Introduction To Seismic Inversion

Post-Stack Seismic Inversion using Band-Limited Impedance Inversion Techniques

Introduction

Post-stack seismic inversion is a critical process in petroleum exploration, where seismic reflection data is transformed into rock properties, such as acoustic impedance. This helps in characterizing reservoirs and identifying subsurface features. A commonly used method for impedance inversion is the band-limited inversion technique, which estimates impedance by integrating seismic data with well-log derived low-frequency models.

Mathematical Method

The seismic inversion process is based on the convolution model of seismic traces:

Equation (Seismic Convolutional Model):

\[ S(t) = R(t) * W(t) \]

Where:

• S(t) represents the seismic trace (the observed data),
• R(t) is the reflectivity series (which is unknown),
• W(t) represents the wavelet (usually known or estimated).

Reflectivity, R(t), is related to impedance Z as follows:

Equation (Reflectivity-Impedance Relationship):

\[ R(t) = \frac{Z(t+\Delta t) - Z(t)}{Z(t+\Delta t) + Z(t)} \]

Band-Limited Inversion

Seismic data are band-limited, missing low-frequency information that is crucial for accurate impedance estimates. Band-limited inversion solves this by using well logs or geological data to provide low-frequency impedance trends. The steps involved in band-limited inversion include:

Step-by-Step Process

1. Step 1: Estimate the low-frequency impedance model from well logs or geological knowledge.
2. Step 2: Derive the relative impedance by integrating the reflectivity series obtained from seismic data.
3. Step 3: Combine the low-frequency model with the relative impedance to obtain the full-band impedance result.

Example Problem

Problem: A seismic section reveals a hydrocarbon reservoir at a depth of 3100 meters. Perform band-limited impedance inversion to estimate the impedance model and predict porosity.

Solution: Applying the band-limited inversion process, the steps are:

1. Extract low-frequency information from well logs.
2. Apply inversion to seismic data to estimate relative impedance.
3. Combine with the low-frequency trend to derive the full-band impedance.
4. Use the derived impedance to predict reservoir porosity.

Applications in the Petroleum Industry

Band-limited inversion is a standard tool in petroleum exploration, with applications including:

• Predicting lithology and porosity distribution.
• Identifying hydrocarbon reservoirs and delineating reservoir boundaries.
• Enhancing well placement strategies by providing a clearer picture of subsurface geology.

Quiz :

1. What does "إِذا وَقَعَتِ الْواقِعَةُ" mean according to Tafsir Al-Qurtubi?

When the Day of Judgment occurs
When the sun rises from the west
When the Prophet migrates to Medina

2. What is the significance of the word "waqi'ah"?

It refers to something that will happen for sure
It refers to a place in paradise
It refers to a specific time of day

3. What is Post-Stack Seismic Inversion used for?

Transforming seismic reflection data into rock properties such as acoustic impedance
Finding hydrocarbon migration paths
Measuring seismic noise levels

4. What does the seismic convolutional model represent?

The relationship between the seismic trace, reflectivity, and wavelet
The velocity of seismic waves
The migration path of the subsurface sound waves