracy synthesis of the absolute velocity. Through simple systematic error correction, predicted pressure values with good accuracy will be obtained. There are many velocity extraction methods available in the literature. Most seismic sonic velocity processing methods are difficult to correct for rock skeleton composition; therefore, it is difficult to avoid the influence of other factors on the pressure analysis.

The aim of modifying the static equilibrium in this paper is to emphasize the mechanical equilibrium state of the rock, and also to reject the idea that stress can be added in the traditional pressure analysis methods. In this paper, we only introduced the basics of these correction methods; however, more improvements are needed. The idea of “equivalent depth” in the pressure prediction of the Junggar Basin is correct; however, it does not necessarily mean that the same porosity or sonic velocity as those determined by using the traditional prediction method would be obtained. The same particle stress may correspond to the same elastic mechanical properties, which may be related to the P-wave sonic velocity, S-wave sonic velocity, density, resistivity and other geophysical parameters. The correspondence between the particle stress and P-wave sonic velocity squared was considered in the pressure study of the Southeast Hainan Basin. This seemed to be more reasonable than the use of a simple “equivalent depth” idea. However, Equation (33) still uses sonic velocity when calculating porosity. As mentioned above, the sonic velocity is a transport property and does not necessarily reflect the absolute pore space proportion. Therefore, selecting the correct parameters and obtaining the porosity accurately are future improvement directions suggested for the continuation of this research work.

5. Conclusions

To enhance the precision of identifying the origin of overpressure and predicting it accurately, this paper presented four practical methods for analyzing formation overpressure, taking into account various factors, such as burial history, rock properties, mechanical models and data quality. These correction methods were utilized in various formations, such as the Songliao, Junggar and Southeast Hainan Basins, and satisfactory results were obtained in terms of overpressure origin analysis and distribution:

(1) This paper revealed that the denudation process will result in a decoupling between the present porosity and the effective stress at the same depth. Aiming at the influence of the burial process, the NCT was adjusted. An application case in the Songliao Basin demonstrates that the model effectively resolves the issue of overestimating pressure values in areas affected by denudation.

(2) It was emphasized that the intricate composition of rock plays a pivotal role in influencing logging parameters. Particularly in source rocks abundant in organic matter, the low density and velocity of solid organic matter will significantly influence the identification of overpressure origin. A normalization process was suggested. The implementation of the novel model has revolutionized our comprehension of the origin of overpressure in the Songliao Basin.

(3) To enhance the rationality of the mechanical relationship comprehension in pressure prediction models, a novel pressure prediction model based on static equilibrium equation was proposed, and two ways of determining particle stress in the model were introduced by taking Junggar Basin and Southeast Hainan Basin as examples. The error analysis results indicate that the novel model’s prediction accuracy satisfies the requirements of oil and gas exploration.

(4) Aiming to improve the accuracy of seismic velocity, a corresponding method for processing seismic data was established. The method introduced in this paper was to obtain relative velocity by using colored inversion and low-frequency velocity through filtering, and finally high-accuracy synthesis of the absolute velocity. In the Southeast Hainan Basin case study, this paper conducted a simple systematic error correction on the processing results, and predicted pressure values with good accuracy were obtained.

(5) The presented examples demonstrate specific situations in which the proposed correction methods can be applied, providing guidance for future users. However, there is still room for improvement in the introduced correction models, especially the pressure calculation model based on the modified static equilibrium equation. This latter model can further improve the accuracy of pressure prediction by finding the sensitive parameters of particle stress and porosity.